====================================================================================
MerQur - Muhendislik - SCENARIO + RESULT + COMMENTARY (EN, MERGED)
Data: english/datasets/Muhendislik/
Each analysis: SCENARIO + VARIABLE SELECTION, then RESULT (screen) + COMMENTARY.
====================================================================================

#1  Descriptive Statistics
    file: 01_descriptive_site_inventory.xlsx
  >> SCENARIO (narration):
    We compiled the inventory of 280 sites/plots. Area, yield, quality, age and cost
    were measured for each. Before any inferential test we want the overall picture
    of the plot stock; so we begin with descriptive statistics.
  >> VARIABLE SELECTION:
    - Variables: area_m2
    - Variables: yield_unit
    - Variables: quality_score
    - Variables: age_year
    - Variables: cost_TL
    - Grouping (categorical): category

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    n = 280 sites/plots
    area: mean = 3,222 m2   |   yield unit: mean = 49.9   |   quality score: mean = 3.38
    age: mean = 30.4 years   |   cost: mean = 9,272 TL

>> COMMENTARY (narration):
    First we draw the overall picture of the site inventory: 280 plots, average area ~3,200 m2, yield unit ~50, quality
    score 3.38 of 5, average age 30 years and ~9,300 TL cost per plot. This descriptive table lays the groundwork for
    every analysis that follows -- type/region comparisons, yield-input relationships, spatial site pattern. In
    field/agricultural engineering, before any inferential test, summarizing the plot stock's basic features (area,
    yield, quality, cost) is essential both to audit data quality and to set planning priorities.

====================================================================================

#2  Normality Tests
    file: 02_normality_yield_biomass.xlsx
  >> SCENARIO (narration):
    We examine whether yield, biomass and strength are normally distributed. Because
    subsequent t-tests, ANOVA and correlation depend on this assumption, we test
    each variable separately.
  >> VARIABLE SELECTION:
    - Variables: yield_kg_da
    - Variables: biomass_kg
    - Variables: strength_MPa

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    3 continuous variables tested:
    yield_kg_da (yield)     : Shapiro-Wilk = 0.996  p = 0.928   KS p = 0.963   Normal
    biomass_kg (biomass)    : Shapiro-Wilk = 0.875  p < .001    KS p = 0.001   Not Normal
    strength_MPa (strength) : Shapiro-Wilk = 0.902  p < .001    KS p = 0.001   Not Normal

>> COMMENTARY (narration):
    We tested whether three continuous variables -- yield, biomass and strength -- are normally distributed. The result
    splits instructively: yield is normal (p = 0.93), but biomass and strength deviate significantly from normality
    (p < .001). This is typical in field data -- biomass and strength measurements are often right-skewed. Practical
    upshot: we can safely use parametric tests (t-test, ANOVA, Pearson) on yield; for biomass and strength,
    nonparametric methods (Mann-Whitney/Kruskal-Wallis) or a transform are more appropriate. The normality check is a
    critical preliminary step that decides, per variable, which test family fits.

====================================================================================

#3  One-Sample t-Test
    file: 03_one_sample_t_yield.xlsx
  >> SCENARIO (narration):
    We investigate whether the plots' mean yield differs from a 400 kg/da target
    threshold. With one group and a fixed reference, the one-sample t-test is
    appropriate.
  >> VARIABLE SELECTION:
    - Test variable: yield_kg_da
    - Test value (mu): 400

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Hypothesis direction (two-sided / right / left): one-sided is more powerful when the direction is known beforehand.
    - Hedges g: small-sample bias-corrected Cohen's d.
    - Effect-size CI: confidence interval around d.
    - Shapiro-Wilk / K-S: normality assumption checks.
    - Descriptives: mean/SD/SE/median/min/max/skewness/kurtosis.
    - Bootstrap CI: distribution-free CI for the mean by resampling.

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    t(99) = 3.077   p = 0.003 **   Cohen d = 0.308 (Small)
    Mean yield = 415.4 kg/da   (test mu = 400, target threshold)   H0 REJECTED

>> COMMENTARY (narration):
    We compared the plots' mean yield against a target threshold of 400 kg/da. The result is significant but small in
    scale: mean 415.4 kg/da, above target -- t(99) = 3.08, p = 0.003, small effect (d = 0.31). Plots are statistically
    above the target yield, but the practical size of the gap is modest. The one-sample t-test is the right way to
    compare a field indicator against a known standard/target (yield goal, norm value); it is widely used in
    agricultural yield evaluation and in checking conformity to a target.

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Hypothesis direction (two-sided / right / left): one-sided is more powerful when the direction is known beforehand.
    - Hedges g: small-sample bias-corrected Cohen's d.
    - Effect-size CI: confidence interval around d.
    - Shapiro-Wilk / K-S: normality assumption checks.
    - Descriptives: mean/SD/SE/median/min/max/skewness/kurtosis.
    - Bootstrap CI: distribution-free CI for the mean by resampling.

====================================================================================

#4  Independent-Samples t-Test
    file: 04_independent_t_fertilizer_yield.xlsx
  >> SCENARIO (narration):
    We compare the mean yield of two fertilizer groups. With two separate groups and
    a continuous measure, the independent-samples t-test is appropriate.
  >> VARIABLE SELECTION:
    - Grouping (categorical): fertilizer
    - Test variable: yield

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Hypothesis direction (two-sided / right / left).
    - Variance assumption: Student (equal var) / Welch (unequal var — safer) / Auto (Levene decides).
    - Effect sizes: Hedges g, Glass's delta, CLES = P(X>Y).
    - Effect-size CI; per-group Shapiro; Levene & Bartlett homogeneity.
    - Per-group descriptives; Bootstrap CI for the mean difference.

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Welch t(113) = -6.438   p < .001 ***   Cohen d = -1.187 (Large)   H0 REJECTED

>> COMMENTARY (narration):
    We compared the mean yield of two fertilizer groups (Welch correction was used because variances were unequal). The
    difference is significant and large: t(113) = -6.44, p < .001, d = -1.19. It shows the between-group difference is
    too pronounced to be chance and is also practically noteworthy. The independent-samples t-test is the standard way
    to compare the means of two separate groups (two fertilizers, two methods, two plot types) on a continuous measure;
    it is a fundamental tool for detecting intervention/treatment differences in the field.

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Hypothesis direction (two-sided / right / left).
    - Variance assumption: Student (equal var) / Welch (unequal var — safer) / Auto (Levene decides).
    - Effect sizes: Hedges g, Glass's delta, CLES = P(X>Y).
    - Effect-size CI; per-group Shapiro; Levene & Bartlett homogeneity.
    - Per-group descriptives; Bootstrap CI for the mean difference.

====================================================================================

#5  Paired-Samples t-Test
    file: 05_paired_t_dbh.xlsx
  >> SCENARIO (narration):
    We compare diameter measured at two times in the same trees. Since the measures
    are paired, the paired t-test is appropriate.
  >> VARIABLE SELECTION:
    - 1st measure / group: dbh_before_cm
    - 2nd measure / group: dbh_post_cm

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Hypothesis direction (two-sided / right / left).
    - Effect sizes: Hedges g; d_av (standardized by the average SD).
    - Effect-size CI; pairwise correlation between the two measures.
    - Shapiro / K-S on the differences; descriptives; Bootstrap CI of the mean difference.

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    t(49) = -19.10   p < .001 ***   Cohen d_z = -2.701 (Large)
    Mean diff (before - after) = -2.70 cm   H0 REJECTED

>> COMMENTARY (narration):
    We paired and compared diameter (dbh) measured at two times in the same trees. The result is very strong: mean
    difference -2.7 cm, t(49) = -19.10, p < .001, d_z = -2.70, a huge effect. Trees gained diameter significantly and
    substantially between the two periods. The paired t-test compares two timed measures on the same unit
    (before/after); by isolating individual change it is more powerful than the independent test and is the right way
    to measure a growth/intervention effect in the field.

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Hypothesis direction (two-sided / right / left).
    - Effect sizes: Hedges g; d_av (standardized by the average SD).
    - Effect-size CI; pairwise correlation between the two measures.
    - Shapiro / K-S on the differences; descriptives; Bootstrap CI of the mean difference.

====================================================================================

#6  One-Way ANOVA
    file: 06_anova_type_dbh.xlsx
  >> SCENARIO (narration):
    We compare the effect of four types on mean diameter. With more than two groups,
    one-way ANOVA is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: dbh_cm
    - Factor (categorical): type

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - ANOVA variant: Classic (Fisher) or Welch (robust to unequal variances).
    - Effect sizes: omega-squared and epsilon-squared (less biased than eta-squared).
    - Assumptions: Levene, Bartlett, per-group Shapiro.
    - Descriptives per group; post-hoc (Tukey/Duncan/Bonferroni/Scheffe/Games-Howell).

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    F(3,136) = 16.54   p < .001 ***   eta^2 = 0.267   H0 REJECTED

>> COMMENTARY (narration):
    We compared mean diameter across four types. The result is significant and strong: F(3,136) = 16.54, p < .001,
    eta^2 = 0.27 -- so about a quarter of diameter variance comes from type differences. At least one type differs
    significantly. One-way ANOVA compares the means of more than two groups at once (avoiding the error inflation of
    many t-tests); in the field it is the core method for comparing different type/region/treatment performance. Which
    pairs differ is then determined by post-hoc tests.

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - ANOVA variant: Classic (Fisher) or Welch (robust to unequal variances).
    - Effect sizes: omega-squared and epsilon-squared (less biased than eta-squared).
    - Assumptions: Levene, Bartlett, per-group Shapiro.
    - Descriptives per group; post-hoc (Tukey/Duncan/Bonferroni/Scheffe/Games-Howell).

====================================================================================

#7  Two-Way ANOVA
    file: 07_two_way_anova_type_region.xlsx
  >> SCENARIO (narration):
    We examine the main effects and interaction of type and region on diameter
    simultaneously. With two categorical factors, two-way ANOVA is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: dbh_cm
    - Factor (categorical): type
    - 2nd Factor: region

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Sum-of-squares type (I/II/III): Type III for unbalanced designs with interaction (SPSS default).
    - Post-hoc (Tukey/Bonferroni/Games-Howell) for 3+ level factors.
    - Effect sizes: partial eta-squared, eta-squared, omega-squared.
    - Levene & residual Shapiro; cell and marginal means tables.

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    type (main effect)   : F(2) = 149.27   p < .001 ***   eta^2p = 0.636
    region (main effect) : F(2) = 9.56     p < .001 ***   eta^2p = 0.101

>> COMMENTARY (narration):
    We examined two factors at once: how do type and region affect diameter? Both main effects are significant (type:
    F(2) = 149.27, eta^2p = 0.64; region: F(2) = 9.56, eta^2p = 0.10). The dominant driver of diameter is type, but
    region also makes an independent contribution. The power of two-way ANOVA is that it tests both factors and their
    interaction in a single model -- isolating each factor's pure effect with the other controlled. It is ideal for
    answering "which variable really makes a difference?" in the field.

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Sum-of-squares type (I/II/III): Type III for unbalanced designs with interaction (SPSS default).
    - Post-hoc (Tukey/Bonferroni/Games-Howell) for 3+ level factors.
    - Effect sizes: partial eta-squared, eta-squared, omega-squared.
    - Levene & residual Shapiro; cell and marginal means tables.

====================================================================================

#8  Repeated-Measures ANOVA
    file: 08_repeated_anova_year_dbh.xlsx
  >> SCENARIO (narration):
    We compare diameter over four consecutive years in the same trees. With repeated
    measures on the same unit, repeated-measures ANOVA is appropriate.
  >> VARIABLE SELECTION:
    - Repeated measures: measurement_1
    - Repeated measures: measurement_2
    - Repeated measures: measurement_3
    - Repeated measures: measurement_4

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Sphericity correction: Greenhouse-Geisser when Mauchly's test is violated.
    - Mauchly's sphericity test (W, p).
    - Generalized eta-squared (ges) effect size.
    - Post-hoc pairwise (Bonferroni/Holm); descriptives per level.

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    F(3,177) = 108.40   p < .001 ***   eta^2p = 0.648   n = 60   H0 REJECTED

>> COMMENTARY (narration):
    We compared diameter measured over four consecutive years in the same 60 trees. The result is very strong:
    F(3,177) = 108.40, p < .001, eta^2p = 0.65 -- the between-year difference is huge and most of the effect is
    time-related. Tree diameter increases significantly across years. Repeated-measures ANOVA compares three or more
    timed measurements on the same unit; by holding individual differences constant it yields high statistical power
    and is the right choice for multi-period growth tracking (yearly diameter, periodic measurement) in the field.

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Sphericity correction: Greenhouse-Geisser when Mauchly's test is violated.
    - Mauchly's sphericity test (W, p).
    - Generalized eta-squared (ges) effect size.
    - Post-hoc pairwise (Bonferroni/Holm); descriptives per level.

====================================================================================

#9  MANOVA
    file: 09_manova_type_3DV.xlsx
  >> SCENARIO (narration):
    We test type's effect on height, diameter and biomass at once. With several
    correlated dependent variables, MANOVA is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: height_m
    - Dependent variable: dbh_cm
    - Dependent variable: biomass_kg
    - Factor (categorical): type

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Reference test for the overall decision: Wilks / Pillai (most robust) / Hotelling-Lawley / Roy.
    - Box's M: equality of covariance matrices across groups.
    - Univariate follow-up ANOVAs (one per dependent variable).
    - Multivariate partial eta-squared; per-group descriptive means.

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Wilks' Lambda = 0.164   F(6,230) = 56.37   p < .001 ***   n = 120
    Dependent: height_m, dbh_cm, biomass_kg   |   Factor: type   H0 REJECTED

>> COMMENTARY (narration):
    We tested type's effect on three dependent variables (height, diameter, biomass) simultaneously. With Wilks' Lambda
    = 0.16, F(6,230) = 56.37, p < .001, the effect is very strong. MANOVA examines several correlated outcomes in one
    test, both preventing the error inflation of many separate ANOVAs and capturing the joint information the variables
    carry together. In the field, when type affects not a single indicator but the height-diameter-biomass "bundle"
    together, MANOVA reveals this multivariate difference as a single decision.

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Reference test for the overall decision: Wilks / Pillai (most robust) / Hotelling-Lawley / Roy.
    - Box's M: equality of covariance matrices across groups.
    - Univariate follow-up ANOVAs (one per dependent variable).
    - Multivariate partial eta-squared; per-group descriptive means.

====================================================================================

#10  ANCOVA
    file: 10_ancova_treatment_dbh.xlsx
  >> SCENARIO (narration):
    We compare post-treatment diameter across groups while controlling baseline
    diameter as a covariate. With a confounding continuous variable, ANCOVA is
    appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: dbh_after
    - Factor (categorical): treatment
    - Covariate: dbh_baseline

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Sum-of-squares type (I/II/III).
    - Homogeneity-of-regression-slopes test (factor x covariate interaction — the key ANCOVA assumption).
    - Effect sizes: omega-squared, epsilon-squared.
    - Levene & residual Shapiro; Bonferroni post-hoc on adjusted (estimated marginal) means.

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Group effect significant   eta^2p = 0.906 (very large)   covariate: dbh_baseline   H0 REJECTED

>> COMMENTARY (narration):
    We compared post-treatment diameter (dbh_after) across groups while controlling baseline diameter (dbh_baseline) as
    a covariate. This rules out the objection that "the groups differed at baseline" and measures the pure group
    effect: the effect is very large (eta^2p = 0.91). ANCOVA makes the group comparison fair by statistically holding a
    confounding continuous variable constant -- it is the answer to "once we equalize baseline diameter, does the
    treatment still make a difference?" and is the standard tool in baseline/post-measure designs in the field.

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Sum-of-squares type (I/II/III).
    - Homogeneity-of-regression-slopes test (factor x covariate interaction — the key ANCOVA assumption).
    - Effect sizes: omega-squared, epsilon-squared.
    - Levene & residual Shapiro; Bonferroni post-hoc on adjusted (estimated marginal) means.

====================================================================================

#11  Bootstrap Confidence Interval
    file: 11_bootstrap_ci_biomass.xlsx
  >> SCENARIO (narration):
    For mean biomass we build a confidence interval via resampling, with no
    distributional assumption. For skewed data, bootstrap is appropriate.
  >> VARIABLE SELECTION:
    - Test variable: biomass_kg

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Observed mean (biomass, kg) = 151.03
    95% Bootstrap CI (via resampling)

>> COMMENTARY (narration):
    For the mean biomass (kg) we produced a 95% confidence interval via resampling -- with no distributional
    assumption: observed mean 151.03 kg. Bootstrap builds the sampling distribution of the statistic empirically by
    resampling the data thousands of times from itself; it is a reliable way to give a confidence interval when
    normality does not hold (biomass is skewed) or no formula is known. In the field it provides more robust estimates
    than classic t-intervals for skewed quantities.

====================================================================================

#12  Permutation Test
    file: 12_permutation_method_yield.xlsx
  >> SCENARIO (narration):
    We test the yield difference between two methods via permutation, with no
    distributional assumption. For small samples/odd distributions, permutation is
    appropriate.
  >> VARIABLE SELECTION:
    - Test variable: yield
    - Grouping (categorical): method

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    t = -6.348   p < .001 ***   significant mean difference between the two groups   H0 REJECTED

>> COMMENTARY (narration):
    We tested the yield difference between two methods without any distributional assumption, via permutation: the null
    distribution was built by randomly swapping group labels, and the observed difference turned out very rare in that
    distribution (p < .001). Because the permutation test is exact and distribution-free, it is a safe alternative to
    the parametric t-test for small samples or odd distributions; in the field it is a robust choice for method
    comparisons where assumptions are in doubt.

====================================================================================

#13  Multiple Comparison
    file: 13_multiple_comparison_method.xlsx
  >> SCENARIO (narration):
    We take the p-values of eight method comparisons together and apply
    multiple-testing correction. With many tests, p-adjustment is appropriate.
  >> VARIABLE SELECTION:
    - Variables: method
    - Variables: yield

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Raw: 6/8 significant   |   After Bonferroni / Holm / BH (FDR): 6/8 significant (all retained)

>> COMMENTARY (narration):
    We took the p-values of eight separate method comparisons together and applied multiple-testing correction. Raw, 6
    comparisons were significant; after Bonferroni/Holm/BH all 6 remained significant -- so these differences are
    strong enough to survive correction. When many tests are run, the rate of false positives that look "significant"
    by chance alone inflates; correction methods tighten the threshold to control this error. In the field, when many
    methods/plots are compared at once, this step protects inference reliability; here it also shows the results are
    robust.

====================================================================================

#14  Mann-Whitney U Test
    file: 14_mann_whitney_agriculture_quality.xlsx
  >> SCENARIO (narration):
    We compare the quality-score distribution of two agriculture types. Since
    normality fails, Mann-Whitney is appropriate.
  >> VARIABLE SELECTION:
    - Grouping (categorical): agriculture_type
    - Test variable: quality_score

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Hypothesis direction; continuity correction.
    - Computation method: auto / exact (precise for small n) / asymptotic.
    - Effect sizes: CLES and Z/sqrt(N) (rank-biserial r already shown).
    - Descriptives (median etc.).

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    U = 1161.00   p = 0.020 *   r = -0.29   H0 REJECTED

>> COMMENTARY (narration):
    We compared the quality-score distribution of two agriculture types (agriculture_type) based on ranks rather than
    means: U = 1161, p = 0.020, small-medium effect (r = -0.29). The difference is significant. Mann-Whitney is the
    nonparametric counterpart of the t-test; when normality fails or the scale is ordinal, it is the right way to
    compare two groups. In the field it is a robust choice for ordinal measures like quality/grade.

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Hypothesis direction; continuity correction.
    - Computation method: auto / exact (precise for small n) / asymptotic.
    - Effect sizes: CLES and Z/sqrt(N) (rank-biserial r already shown).
    - Descriptives (median etc.).

====================================================================================

#15  Wilcoxon Signed-Rank
    file: 15_wilcoxon_tree_health.xlsx
  >> SCENARIO (narration):
    We compare health scores measured before/after in the same trees, without
    assuming normality. For paired non-normal data, Wilcoxon is appropriate.
  >> VARIABLE SELECTION:
    - 1st measure / group: health_before
    - 2nd measure / group: health_post

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Hypothesis direction; continuity correction.
    - Zero-difference handling: wilcox (drop) / pratt / zsplit.
    - Descriptives for both measures and their difference.

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    W = 0.00   p < .001 ***   r = 0.89   n (non-zero) = 31   H0 REJECTED

>> COMMENTARY (narration):
    We compared health scores measured before/after in the same trees -- without assuming normality, on a rank basis:
    W = 0, p < .001, very large effect (r = 0.89). Health changed consistently and strongly after the intervention.
    Wilcoxon is the nonparametric counterpart of the paired t-test; it is the right choice for ordinal or non-normal
    before/after measures. In the field it gives reliable results for pre/post-treatment health measurements.

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Hypothesis direction; continuity correction.
    - Zero-difference handling: wilcox (drop) / pratt / zsplit.
    - Descriptives for both measures and their difference.

====================================================================================

#16  Kruskal-Wallis Test
    file: 16_kruskal_soil_yield.xlsx
  >> SCENARIO (narration):
    We compare the yield distribution across three soil types. Since
    normality/variance homogeneity fails, Kruskal-Wallis is appropriate.
  >> VARIABLE SELECTION:
    - Grouping (categorical): soil
    - Test variable: yield_ton_ha

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Epsilon-squared effect size.
    - Dunn post-hoc pairwise comparison (tie-corrected, Bonferroni/Holm).
    - Descriptives per group.

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    H(2) = 17.06   p < .001 ***   eta^2_H = 0.36   H0 REJECTED

>> COMMENTARY (narration):
    We compared the yield (ton/ha) distribution across three soil types (soil) by ranks rather than means: H(2) =
    17.06, p < .001, eta^2_H = 0.36, a strong effect. At least one group differs significantly. Kruskal-Wallis is the
    nonparametric counterpart of one-way ANOVA; when normality or variance homogeneity fails, it is the right way to do
    multi-group comparison. In the field it is robust for detecting group differences on skewed or ordinal measures.

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Epsilon-squared effect size.
    - Dunn post-hoc pairwise comparison (tie-corrected, Bonferroni/Holm).
    - Descriptives per group.

====================================================================================

#17  Friedman Test
    file: 17_friedman_method.xlsx
  >> SCENARIO (narration):
    We compare scores measured under four conditions in the same units. As a
    nonparametric repeated measure, Friedman is appropriate.
  >> VARIABLE SELECTION:
    - Repeated measures: condition_A
    - Repeated measures: condition_B
    - Repeated measures: condition_C
    - Repeated measures: condition_D

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Pairwise Wilcoxon signed-rank post-hoc (Bonferroni/Holm).
    - Descriptives per condition.

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    chi^2(3) = 39.08   p < .001 ***   Kendall W = 0.434   n = 30   H0 REJECTED

>> COMMENTARY (narration):
    We compared scores measured under four conditions/methods (condition_A..D) in the same 30 units -- as a
    nonparametric repeated measure: chi^2(3) = 39.08, p < .001, Kendall W = 0.43 (moderate concordance). The
    between-condition difference is significant. Friedman is the nonparametric counterpart of repeated-measures ANOVA;
    it is the right choice for ordinal or non-normal paired multi-condition measures. In the field it is used to
    compare the same plot's rankings across different methods/periods.

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Pairwise Wilcoxon signed-rank post-hoc (Bonferroni/Holm).
    - Descriptives per condition.

====================================================================================

#18  Binomial Test
    file: 18_binomial_seedling.xlsx
  >> SCENARIO (narration):
    We test the proportion of surviving seedlings against an expected 50%. With a
    binary outcome and a theoretical proportion, the binomial test is appropriate.
  >> VARIABLE SELECTION:
    - Test variable: yasiyor
    - Expected proportion: 0.50
    - Success value: 1

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Observed proportion = 0.739   (expected p = 0.50)   p < .001 ***   H0 REJECTED

>> COMMENTARY (narration):
    We tested the proportion of surviving seedlings against an expected 50%: observed proportion 73.9%, well above
    expectation (p < .001). The seedling-survival rate is too high to be chance. The binomial test is the exact method
    for comparing the observed proportion of a binary (survives/not) outcome with a theoretical proportion; in the
    field it directly tests whether survival/germination/success rates meet a target or a 50:50 expectation.

====================================================================================

#19  Sign Test
    file: 19_sign_test_nitrogen.xlsx
  >> SCENARIO (narration):
    We look at the direction of before/after nitrogen in the same units. When only
    directional information is reliable, the sign test is appropriate.
  >> VARIABLE SELECTION:
    - 1st measure / group: nitrogen_before
    - 2nd measure / group: nitrogen_post

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Positive diffs (before > after) = 28   p < .001 ***   H0 REJECTED

>> COMMENTARY (narration):
    We looked at the direction of change in nitrogen measured before/after in the same units: the large majority of
    changes go in one direction, p < .001 for a significant directional change. The sign test uses only the direction
    of the difference (increase/decrease), not its magnitude, so it is the before/after test that requires the fewest
    assumptions. In the field it is a robust choice when the measure is skewed or only directional information is
    reliable (did nitrogen go up or down).

====================================================================================

#20  Runs Test
    file: 20_runs_test_yield.xlsx
  >> SCENARIO (narration):
    We test whether the yield sequence (around the median) is random. For sequence
    randomness, the runs test is appropriate.
  >> VARIABLE SELECTION:
    - Column: yield_mean

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Observed runs = 27   Z = -1.042   p = 0.298 ns   data may be considered random

>> COMMENTARY (narration):
    We tested whether the binary sequence of yields (yield_mean, around the median) is random: 27 runs, Z = -1.04,
    p = 0.30 -- no pattern, the sequence is random. The runs test checks whether values in a sequence form a systematic
    pattern (clusters, cycles, trend). In the field it is used to determine whether systematic patterns or randomness
    dominate in yield/measurement series, and in checking process control and the independence assumption.

====================================================================================

#21  Chi-Square Independence
    file: 21_chisquare_type_health.xlsx
  >> SCENARIO (narration):
    We test whether type and health status are related. With two categorical
    variables, chi-square is appropriate.
  >> VARIABLE SELECTION:
    - Variables: type
    - Variables: health_status

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Yates continuity correction (2x2 tables).
    - G-test (likelihood-ratio chi-square) alternative.
    - Effect sizes: phi (2x2) and contingency coefficient C (besides Cramer's V).
    - Expected-counts table; standardized residuals (|>2| flags the deviating cell).

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    chi^2(2) = 13.23   p = 0.001 **   Cramer's V = 0.135 (Moderate)   H0 REJECTED

>> COMMENTARY (narration):
    We tested whether two categorical variables -- type and health status -- are related: chi^2(2) = 13.23, p = 0.001,
    Cramer's V = 0.13, a significant but moderate-to-weak dependency. The categories are not fully independent. The
    chi-square test of independence detects the relationship between two qualitative variables from a cross-tab; in the
    field it is the core method for revealing categorical relationships such as type-health, region-treatment. Cramer's
    V measures the practical strength of the relationship.

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Yates continuity correction (2x2 tables).
    - G-test (likelihood-ratio chi-square) alternative.
    - Effect sizes: phi (2x2) and contingency coefficient C (besides Cramer's V).
    - Expected-counts table; standardized residuals (|>2| flags the deviating cell).

====================================================================================

#22  Chi-Square Goodness-of-Fit
    file: 22_chisquare_goodnessfit_quality.xlsx
  >> SCENARIO (narration):
    We test whether a four-category variable's observed distribution fits an equal
    expected distribution. For one categorical variable, goodness-of-fit is
    appropriate.
  >> VARIABLE SELECTION:
    - Variables: quality

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Effect sizes: Cohen's w and Cramer's V.
    - G-test (likelihood ratio) alternative.
    - Standardized residuals per category (|>2| = notable deviation).

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    chi^2(3) = 37.00   p < .001 ***   N = 200, k = 4 (expected: equal distribution)   H0 REJECTED

>> COMMENTARY (narration):
    We tested whether the observed distribution of a four-category variable (quality) fits an equal (1/k) expected
    distribution: chi^2(3) = 37.00, p < .001 -- the categories are not equally distributed, some are clearly more
    frequent. The goodness-of-fit test compares the observed frequencies of a single categorical variable with a
    theoretical expectation (equal proportions, a known ratio); in the field it tests whether quality/class
    distributions match an expected profile.

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Effect sizes: Cohen's w and Cramer's V.
    - G-test (likelihood ratio) alternative.
    - Standardized residuals per category (|>2| = notable deviation).

====================================================================================

#23  Fisher's Exact Test
    file: 23_fisher_method.xlsx
  >> SCENARIO (narration):
    In a 2x2 table we test the method-retention relationship exactly, due to small
    cell frequencies. For few observations, Fisher is appropriate.
  >> VARIABLE SELECTION:
    - Variables: method
    - Variables: retention

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Fisher exact p = 0.009 **   Odds Ratio = 0.091   Phi = 0.517 (Strong)   H0 REJECTED

>> COMMENTARY (narration):
    In a 2x2 cross-tab (method x retention) we tested the relationship exactly -- using Fisher instead of chi-square
    because of small cell frequencies: p = 0.009, with a strong relationship (Phi = 0.52). Fisher's exact test is the
    right choice when expected frequencies are low and the chi-square approximation is unreliable; it computes the
    probability exactly rather than approximately. In the field it gives reliable results for small-sample pilot/trial
    comparisons (does the new method retain).

====================================================================================

#24  McNemar Test
    file: 24_mcnemar_test.xlsx
  >> SCENARIO (narration):
    We compare the binary outcome of two methods paired in the same units. For
    paired binary change, McNemar is appropriate.
  >> VARIABLE SELECTION:
    - 1st measure / group: test_a
    - 2nd measure / group: test_b

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    McNemar (exact) min(b,c) = 2   p = 0.004 **   discordant b = 14, c = 2   OR = 7.00   H0 REJECTED

>> COMMENTARY (narration):
    We tested the direction of change in a binary outcome of two methods (test_a vs test_b) paired in the same units:
    the changes lean clearly one way (b = 14, c = 2), p = 0.004, significant. McNemar tests the before/after (or
    two-method) binary status change in the same unit and looks only at discordant pairs. In the field it is the right
    tool for detecting whether two methods' binary outcomes differ systematically; the exact (binomial) version is used
    for small discordant counts.

====================================================================================

#25  Cohen's Kappa
    file: 25_kappa_expert.xlsx
  >> SCENARIO (narration):
    We measure the agreement of two experts classifying the same units. For
    categorical agreement, kappa is appropriate.
  >> VARIABLE SELECTION:
    - 1st measure / group: expert_a
    - 2nd measure / group: expert_b

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Kappa = 0.724 (substantial agreement)

>> COMMENTARY (narration):
    We measured the agreement of two experts (expert_a vs expert_b) classifying the same units into the same
    categories -- excluding chance agreement: kappa = 0.72, substantial. Unlike raw percent agreement, kappa reports
    categorical agreement after removing the chance-agreement share, so it is more honest. In the field it is the
    standard index for measuring how consistent two experts' classifications (species ID, quality class, damage grade)
    are.

====================================================================================

#26  Cochran-Mantel-Haenszel
    file: 26_cmh_region_method.xlsx
  >> SCENARIO (narration):
    We test the method-high yield relationship controlling for region strata. For a
    stratum-controlled relationship, CMH is appropriate.
  >> VARIABLE SELECTION:
    - Variables: method
    - Variables: high_yield
    - Stratum: region

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    CMH chi^2(1) = 31.88   p < .001 ***   Common OR (MH) = 0.277 [0.176, 0.437]
    Breslow-Day p = 0.478 (OR homogeneous)   H0 REJECTED

>> COMMENTARY (narration):
    We tested the method-high yield relationship while controlling for region strata: the common Odds Ratio across
    strata = 0.28 [0.18, 0.44], p < .001; Breslow-Day p = 0.48 means this relationship is consistent across all strata.
    (OR < 1 indicates the method group lowers the odds of high yield.) CMH measures the pure strength of the
    association by holding a confounding stratum variable constant (preventing Simpson's paradox). In the field it is
    ideal for robustly estimating a method-outcome relationship while controlling region differences.

====================================================================================

#27  Log-Linear Analysis
    file: 27_log_linear_type_region_disease.xlsx
  >> SCENARIO (narration):
    We model the joint relationship structure of three categorical variables. For
    more than two categorical dimensions, log-linear is appropriate.
  >> VARIABLE SELECTION:
    - Variables: type
    - Variables: region
    - Variables: disease

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    AIC = 48.91   Pearson chi^2 = 0.407   joint relationship of 3 categorical variables (type, region, disease) modeled

>> COMMENTARY (narration):
    We examined the joint relationship structure of three categorical variables (type, region, disease) with a
    log-linear model. The model explains cell frequencies via main effects and interactions; it reveals which
    pairs/triples of variables vary together. It is the multivariable generalization of the two-way cross-tab. In the
    field it is used to analyze the joint dependency pattern of more than three categorical dimensions (type x region x
    disease), balancing parsimony with AIC to select the most explanatory structure.

====================================================================================

#28  Cross-Tabulation
    file: 28_cross_age_answer.xlsx
  >> SCENARIO (narration):
    We examine age group and answer in a cross-tab. For the relationship of two
    qualitative variables, cross-tab is appropriate.
  >> VARIABLE SELECTION:
    - Variables: age
    - Variables: answer

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    chi^2(6) = 14.75   p = 0.022 *   Cramer's V = 0.145 (Moderate)   H0 REJECTED

>> COMMENTARY (narration):
    We examined two categorical variables (age group x answer) in a cross-tab: chi^2(6) = 14.75, p = 0.022, V = 0.15 --
    a significant but moderate-to-weak relationship. Cross-tab + chi-square shows the direction and strength of the
    association between two qualitative variables at the cell level. In the field it is used to describe
    demography/group-answer relationships and to correctly interpret significant but practically modest (V = 0.15)
    associations.

====================================================================================

#29  Multiple Response - Frequency
    file: 29_mr_frequency_applications.xlsx
  >> SCENARIO (narration):
    We analyze a multi-select applications question. For a multi-select question,
    multiple-response frequency is appropriate.
  >> VARIABLE SELECTION:
    - Variables: applications (coklu yanit / multi-response)

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Total cases n = 250   Respondents = 250 (100%)   multi-select "applications" question

>> COMMENTARY (narration):
    We analyzed a question where several options could be checked (agricultural practices applied): each of 250 farmers
    listed one or more practices. Multiple-response frequency analysis gives the count of checks per option and both
    the response and case percentages separately (percentages sum to over 100, because one farmer applies several). In
    the field it is the standard method for correctly summarizing multi-select practice questions (methods used,
    inputs).

====================================================================================

#30  Multiple Response - Cross-Tab
    file: 30_mr_categorical_region.xlsx
  >> SCENARIO (narration):
    We cross-tabulate the multi-response applications question by region. To break a
    multi-select by a category, this is appropriate.
  >> VARIABLE SELECTION:
    - Variables: applications (coklu yanit / multi-response)
    - Grouping (categorical): region

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Total cases n = 220   Group column: region   |   multi-response "applications" x region

>> COMMENTARY (narration):
    We cross-tabulated the multi-response applications question by a single category (region): we compared the
    per-application check rates for each region. A multiple-response cross-tab answers "does one group apply certain
    options more often than another?". In the field it is used to compare regions'/groups' multi-select practice
    profiles (methods used, inputs).

====================================================================================

#31  Multiple Response x Multiple Response
    file: 31_mr_mr.xlsx
  >> SCENARIO (narration):
    We cross-tabulate two multi-response questions against each other. For
    many-to-many co-occurrence, this is appropriate.
  >> VARIABLE SELECTION:
    - Variables: group_a (coklu / multi)
    - Variables: group_b (coklu / multi)

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Total cases n = 180   two multi-responses (group_a x group_b) cross-tabulated

>> COMMENTARY (narration):
    We cross-tabulated two separate multi-response questions against each other. This is the most complex form of
    tabulation: on both axes a unit contributes to more than one cell. Multiple-response by multiple-response reveals
    many-to-many co-occurrences such as "which options appear together with which options?". In the field it is used to
    examine the matching pattern of nested practice bundles (method used x target outcome).

====================================================================================

#32  Cochran's Q Test
    file: 32_cochran_q_season.xlsx
  >> SCENARIO (narration):
    We test whether a binary outcome varies across seasons in the same sites. For 3+
    repeated binary measures, Cochran's Q is appropriate.
  >> VARIABLE SELECTION:
    - Columns: mevsim-bazli ikili sutunlar / season-wise binary columns

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Cochran's Q = 0.00   p = 1.000 ns   H0 NOT REJECTED

>> COMMENTARY (narration):
    We tested whether the binary outcome (good yield yes/no) measured for different seasons in the same sites varies
    significantly from season to season: Q = 0, p = 1.00 -- no difference across seasons. Cochran's Q is the
    generalization of McNemar to more than two repeated conditions; it compares 3+ binary measures in the same unit. In
    the field it is the right method for comparing whether the same plots give good yield across multiple
    seasons/conditions.

====================================================================================

#33  Correlation Analysis
    file: 33_correlation_5degisken.xlsx
  >> SCENARIO (narration):
    We examine all pairwise correlations among five field variables. For
    relationship direction and strength, the correlation matrix is appropriate.
  >> VARIABLE SELECTION:
    - Variables: irrigation_mm
    - Variables: fertilizer_kg_da
    - Variables: temperature_C
    - Variables: moisture_pct
    - Variables: yield_kg_da

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - p-values are now produced for ALL methods (Pearson/Spearman/Kendall), not only Pearson.
    - Hypothesis direction (two-sided / right / left).
    - Multiple-comparison p-adjustment across pairs: Bonferroni / Holm / FDR (Benjamini-Hochberg).
    - Confidence interval for r via Fisher z (Pearson/Spearman) or Kendall SE.

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    5 variables: irrigation_mm, fertilizer_kg_da, temperature_C, moisture_pct, yield_kg_da
    Strong relationship (|r| >= 0.75): 1 pair -> fertilizer_kg_da with yield_kg_da: r = +0.847 (p < .001)

>> COMMENTARY (narration):
    We computed all pairwise Pearson correlations among five field variables: the strongest relationship is between
    fertilizer and yield (r = 0.85, p < .001); the others are weaker. So as fertilizer rises, yield rises markedly,
    while the remaining measures move more independently. The correlation matrix summarizes the direction and strength
    of relationships at a glance; in the field it is the first step in spotting overlap among inputs (multicollinearity
    risk) and seeing which variables are truly related to yield.

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - p-values are now produced for ALL methods (Pearson/Spearman/Kendall), not only Pearson.
    - Hypothesis direction (two-sided / right / left).
    - Multiple-comparison p-adjustment across pairs: Bonferroni / Holm / FDR (Benjamini-Hochberg).
    - Confidence interval for r via Fisher z (Pearson/Spearman) or Kendall SE.

====================================================================================

#34  Bland-Altman Agreement
    file: 34_bland_altman_dbh.xlsx
  >> SCENARIO (narration):
    We examine the agreement of two methods (clinometer/laser) measuring the same
    diameter. For method interchangeability, Bland-Altman is appropriate.
  >> VARIABLE SELECTION:
    - 1st measure / group: dbh_clinometer
    - 2nd measure / group: dbh_laser

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Clinometer (dbh_clinometer): mean = 26.23   |   Laser (dbh_laser): mean = 25.55
    Bias (mean difference) ~ 0.68 cm   |   limits of agreement (LoA) computed

>> COMMENTARY (narration):
    We examined how well two methods measuring the same diameter (clinometer vs laser) agree: the mean systematic
    difference (bias) is ~0.7 cm, and 95% limits of agreement were reported. Unlike correlation, Bland-Altman answers
    "can the two methods be used interchangeably?" -- high correlation does not mean agreement, there may be a
    systematic shift. In the field it is the standard method for testing the interchangeability of two measuring
    instruments/methods.

====================================================================================

#35  Effect Size
    file: 35_effect_size_method.xlsx
  >> SCENARIO (narration):
    We measure the practical size of the yield difference between two methods. For
    importance beyond the p-value, effect size is appropriate.
  >> VARIABLE SELECTION:
    - Test variable: yield
    - Grouping (categorical): method

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Cohen's d = -1.498 (large effect)   yield difference between two methods (method)

>> COMMENTARY (narration):
    We measured the practical size of the yield difference between two methods, independent of the p-value, with
    Cohen's d: d = -1.50, a very large effect. The p-value answers "is there a difference?"; effect size answers "how
    important is it?". Because large samples can produce significant but trivial differences, reporting effect size is
    essential. In the field this measure clarifies whether the difference between two methods/treatments is practically
    noteworthy; d=1.5 is a large difference.

====================================================================================

#36  Canonical Correlation (CCA)
    file: 36_cca_physical_bio.xlsx
  >> SCENARIO (narration):
    We examine the joint structure between the physical/structural set and the
    biological set. For the relationship between two multivariate sets, CCA is
    appropriate.
  >> VARIABLE SELECTION:
    - X variables: dbh
    - X variables: height_m
    - X variables: age
    - X variables: crown_diameter
    - X variables: bark_thick
    - Y variables: biomass
    - Y variables: leaf_area
    - Y variables: chlorophyll
    - Y variables: health_score

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    CC1: r = 0.986   chi^2(20) = 1129.08   p < .001 ***
    CC2: r = 0.958   chi^2(12) = 610.30    p < .001 ***
    Set-X (physical): dbh, height_m, age, crown_diameter, bark_thick  |  Set-Y (bio): biomass, leaf_area, chlorophyll, health_score

>> COMMENTARY (narration):
    We resolved the joint structure between two multivariate measure sets -- physical/structural measures (diameter,
    height, age, crown diameter, bark thickness) and biological measures (biomass, leaf area, chlorophyll, health
    score) -- with canonical correlation. The first two canonical functions are very strong (r = 0.986 and 0.958,
    p < .001): the two sets are intensely related. CCA answers "how is one variable set related to another?" in a
    single step -- it is the multivariate-on-both-sides version of multiple regression. In the field it reveals the
    latent relationship structure between the physical bundle and the biological bundle.

====================================================================================

#37  Correspondence Analysis
    file: 37_ca_plant_season.xlsx
  >> SCENARIO (narration):
    We map the relationship between plant and planting season. To see the structure
    of two categorical variables, CA is appropriate.
  >> VARIABLE SELECTION:
    - Variables: plant
    - Variables: planting_season

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Total inertia = 0.556   (2 dimensions)   plant x planting_season

>> COMMENTARY (narration):
    We mapped the relationship in the cross-tab of two categorical variables (plant x planting season) into a visual
    space with correspondence analysis: total inertia 0.556 (moderate-strong relationship) resolved over two
    dimensions. CA positions the chi-square relationship in a two-dimensional space, showing which categories are close
    (co-occurring). In the field it is powerful for visually interpreting the structure of qualitative relationships
    such as plant-season, type-region.

====================================================================================

#38  Variable Clustering (VarClus)
    file: 38_varclus_18madde.xlsx
  >> SCENARIO (narration):
    We cluster eighteen items (soil/climate/genetic) by their similarity. To find
    the latent dimension structure, VarClus is appropriate.
  >> VARIABLE SELECTION:
    - Variables: soil_m1..6, climate_m1..6, genetic_m1..6 (18 madde / items)

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Number of clusters = 3   (18 items: soil_m1..6, climate_m1..6, genetic_m1..6)

>> COMMENTARY (narration):
    We clustered eighteen measurement items (soil, climate, genetic, 6 each) by how related they are: they grouped into
    3 main dimensions -- most likely matching the natural soil/climate/genetic groups. VarClus groups the VARIABLES,
    not the observations -- by placing highly correlated items in the same cluster it reveals the latent dimensional
    structure of the data set. In the field it is practical for reducing a long indicator set to a few core dimensions
    and for spotting redundant items.

====================================================================================

#39  Multiple Linear Regression
    file: 39_multiple_regression_yield.xlsx
  >> SCENARIO (narration):
    We model yield with four predictors (irrigation, nitrogen, phosphorus, planting
    year). To explain a continuous outcome with multiple variables, multiple
    regression is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: yield_kg_da
    - Predictor(s): irrigation_mm
    - Predictor(s): nitrogen_kg_ha
    - Predictor(s): phosphorus_kg_ha
    - Predictor(s): planting_year

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Robust standard errors (HC0-HC3): heteroscedasticity-robust SE; HC3 recommended for small n.
    - Standardized (beta) coefficients to compare relative effect.
    - (Diagnostics VIF, Durbin-Watson, Breusch-Pagan, residual Shapiro are already reported.)

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    R^2 = 0.945   Adj. R^2 = 0.944   predictors: irrigation_mm, nitrogen_kg_ha, phosphorus_kg_ha, planting_year

>> COMMENTARY (narration):
    We modeled yield (yield_kg_da) with four predictors (irrigation, nitrogen, phosphorus, planting year) at once: the
    model explains 94.5% of variance (Adj. R^2 = 0.94) -- extraordinarily strong explanatory power. Multiple regression
    gives each predictor's pure contribution to yield with the others held constant; thus it answers "which input
    really raises yield?" while controlling confounders. In the field it is the core method for identifying the drivers
    of yield and for prediction.

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Robust standard errors (HC0-HC3): heteroscedasticity-robust SE; HC3 recommended for small n.
    - Standardized (beta) coefficients to compare relative effect.
    - (Diagnostics VIF, Durbin-Watson, Breusch-Pagan, residual Shapiro are already reported.)

====================================================================================

#40  Logistic Regression
    file: 40_logistic_disease.xlsx
  >> SCENARIO (narration):
    We model disease (present/absent) with three predictors. For a binary outcome,
    logistic regression is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: disease
    - Predictor(s): age
    - Predictor(s): moisture_pct
    - Predictor(s): temperature_C

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Pseudo-R squared: Cox-Snell and Nagelkerke (besides McFadden).
    - Classification metrics: accuracy / sensitivity / specificity / AUC (cutoff 0.5).
    - Hosmer-Lemeshow goodness-of-fit test; VIF for predictors.

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Pseudo R^2 = 0.142   binary outcome: disease   predictors: age, moisture_pct, temperature_C

>> COMMENTARY (narration):
    We modeled a binary outcome (disease present/absent) with three predictors: the model has moderate-to-weak
    explanatory power (pseudo R^2 = 0.14) and gives each predictor's effect on the odds. Logistic regression replaces
    linear regression when the outcome is binary; coefficients are converted to Odds Ratios to read "how many times
    does the disease odds change per unit increase in this variable?". In the field it is the core model for predicting
    yes/no outcomes such as disease/damage.

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Pseudo-R squared: Cox-Snell and Nagelkerke (besides McFadden).
    - Classification metrics: accuracy / sensitivity / specificity / AUC (cutoff 0.5).
    - Hosmer-Lemeshow goodness-of-fit test; VIF for predictors.

====================================================================================

#41  Count (Poisson) Regression
    file: 41_poisson_insect.xlsx
  >> SCENARIO (narration):
    We model the insect count with temperature and moisture. For a count outcome,
    Poisson regression is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: insect_count
    - Predictor(s): temperature_C
    - Predictor(s): moisture_pct

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    AIC = 985.77   Deviance = 184.65   count outcome: insect_count   predictors: temperature_C, moisture_pct

>> COMMENTARY (narration):
    We modeled a count variable (insect count) with temperature and moisture. Poisson regression is the right model
    when the outcome is a count (0,1,2,... items); linear regression is unsuitable because it can produce
    negative/fractional predictions. Coefficients give the effect on the count rate. In the field/ecology it is used to
    explain count outcomes such as insect count, colony count, pest density with environmental conditions.

====================================================================================

#42  Multinomial Logistic
    file: 42_multinomial_type.xlsx
  >> SCENARIO (narration):
    We model the multi-category type preference with two predictors. For a nominal
    multi-class outcome, multinomial logistic is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: type_preference
    - Predictor(s): humidity
    - Predictor(s): pH

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    AIC = 243.69   Reference class: 'beech'   outcome: type_preference (>2 categories)   predictors: humidity, pH

>> COMMENTARY (narration):
    We modeled a more-than-two-category outcome (type preference) with two predictors (humidity, pH). Multinomial
    logistic compares each category against a reference class (here 'beech') with a separate logistic equation;
    coefficients are read as "as X increases, how does the chance of being in this type change relative to the
    reference?". When the outcome is nominal with more than two classes (type, phase, category) it is the right choice.
    In the field it is the standard model for multi-option class prediction.

====================================================================================

#43  Ordinal Logistic
    file: 43_ordinal_quality.xlsx
  >> SCENARIO (narration):
    We model ordinal quality with irrigation and fertilizer. For an ordinal outcome,
    ordinal logistic is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: quality
    - Predictor(s): irrigation
    - Predictor(s): fertilizer

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    AIC = 378.80   ordinal outcome: quality   predictors: irrigation, fertilizer

>> COMMENTARY (narration):
    We modeled an ordinal outcome (quality: low/medium/high) with irrigation and fertilizer. Ordinal logistic uses the
    ORDER information between categories (which multinomial ignores); with a "proportional odds" assumption it explains
    all thresholds with one coefficient set. In the field it is the right and more powerful choice for modeling
    naturally ordered outcomes such as quality level, grade, class.

====================================================================================

#44  PLS Regression
    file: 44_pls_spectral_NDVI.xlsx
  >> SCENARIO (narration):
    We predict NDVI from 12 spectral bands. For many highly correlated predictors,
    PLS is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: NDVI
    - Predictor(s): band_01..12

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    R^2 (train) = 0.934   R^2 (5-fold CV) = 0.925   outcome: NDVI   predictors: band_01..12 (12 spectral bands)

>> COMMENTARY (narration):
    We predicted NDVI from 12 spectral bands. Because the bands are highly correlated (multicollinearity), classic
    regression becomes unstable; PLS reduces them to a few latent components and regresses on those. With
    cross-validated R^2 = 0.93, the model is both strong and generalizable. PLS is ideal when predictors are numerous
    or highly correlated; in remote sensing/chemometrics (estimating NDVI/index from spectral bands) it is widely used.

====================================================================================

#45  Probit Regression
    file: 45_probit_dose_response.xlsx
  >> SCENARIO (narration):
    We estimate the probability of death from dose with a probit model. For a binary
    dose-response outcome, probit is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: death
    - Predictor(s): dose_lt_ha

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Classification metrics added: accuracy / sensitivity / specificity / AUC (marginal effects + McFadden already shown).

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    AIC = 133.0   Pseudo R^2 (McFadden) = 0.482   binary outcome: death   predictor: dose_lt_ha

>> COMMENTARY (narration):
    We estimated the dose-response relationship -- the probability of death from dose (lt/ha) -- with a probit model:
    the model is strong (pseudo R^2 = 0.48). Probit, like logistic, applies to binary outcomes; the difference is that
    its link function is the normal distribution. Probit is classic in dose-response studies (LD50 estimation). In the
    field it is a robust choice for modeling a pesticide/agent dose-response relationship.

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Classification metrics added: accuracy / sensitivity / specificity / AUC (marginal effects + McFadden already shown).

====================================================================================

#46  Tobit Regression
    file: 46_tobit_investment.xlsx
  >> SCENARIO (narration):
    We model a threshold-piled investment variable with area and support presence.
    For a censored outcome, tobit is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: investment_TL
    - Predictor(s): area_m2
    - Predictor(s): support_present

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    AIC = 2353.77   Left censor   outcome: investment_TL (censored)   predictors: area_m2, support_present

>> COMMENTARY (narration):
    We modeled a lower-bounded (threshold-piled) investment variable with area and support presence. Tobit is for
    "censored" dependent variables that pile up at a threshold; ordinary regression gives biased estimates by ignoring
    this pile-up. In the field it is the right model for floor-effect outcomes (zero investment, below-threshold
    spending); coefficients reflect the true (uncensored) relationship.

====================================================================================

#47  Bayesian Linear Regression
    file: 47_bayesian_NPK.xlsx
  >> SCENARIO (narration):
    We model yield with NPK inputs in a Bayesian framework. To express uncertainty
    probabilistically, Bayesian regression is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: yield_kg
    - Predictor(s): N_kg_ha
    - Predictor(s): P_kg_ha
    - Predictor(s): K_kg_ha

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    sigma^2 posterior mean = 18.88 (sd = 2.70)   outcome: yield_kg   predictors: N_kg_ha, P_kg_ha, K_kg_ha
    coefficient posteriors + P(beta>0) reported

>> COMMENTARY (narration):
    We modeled yield with NPK (nitrogen, phosphorus, potassium) inputs in a Bayesian framework: instead of point
    estimates we obtained each coefficient's full posterior distribution and the "probability the effect is positive".
    The Bayesian approach expresses uncertainty directly in probability language and can incorporate prior knowledge.
    In the field, when the sample is small or prior-season information is valuable, it offers intuitive interpretations
    like "the input effect is probably positive".

====================================================================================

#48  Nonlinear Regression
    file: 48_nonlinear_growth.xlsx
  >> SCENARIO (narration):
    We model the S-shaped growth of tree height with age via a logistic curve. For a
    curved relationship, nonlinear regression is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: height_m
    - Predictor(s): age_year
    - Value: fonksiyon/function: logistic

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Function: y = K / (1 + exp(-r*(x-x0)))  (logistic growth)   R^2 = 0.982

>> COMMENTARY (narration):
    We modeled the relationship of tree height (height_m) with age (age_year) not as a straight line but as an S-shaped
    logistic growth curve: the fit is very high (R^2 = 0.98). Nonlinear regression fits a theoretical function form
    directly to the data when the relationship is curved (saturation, threshold, exponential growth) and makes the
    parameters (ceiling K, rate r, inflection x0) interpretable. In the field it is the right tool for modeling tree
    growth curves, saturating growth and yield-time processes.

====================================================================================

#49  Ridge Regression
    file: 49_ridge_soil_yield.xlsx
  >> SCENARIO (narration):
    We predict yield from 15 soil parameters with ridge. For multicollinearity,
    ridge is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: yield
    - Predictor(s): soil_p01..15

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Auto-alpha via cross-validation (RidgeCV): selects the optimal regularization strength automatically.

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    alpha = 1.0   R^2 = 0.774   outcome: yield   predictors: soil_p01..15 (15 soil parameters)

>> COMMENTARY (narration):
    We predicted yield from 15 soil parameters with ridge regression (R^2 = 0.77). Ridge adds an L2 penalty to shrink
    all coefficients in magnitude without zeroing them; this prevents the instability caused by high correlation among
    soil parameters (multicollinearity). Because soil/environmental measurements are inherently correlated, ridge gives
    stable results on such data. In the field it is preferred for prediction with many co-varying measurements.

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Auto-alpha via cross-validation (RidgeCV): selects the optimal regularization strength automatically.

====================================================================================

#50  Lasso Regression
    file: 50_lasso.xlsx
  >> SCENARIO (narration):
    We model quality from 30 candidate features with lasso, selecting the important
    ones. For automatic variable selection, lasso is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: quality
    - Predictor(s): x01..30

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Auto-alpha via cross-validation (LassoCV): selects the optimal regularization strength automatically.

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    alpha = 0.1   R^2 = 0.712   16 of 30 features shrunk to zero (automatic variable selection)

>> COMMENTARY (narration):
    We modeled quality from 30 candidate features with lasso regression: R^2 = 0.71, and lasso shrank 16 of the 30
    feature coefficients exactly to zero, selecting only the effective variables. This is its difference from ridge:
    because lasso can zero coefficients, it performs prediction and variable selection at the same time. In the field
    it is very useful for automatically winnowing the "few truly important factors" out of many candidate
    indicators/parameters (a sparse, interpretable model).

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Auto-alpha via cross-validation (LassoCV): selects the optimal regularization strength automatically.

====================================================================================

#51  Mediation Analysis
    file: 51_mediation_nitrogen_yield.xlsx
  >> SCENARIO (narration):
    We test the nitrogen -> chlorophyll -> yield chain. To resolve the intermediate
    mechanism, mediation analysis is appropriate.
  >> VARIABLE SELECTION:
    - Predictor(s): nitrogen_kg_ha
    - Value: M (araci/mediator): chlorophyll_idx
    - Dependent variable: yield_kg

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Indirect effect = 0.178   95% CI [0.063, 0.291]   (excludes zero -> significant)
    X: nitrogen_kg_ha  M: chlorophyll_idx  Y: yield_kg

>> COMMENTARY (narration):
    We tested the chain "nitrogen (X) -> chlorophyll (M) -> yield (Y)": the indirect effect is 0.178, its 95% CI
    excludes zero -- so nitrogen's effect on yield occurs substantially through chlorophyll. Mediation analysis
    resolves "why/how does X affect Y?" through an intermediate mechanism. In the field it is powerful for
    understanding which intermediate process (chlorophyll, photosynthesis) an input's (nitrogen) effect flows through.

====================================================================================

#52  Path Analysis
    file: 52_path_climate_yield.xlsx
  >> SCENARIO (narration):
    We test direct/indirect relationships as a single causal diagram. For a
    relationship network, path analysis is appropriate.
  >> VARIABLE SELECTION:
    - Value: yield_score ~ climate_score + soil_quality + maintenance_score
    - Value: soil_quality ~ climate_score

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    CFI = 0.869   RMSEA = 0.273   model: yield_score ~ climate + soil + maintenance; soil_quality ~ climate_score

>> COMMENTARY (narration):
    We tested the direct and indirect relationships among several variables as a single causal diagram. The fit indices
    (CFI = 0.87, RMSEA = 0.27) show the model fits the data partially, with room for improvement. Path analysis
    estimates the whole relationship network at once instead of separate regressions; it shows how variables affect
    each other and a common outcome. In the field it is used to test theory-based relationship chains (climate -> soil
    -> yield).

====================================================================================

#53  Linear Mixed Model (LMM)
    file: 53_lmm_plot_year.xlsx
  >> SCENARIO (narration):
    We model yield measured repeatedly across years in the same plots, taking plot
    as a random effect. For repeated/nested data, LMM is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: yield
    - Predictor(s): year
    - Cluster: plot_id (random)

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Nakagawa marginal R-squared (fixed effects) and conditional R-squared (fixed + random), beside ICC.

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    ICC = 0.832   Group variance (random intercept) = 437.11   outcome: yield   fixed: year   group: plot_id

>> COMMENTARY (narration):
    We modeled yield measured repeatedly across years in the same plots, taking plot identity as a random effect. ICC =
    0.83 is high: most of the yield variability comes from between-plot differences, while within-plot years are
    similar. LMM correctly handles dependency in nested/repeated (measurements within plot) data; it solves the
    "independence" assumption that ordinary regression violates via random effects. In the field it is the right choice
    for panel/repeated-measure data.

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Nakagawa marginal R-squared (fixed effects) and conditional R-squared (fixed + random), beside ICC.

====================================================================================

#54  Multiple Imputation
    file: 54_multiple_imputation.xlsx
  >> SCENARIO (narration):
    Instead of deleting missing data we fill it with 5 plausible value sets. To
    handle missingness without bias, multiple imputation is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: yield
    - Predictor(s): area_m2
    - Predictor(s): irrigation_mm
    - Predictor(s): fertilizer_kg_ha

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    m (imputation) = 5   outcome: yield   predictors: area_m2, irrigation_mm, fertilizer_kg_ha

>> COMMENTARY (narration):
    Instead of deleting missing data, we analyzed by producing 5 plausible value sets (m = 5) and combining the
    results. Multiple imputation -- unlike filling gaps with a single estimate (which ignores uncertainty) -- accounts
    for imputation uncertainty too, yielding unbiased estimates and correct standard errors. In the field it is the
    modern standard for handling measurement dropouts/missing records without shrinking the sample or distorting
    results.

====================================================================================

#55  GEE
    file: 55_gee_drug_yield.xlsx
  >> SCENARIO (narration):
    We model yield in repeated visit measures of the same plots. For a
    population-average effect, GEE is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: yield
    - Predictor(s): visit
    - Cluster: plot_id

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    visit coef = 5.086   p < .001 ***   QIC = 306.33   outcome: yield   group: plot_id

>> COMMENTARY (narration):
    We modeled yield in repeated visit measures of the same plots; the visit effect is significant (b = 5.09, p <
    .001). GEE estimates the POPULATION-AVERAGE effect rather than individual effects in repeated/clustered data and
    corrects within-group correlation with a "working correlation structure". While LMM focuses on individual random
    effects, GEE focuses on the average trend. In the field it is preferred for population-level questions like "what
    is the visit/time effect in the average plot?".

====================================================================================

#56  GLMM
    file: 56_glmm_insect.xlsx
  >> SCENARIO (narration):
    We model a repeatedly measured insect count at the same sites with time and
    drug, taking site as a random effect. For repeated counts, GLMM is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: insect_count
    - Predictor(s): month
    - Predictor(s): drug
    - Cluster: site_id (Poisson)

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    drug coef = -0.749   p < .001 ***   outcome: insect_count (count, Poisson)   group: site_id

>> COMMENTARY (narration):
    We modeled a COUNT outcome (insect count) measured repeatedly at the same sites with time and drug, taking site as
    a random effect; the drug effect is significant and negative (b = -0.75, p < .001) -- the drug reduces insect
    count. GLMM extends LMM to non-normal outcomes (count, binary): it handles both the distribution (Poisson) and the
    clustering (random effect) at the same time. In the field/ecology it is the right model for repeatedly measured
    count outcomes (site-wise pest count).

====================================================================================

#57  Elastic Net
    file: 57_elasticnet.xlsx
  >> SCENARIO (narration):
    We model an index from 40 predictors with Elastic Net. For many clustered
    predictors, Elastic Net is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: index
    - Predictor(s): x01..40

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    alpha = 0.135   L1 ratio = 0.50   R^2 (train) = 0.454   40 predictors

>> COMMENTARY (narration):
    We modeled an index from 40 predictors with Elastic Net. Elastic Net blends the ridge (L2) and lasso (L1) penalties
    (L1 ratio = 0.5): it both keeps groups of correlated variables together (ridge property) and zeroes out redundant
    ones (lasso property). It thus provides a balanced model with high-dimensional, clustered predictors. In the field
    it is chosen when there are many clustered measurements, where lasso or ridge alone is insufficient.

====================================================================================

#58  Robust Regression
    file: 58_robust_area_yield.xlsx
  >> SCENARIO (narration):
    We model yield with area, down-weighting outliers. For data with outliers,
    robust regression is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: yield_kg
    - Predictor(s): area_m2

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Robust Intercept = 55.88   OLS Intercept = 110.25   outcome: yield_kg   predictor: area_m2

>> COMMENTARY (narration):
    When modeling yield with area, we used robust regression to prevent outliers from distorting the estimate. The
    large gap between the robust and OLS intercepts (55.88 vs 110.25) shows a few outlying plots pull the classic
    estimate heavily; the robust method down-weights them to reflect the "typical" relationship. In the field it is the
    right way to get robust estimates without deleting outliers (abnormal plot, erroneous record) in data that contains
    them.

====================================================================================

#59  Quantile Regression
    file: 59_quantile_yield.xlsx
  >> SCENARIO (narration):
    We model different points of yield's distribution (lower 10%, median, upper 90%)
    separately. For varying effects, quantile regression is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: yield
    - Predictor(s): irrigation
    - Predictor(s): fertilizer
    - Quantiles: 0.10 / 0.50 / 0.90

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    separate slopes reported for q=0.10, q=0.50, q=0.90   outcome: yield   predictors: irrigation, fertilizer

>> COMMENTARY (narration):
    We modeled not just yield's mean but different points of the distribution (lower 10%, median, upper 90%)
    separately. Predictor effects can vary by quantile -- an input may be strong for low-yield plots and weak for
    high-yield ones. Quantile regression gives the true picture when the "mean effect" is misleading (effect varies
    across the distribution). In the field it shows what classic regression misses by examining low/high-yield plot
    behavior and yield variability.

====================================================================================

#60  ROC Curve
    file: 60_roc_quality.xlsx
  >> SCENARIO (narration):
    We assess how well a quality score separates a binary outcome with ROC. For
    discrimination and threshold selection, ROC is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: good_quality
    - Predictor(s): quality_score

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    AUC = 0.970 (excellent discrimination)   Youden optimum threshold = 0.361   Sensitivity = 0.964, 1-Specificity = 0.100
    n = 250 (positive 110, negative 140)

>> COMMENTARY (narration):
    We assessed how well a quality score separates a binary outcome (good_quality) with a ROC curve: AUC = 0.97,
    excellent discrimination; the optimum decision threshold was set at 0.36 via Youden. ROC shows the
    sensitivity-specificity trade-off at all possible thresholds and evaluates the model without being tied to a single
    threshold. In the field it is the standard tool for measuring a quality/class model's discriminative power and
    selecting the best decision threshold.

====================================================================================

#61  True Skill Statistic (TSS)
    file: 61_tss_type_distribution.xlsx
  >> SCENARIO (narration):
    We measure a species distribution/presence model's discrimination with TSS. For
    a fair measure under class imbalance, TSS is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: type_present
    - Predictor(s): f1
    - Predictor(s): f2

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    TSS = 0.31 (acceptable)   Sensitivity = 0.74   Specificity = 0.57   N = 200
    binary outcome: type_present   predictors: f1, f2

>> COMMENTARY (narration):
    We measured a species distribution/presence model's discrimination with TSS: TSS = 0.31 (sensitivity 0.74,
    specificity 0.57). TSS = sensitivity + specificity - 1; it excludes chance-expected success and gives a fair
    performance measure even with imbalanced classes. TSS is a common metric in species distribution modeling (SDM) and
    ecology. While accuracy can be biased, TSS evaluates the power to capture both presence and absence together. In
    the field/ecology it is robust for reporting the true discriminative power of presence-absence models.

====================================================================================

#62  Confusion Matrix Metrics
    file: 62_complexity.xlsx
  >> SCENARIO (narration):
    We evaluate a classifier's predictions against true labels. For detailed
    performance, the confusion matrix is appropriate.
  >> VARIABLE SELECTION:
    - 1st measure / group: actual_label
    - 2nd measure / group: prediction_label

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Accuracy = 0.93   F1 = 0.918   (true label vs predicted label)

>> COMMENTARY (narration):
    We evaluated a classifier's predictions against true labels via a confusion matrix: accuracy 93%, F1 = 0.92. The
    confusion matrix gathers true/false positives and negatives in one table, from which sensitivity, specificity,
    precision and F1 are derived. Because a single accuracy number can mislead (especially with imbalanced classes),
    this metric set shows where the model errs. In the field it is fundamental for detailed reporting of
    prediction/classification model performance.

====================================================================================

#63  Random Forest
    file: 63_rf_tree_type.xlsx
  >> SCENARIO (narration):
    We classify tree type from five features with a random forest. For nonlinear
    prediction, random forest is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: type
    - Predictor(s): dbh_cm
    - Predictor(s): height_m
    - Predictor(s): biomass
    - Predictor(s): age
    - Predictor(s): health

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Accuracy = 1.00   outcome: type   predictors: dbh_cm, height_m, biomass, age, health

>> COMMENTARY (narration):
    We classified tree type (type) from five features with a random forest: accuracy 100% -- types are perfectly
    separable with these measures (very high accuracy should be confirmed against overfitting via cross-validation).
    Random forest combines the votes of hundreds of decision trees; it automatically captures nonlinear relationships
    and interactions and also gives a variable-importance ranking. In the field it is widely used for complex
    classification problems (species ID) because it offers both high accuracy and "which variable matters" information.

====================================================================================

#64  Support Vector Machines (SVM)
    file: 64_svm_health.xlsx
  >> SCENARIO (narration):
    We classify healthy/unhealthy from four features with SVM. For well-separable
    classes, SVM is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: healthy
    - Predictor(s): x1
    - Predictor(s): x2
    - Predictor(s): x3
    - Predictor(s): x4

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Accuracy = 1.00   outcome: healthy   predictors: x1, x2, x3, x4

>> COMMENTARY (narration):
    We classified healthy/unhealthy from four features with SVM: accuracy 100% -- the classes are perfectly separable
    with these features (very high accuracy should be confirmed against overfitting via cross-validation). SVM finds
    the decision boundary separating classes with the widest margin; with the kernel trick it can also do nonlinear
    separation. In the field it is a strong, stable classifier for well-separable class problems, especially on
    small-to-medium data.

====================================================================================

#65  Gradient Boosting
    file: 65_gradient_boosting.xlsx
  >> SCENARIO (narration):
    We classify the risk class from four predictors with gradient boosting. For top
    accuracy, gradient boosting is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: risk
    - Predictor(s): x1
    - Predictor(s): x2
    - Predictor(s): x3
    - Predictor(s): x4

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Accuracy = 0.857   outcome: risk   predictors: x1, x2, x3, x4

>> COMMENTARY (narration):
    We classified the risk class from four predictors with gradient boosting: accuracy 85.7%. Gradient boosting adds
    weak trees sequentially -- each new tree corrects the previous model's errors; this is why it wins most prediction
    competitions. While random forest votes in parallel, boosting reduces error step by step. In the field it is
    preferred where the highest predictive accuracy is sought (risk classification, outcome prediction); it requires
    tuning against overfitting.

====================================================================================

#66  K-Means Clustering
    file: 66_kmeans_4kume.xlsx
  >> SCENARIO (narration):
    We cluster plots by two features. For plot grouping, k-means is appropriate.
  >> VARIABLE SELECTION:
    - Variables: green_ratio
    - Variables: biomass
    - Number of clusters: 4

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    n_clusters = 4   Silhouette = 0.591   variables: green_ratio, biomass

>> COMMENTARY (narration):
    We split plots into 4 clusters by two features (green ratio, biomass): silhouette = 0.59, a good separation.
    K-means assigns observations to the nearest cluster center and iteratively updates the centers; it groups similar
    plots into natural clusters. No labels are needed (unsupervised). In the field it is the core method for grouping
    plots/sites and discovering patterns; silhouette checks the appropriateness of the cluster count.

====================================================================================

#67  Hierarchical Clustering
    file: 67_hierarchic_5tur.xlsx
  >> SCENARIO (narration):
    We hierarchically cluster plots by ten features. For nested group structure,
    hierarchical clustering is appropriate.
  >> VARIABLE SELECTION:
    - Variables: feat_01..10
    - Number of clusters: 5

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    n_clusters = 5   Silhouette = 0.112   variables: feat_01..10 (10 features)

>> COMMENTARY (narration):
    We split plots into 5 groups by ten features with hierarchical clustering (silhouette = 0.11, weak separation --
    groups partly overlap). Hierarchical clustering merges observations step by step to build a tree (dendrogram); its
    difference from k-means is not having to fix the cluster count in advance and seeing the nested structure. In the
    field it is used to explore a hierarchy of types/groups (main group -> sub-group) and to read the natural cluster
    count from the dendrogram.

====================================================================================

#68  DBSCAN Clustering
    file: 68_dbscan.xlsx
  >> SCENARIO (narration):
    We cluster site locations with density-based DBSCAN. For spatial clusters and
    outliers, DBSCAN is appropriate.
  >> VARIABLE SELECTION:
    - Variables: lat
    - Variables: lon

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    n_clusters = 4   Silhouette = 0.909   variables: lat, lon (location)

>> COMMENTARY (narration):
    We clustered site locations (lat, lon) with density-based DBSCAN: 4 dense clusters, silhouette = 0.91, very good
    separation. Unlike k-means, DBSCAN does not require the cluster count in advance, can find clusters of any shape,
    and marks sparse points as "noise". In the field it is ideal for detecting spatial concentrations (plot clusters,
    planting zones) and isolating outlier locations.

====================================================================================

#69  Principal Component Analysis (PCA)
    file: 69_pca_6ozellik.xlsx
  >> SCENARIO (narration):
    We reduce six correlated indicators to a few components with PCA. For
    dimensionality reduction, PCA is appropriate.
  >> VARIABLE SELECTION:
    - Variables: area
    - Variables: yield
    - Variables: nitrogen
    - Variables: phosphorus
    - Variables: potassium
    - Variables: ph

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    PC1 explains 91.7% of variance   variables: area, yield, nitrogen, phosphorus, potassium, ph

>> COMMENTARY (narration):
    We reduced six correlated indicators to a few components with PCA: the first component alone explains 91.7% of
    variance -- so these six measures largely reflect a single latent dimension (overall fertility/size). PCA
    transforms correlated variables into mutually independent components; it reduces dimensions, eases visualization
    and resolves multicollinearity. In the field it is fundamental for summarizing multi-indicator measurements and
    building a "composite index".

====================================================================================

#70  t-SNE
    file: 70_tsne_5tur.xlsx
  >> SCENARIO (narration):
    We reduce 12-dimensional data to 2 dimensions with t-SNE for visualization. For
    nonlinear cluster discovery, t-SNE is appropriate.
  >> VARIABLE SELECTION:
    - Variables: measurement_01..12

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    KL Divergence = 0.571 (good)   high-dimensional 12 measurements embedded into 2 dimensions

>> COMMENTARY (narration):
    We reduced 12-dimensional data to 2 dimensions for visualization with t-SNE (KL = 0.57, good quality). t-SNE tries
    to preserve high-dimensional neighborhoods, placing similar observations near and dissimilar ones far; it reveals
    nonlinear cluster structures visually that PCA misses. Interpretation is visual (the axes have no absolute
    meaning). In the field it is used for exploratory visualization of hidden type/group clusters in high-dimensional
    measurement data.

====================================================================================

#71  Multidimensional Scaling (MDS)
    file: 71_mds_3grup.xlsx
  >> SCENARIO (narration):
    We place the inter-tree similarity structure onto a 2D map. For similarity maps,
    MDS is appropriate.
  >> VARIABLE SELECTION:
    - Variables: dbh
    - Variables: height
    - Variables: biomass
    - Variables: age

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Stress (Kruskal-1) = 0.042 (good)   variables: dbh, height, biomass, age

>> COMMENTARY (narration):
    We placed the distance/similarity structure among trees onto a 2-dimensional map with low stress (0.04): low stress
    means the map represents the true distances well. MDS positions observations in an interpretable space by
    preserving inter-observation distances; its difference from t-SNE is the aim of preserving global distance
    structure. In the field it is used to draw tree/plot similarity maps and for positioning between groups.

====================================================================================

#72  UMAP
    file: 72_umap_5tip.xlsx
  >> SCENARIO (narration):
    We reduce 25-dimensional feature data to 2 dimensions with UMAP. For both local
    and global structure, UMAP is appropriate.
  >> VARIABLE SELECTION:
    - Variables: feat_01..25

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    25 features embedded into 2 dimensions   (local-global balance via n_neighbors / min_dist)

>> COMMENTARY (narration):
    We reduced 25-dimensional feature data to 2 dimensions with UMAP. UMAP does nonlinear dimensionality reduction like
    t-SNE but preserves both local and global structure better and is faster. Larger n_neighbors emphasizes broader
    groups, larger min_dist emphasizes the gaps between clusters. In the field it is a modern choice for visualizing
    high-dimensional measurement data and exploring natural cluster structure.

====================================================================================

#73  Cronbach's Alpha
    file: 73_cronbach_21.xlsx
  >> SCENARIO (narration):
    We measure the internal consistency of a 21-item scale. For scale reliability,
    Cronbach's alpha is appropriate.
  >> VARIABLE SELECTION:
    - Variables: item_01..21

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Cronbach alpha = 0.974 (excellent internal consistency)   21 items

>> COMMENTARY (narration):
    We measured the internal consistency of a 21-item scale with Cronbach's alpha: alpha = 0.97, excellent -- the items
    measure the same construct consistently. Cronbach's alpha shows how much the items of a scale "move together"; above
    0.70 is considered acceptable. (A very high value can also signal item redundancy.) In the field it is the standard
    index for reporting the reliability of rating/evaluation scales.

====================================================================================

#74  Likert Scale Analysis
    file: 74_likert_3boyut.xlsx
  >> SCENARIO (narration):
    We analyze a 15-item Likert set of three dimensions (soil/climate/genetic). For
    ordinal scale summary and reliability, Likert analysis is appropriate.
  >> VARIABLE SELECTION:
    - Variables: soil_1..5 / climate_1..5 / genetic_1..5

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Number of items k = 15   Cronbach alpha = 0.767 (acceptable)

>> COMMENTARY (narration):
    We analyzed a 15-item Likert set of three dimensions (soil, climate, genetic): reliability is acceptable (alpha =
    0.77), and item distributions and central tendencies were reported. Likert analysis describes ordinal scale
    responses (1-5) with appropriate summaries (median, distribution, pile-up) and checks scale reliability. In the
    field it is used for correctly summarizing and interpreting evaluation/perception scales.

====================================================================================

#75  Exploratory Factor Analysis (EFA)
    file: 75_efa_18.xlsx
  >> SCENARIO (narration):
    We discover the latent factors behind eighteen items. For scale-structure
    discovery, EFA is appropriate.
  >> VARIABLE SELECTION:
    - Variables: q01..18

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    KMO = 0.905 (excellent)   factor analysis appropriate   18 items (q01..18)

>> COMMENTARY (narration):
    We applied EFA to discover how many latent factors lie behind eighteen items: KMO = 0.91, the data is very suitable
    for factor analysis. EFA reduces observed items to a few unobserved "factors"; it reveals which items measure the
    same dimension. In the field it is fundamental when developing a new scale (discovering structure) and mapping item
    groups to theoretical dimensions; KMO and Bartlett are prerequisite tests.

====================================================================================

#76  Intraclass Correlation (ICC)
    file: 76_icc_3uzman.xlsx
  >> SCENARIO (narration):
    We measure the consistency of continuous scores from three experts. For
    inter-rater reliability on continuous scores, ICC is appropriate.
  >> VARIABLE SELECTION:
    - Variables: expert_a
    - Variables: expert_b
    - Variables: expert_c

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    ICC(1,1) = 0.881 (Excellent)   95% CI [0.820, 0.930]   3 experts (expert_a/b/c)

>> COMMENTARY (narration):
    We measured the consistency of continuous scores three experts gave to the same units with ICC: ICC = 0.88,
    excellent -- the experts score almost identically. Unlike kappa, ICC measures inter-rater reliability on CONTINUOUS
    scores and can assess both consistency and absolute agreement. In the field it is the standard index for
    determining how reliable/interchangeable experts'/auditors' scores (quality, damage, type grade) are.

====================================================================================

#77  Confirmatory Factor Analysis (CFA)
    file: 77_cfa_12_3.xlsx
  >> SCENARIO (narration):
    We test whether a predefined three-factor structure fits the data. For construct
    validity, CFA is appropriate.
  >> VARIABLE SELECTION:
    - Value: f1: f1_1..4
    - Value: f2: f2_1..4
    - Value: f3: f3_1..4

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    CFI = 0.999   RMSEA = 0.011   3 factors: f1 / f2 / f3 (4 items each)

>> COMMENTARY (narration):
    Unlike EFA, we TESTED whether a pre-defined three-factor structure fits the data with CFA: the fit indices are
    excellent (CFI = 1.00, RMSEA = 0.01). CFA tests a theoretical scale model -- which item loads on which factor is
    fixed in advance, and the question is "does the model fit the data?". In the field it is a mandatory step for
    confirming the construct validity of a developed scale/measurement model.

====================================================================================

#78  Survey Mean
    file: 78_survey_means.xlsx
  >> SCENARIO (narration):
    We estimate the yield mean in a stratified/weighted sample. For a complex
    sample, design-based mean is appropriate.
  >> VARIABLE SELECTION:
    - Variables: yield
    - Weight: weight
    - Stratum: region

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    yield: M_hat = 183.32   SE = 1.59   95% CI [180.19, 186.44]   CV 0.87%   weight: weight, stratum: region

>> COMMENTARY (narration):
    In a stratified/weighted sample design we estimated the yield mean while accounting for the design: M = 183.32,
    with a Taylor-linearization SE and 95% CI [180, 186]. Complex-sample methods account for unequal selection
    probabilities (weights) and stratification; ignoring these biases the standard errors. In the field it is the right
    way to produce correct point estimates and confidence intervals from regional representative samples.

====================================================================================

#79  Survey Frequency
    file: 79_survey_freq.xlsx
  >> SCENARIO (narration):
    We estimate category proportions of a categorical variable accounting for the
    design. For a complex sample, design-based frequency is appropriate.
  >> VARIABLE SELECTION:
    - Variables: yield_category
    - Weight: weight
    - Stratum: region

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    weighted proportions + Taylor SE + 95% CI for yield_category categories
    (e.g. 'high' p_hat = 0.173, 'high high' p_hat = 0.074)

>> COMMENTARY (narration):
    We estimated the category proportions of a categorical variable (yield category) under sampling weights and
    stratification; each proportion has a design-based SE and confidence interval. Complex-sample frequency analysis,
    unlike a simple percentage, estimates population proportions without bias by accounting for the sampling design. In
    the field it is used to correctly report category distributions from regional representative samples.

====================================================================================

#80  Survey Total
    file: 80_survey_total.xlsx
  >> SCENARIO (narration):
    We estimate the population total (total production) from the sample. For a
    complex sample, design-based total is appropriate.
  >> VARIABLE SELECTION:
    - Variables: production_ton
    - Weight: weight
    - Stratum: stratum

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    production_ton: T_hat = 265,922   SE = 3,738.63   95% CI [258,562, 273,282]   stratum: stratum

>> COMMENTARY (narration):
    We estimated the population TOTAL (total production, tons) from the sample: T = 265,922, 95% CI [258,562, 273,282].
    Weights tell how many population units each observation represents; the total is estimated by summing those
    weights, with uncertainty reported via Taylor SE. In the field it is the right method for producing
    population-scaled totals (total production, total area) from a sample.

====================================================================================

#81  Survey Regression
    file: 81_survey_reg.xlsx
  >> SCENARIO (narration):
    We regress annual income accounting for the design. For relationships in complex
    samples, design-based regression is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: annual_income_TL
    - Predictor(s): age
    - Predictor(s): education_year
    - Weight: weight
    - Stratum: region

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    R^2 = 0.737   age coef = 70.48 (p < .001)   outcome: annual_income_TL   predictors: age, education_year

>> COMMENTARY (narration):
    We regressed an outcome (annual income) while accounting for the sampling design (weight, stratum): age is a
    significant predictor (b = 70.48, p < .001), and the model explains 74% of variance. Design-based regression
    incorporates weights and the cluster/stratum structure into coefficient and standard-error calculation; ordinary
    regression ignores these and gives biased inference. In the field it is the right way to model relationships in
    representative farmer/plot sample data.

====================================================================================

#82  Survey Logistic Regression
    file: 82_survey_logistic.xlsx
  >> SCENARIO (narration):
    We model modern-method use with design-weighted logistic. For binary outcomes in
    complex samples, this is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: modern_method
    - Predictor(s): age
    - Predictor(s): education
    - Weight: weight
    - Stratum: region

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    age: OR = 0.966   p = 0.042 *   binary outcome: modern_method   predictors: age, education   weight: weight

>> COMMENTARY (narration):
    We modeled a binary outcome (modern method use yes/no) with design-weighted logistic regression: each one-unit
    increase in age lowers the odds of using a modern method by ~3.4% (OR = 0.966, p = 0.042) -- younger farmers adopt
    modern methods more. This method extends logistic regression to complex sample designs -- weight and stratum are
    reflected in the standard errors. In the field it is used to correctly estimate binary adoption/preference
    probability from representative samples.

====================================================================================

#83  Generalized Additive Model (GAM)
    file: 83_gam_temperature_yield.xlsx
  >> SCENARIO (narration):
    We model yield with temperature via a flexible curve. For a nonlinear effect,
    GAM is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: yield
    - Predictor(s): temperature (smooth)

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Pseudo R^2 (explained) = 0.897   outcome: yield   predictor: temperature (smooth term)

>> COMMENTARY (narration):
    We modeled yield with temperature, without assuming a straight line in advance, via a flexible curve (smooth): the
    explained variance is very high (pseudo R^2 = 0.90). GAM extends linear regression -- it models each predictor's
    effect as a smooth function learned from the data, capturing curved relationships without losing interpretability.
    In the field it is a more explanatory choice than black-box models for relationships where the effect is nonlinear
    (optimum temperature, saturation).

====================================================================================

#84  Discriminant Analysis
    file: 84_diskriminant_3sinif.xlsx
  >> SCENARIO (narration):
    We classify class from five continuous measures. To assign to predefined
    classes, discriminant analysis is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: class
    - Predictor(s): dbh
    - Predictor(s): biomass
    - Predictor(s): quality
    - Predictor(s): age
    - Predictor(s): biochemical

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Accuracy = 1.00   outcome: class   predictors: dbh, biomass, quality, age, biochemical

>> COMMENTARY (narration):
    We classified class from five continuous measures with discriminant analysis: accuracy 100% -- the classes are
    fully separable with these measures (overfitting risk should be checked via cross-validation). Discriminant
    analysis finds the linear combinations that best separate groups; it both classifies and shows which variable is
    most influential in separation. In the field it is used to assign new samples/trees to predefined classes and to
    identify discriminating features.

====================================================================================

#85  Conditional Logit
    file: 85_conditional_logit.xlsx
  >> SCENARIO (narration):
    We model farmers' choices among alternatives by option features. For
    discrete-choice data, conditional logit is appropriate.
  >> VARIABLE SELECTION:
    - Chooser: farmer_id
    - Choice: chosen
    - Alternative features: cost
    - Alternative features: yield

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    McFadden pseudo R^2 = 0.049   chooser: farmer_id   choice: chosen   features: cost, yield

>> COMMENTARY (narration):
    We modeled the choices farmers made among alternatives by the alternatives' features (cost, yield) with a
    conditional logit (pseudo R^2 = 0.05, weak explanation). This model is for "discrete choice" data where each
    individual picks one from a choice set; it estimates how an option's features affect its probability of being
    chosen. Its difference from standard logistic is that the choice is conditional on the individual's option set. In
    the field it is the core method for farmer preference modeling (cost-yield effect).

====================================================================================

#86  Kaplan-Meier Survival
    file: 86_km_tree.xlsx
  >> SCENARIO (narration):
    We examine trees' time to an event and group differences. For censored time
    data, Kaplan-Meier is appropriate.
  >> VARIABLE SELECTION:
    - Time: duration_year
    - Event: death
    - Grouping (categorical): type

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Median survival = 8.11   Log-rank chi^2(1) = 4.02, p = 0.045 *   time: duration_year, event: death, group: type

>> COMMENTARY (narration):
    We examined the time trees take to reach an event (death) with Kaplan-Meier: median survival 8.11 years; type
    survival curves were compared with the log-rank test (p = 0.045, a significant difference). KM correctly handles
    censored time data (those whose event has not yet occurred); a plain average ignores these observations and is
    biased. In the field/forestry it is fundamental for tree "lifetime", durability and death-timing analysis.

====================================================================================

#87  Cox Proportional Hazards
    file: 87_cox_hazard.xlsx
  >> SCENARIO (narration):
    We examine death risk with continuous predictors in a Cox model. For multiple
    predictors in censored time, Cox is appropriate.
  >> VARIABLE SELECTION:
    - Time: duration_year
    - Event: death
    - Predictor(s): age
    - Predictor(s): moisture_pct
    - Predictor(s): healthy

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Proportional-hazards assumption test (Schoenfeld): per-covariate chi-square/p; significant = PH violated, consider a time-varying effect.

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Concordance = 0.689   age: HR = 1.025   p < .001 ***   (each age unit ~ 2.5% higher death risk)
    time: duration_year, event: death   predictors: age, moisture_pct, healthy

>> COMMENTARY (narration):
    We examined death risk with continuous and categorical predictors in a Cox model: each one-unit increase in age
    raises the event (death) hazard by ~2.5% (HR = 1.025, p < .001), concordance 0.69 (reasonable discrimination). Cox
    regression gives the effect of several predictors on "event time" as hazard ratios (HR) in censored time data,
    making no assumption about the baseline hazard's shape. In the field/forestry it is the gold standard for
    identifying the factors that drive death/degradation risk.

  >> ADVANCED PARAMETERS (optional in the form — what they do):
    - Proportional-hazards assumption test (Schoenfeld): per-covariate chi-square/p; significant = PH violated, consider a time-varying effect.

====================================================================================

#88  Parametric Survival (AFT)
    file: 88_aft_weibull.xlsx
  >> SCENARIO (narration):
    We model survival time assuming a Weibull distribution. For explicit time
    estimation, AFT is appropriate.
  >> VARIABLE SELECTION:
    - Time: duration_year
    - Event: death
    - Predictor(s): type

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Distribution: Weibull   Median survival = 13.19   time: duration_year, event: death, predictor: type

>> COMMENTARY (narration):
    We modeled survival time by assuming a parametric (Weibull) distribution: median survival ~13.2 years. AFT
    (accelerated failure time) models, unlike Cox, choose an explicit distribution for the hazard shape and directly
    interpret how predictors "accelerate/decelerate" time. If the data fit the assumed distribution they are more
    powerful than Cox. In the field it is preferred when explicit time estimation and extrapolation are needed.

====================================================================================

#89  Competing Risks
    file: 89_competing_risks.xlsx
  >> SCENARIO (narration):
    We model a setting where a tree can meet several distinct ends. For mutually
    exclusive events, competing risks is appropriate.
  >> VARIABLE SELECTION:
    - Time: duration_year
    - Event: death_cause -> olay tipi / event type
    - Predictor(s): age_covariate

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Censored (0) = 60   different death causes (death_cause) modeled as distinct event types

>> COMMENTARY (narration):
    We examined a setting where a tree can meet several distinct ends (death causes) in the competing-risks framework:
    60 observations censored, the rest split into distinct event types. While standard survival treats all events
    alike, the competing-risks method accounts for the fact that "once one occurs the others no longer can" and gives a
    separate cumulative incidence for each event type. In the field/forestry it is necessary to correctly model a
    tree's mutually exclusive distinct ends (death from disease, fire, drought).

====================================================================================

#90  Time-Dependent Cox
    file: 90_tvcox.xlsx
  >> SCENARIO (narration):
    We build a Cox model where the predictor (stress score) changes over time. For a
    time-varying covariate, time-dependent Cox is appropriate.
  >> VARIABLE SELECTION:
    - Unit (id): tree_id
    - Start: start
    - Stop: end
    - Event: event
    - Predictor(s): stress_score

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    stress_score: HR = 1.006   p = 0.591 ns   (time-varying covariate)   id: tree_id, start/stop intervals

>> COMMENTARY (narration):
    We built a Cox model where the predictor (stress score) CHANGES over time: for each tree the current stress value
    was used via start-stop intervals; the effect here is non-significant (HR = 1.006, p = 0.59). Time-dependent Cox
    correctly handles non-constant covariates (changing stress, changing condition) -- it uses the predictor's current
    value at the event time. In the field it is the right method for modeling the effect of time-varying risk factors
    (changing stress, drought) on an event.

====================================================================================

#91  Survey Cox Regression
    file: 91_survey_phreg.xlsx
  >> SCENARIO (narration):
    We carry survival analysis into a complex survey design (weight+cluster). For
    design-faithful event time, survey_phreg is appropriate.
  >> VARIABLE SELECTION:
    - Time: duration_month
    - Event: event
    - Predictor(s): region (faktorize/factorized)
    - Weight: weight
    - Cluster: cluster_id

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Concordance = 0.534   region_n: p = 0.967 ns   time: duration_month, event: event   weight: weight, cluster: cluster_id

>> COMMENTARY (narration):
    We carried survival analysis into a complex survey design (weight + cluster) with a Cox model: the region effect is
    non-significant (p = 0.97), concordance 0.53 (weak discrimination). survey_phreg extends the proportional-hazards
    model to a stratum/cluster/weight structure -- standard errors are corrected for the design. In the field it is the
    design-faithful way to model event time in representative project/plot data.

====================================================================================

#92  Interval-Censored Survival
    file: 92_interval_censored.xlsx
  >> SCENARIO (narration):
    We model data where the event is known only within an interval. For interval
    censoring, this is appropriate.
  >> VARIABLE SELECTION:
    - Lower bound: left_censor
    - Upper bound: survival_censor

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Number of events = 35   Median survival = 6.0   (lower bound: left_censor, upper bound: survival_censor)

>> COMMENTARY (narration):
    We modeled data where the exact event time is unknown and only known to have occurred within an INTERVAL: median
    survival 6 units, 35 events. Interval-censored methods are for cases where the event lies "somewhere between two
    observations" (between periodic measurements); fixing the event to the interval's mid/end point biases results,
    while this method carries the uncertainty correctly. In the field it is used to correctly model events occurring
    between periodic inspections (deterioration between two measurements).

====================================================================================

#93  Frailty Cox Model
    file: 93_frailty_cox.xlsx
  >> SCENARIO (narration):
    We model the site-specific hidden risk as frailty in clustered survival data.
    For shared hidden risk, frailty Cox is appropriate.
  >> VARIABLE SELECTION:
    - Time: duration_year
    - Event: event
    - Predictor(s): clinical_group (faktorize/factorized)
    - Cluster: site_id

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Concordance = 0.488   cg_n: p = 0.466 ns   time: duration_year, event: event   cluster: site_id (frailty)

>> COMMENTARY (narration):
    In clustered survival data (units within the same site) we modeled the site-specific unobserved risk as "frailty"
    (a random effect); the clinical-group effect is non-significant (p = 0.47). Frailty Cox accounts for the hidden
    risk shared by units in the same cluster -- solving the independence assumption that standard Cox violates. In the
    field it is the right choice for event data clustered within a site/plot (shared hidden risk).

====================================================================================

#94  Time Series Analysis
    file: 94_ts.xlsx
  >> SCENARIO (narration):
    We examine a monthly yield series (trend, season, stationarity). For
    time-dependent structure, time series analysis is appropriate.
  >> VARIABLE SELECTION:
    - Date: date
    - Value: yield

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    60 observations (monthly)   ADF p = 0.991 (not stationary)   Trend: increasing   Seasonality detected

>> COMMENTARY (narration):
    We examined a monthly yield series: the ADF test shows it is not stationary (p = 0.99), with an increasing trend
    and seasonality. Time series analysis reveals the time-dependent structure (trend, season, autocorrelation) of
    observations; ordinary statistics are misleading because of this dependency. Stationarity is a prerequisite for
    models like ARIMA; if non-stationary, differencing is needed. In the field it is the starting step for analyzing
    crop/yield series.

====================================================================================

#95  STL Decomposition
    file: 95_stl.xlsx
  >> SCENARIO (narration):
    We decompose the measurement series into trend, season and residual. For
    seasonal decomposition, STL is appropriate.
  >> VARIABLE SELECTION:
    - Date: date
    - Value: measurement

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Season period = 7   series decomposed into trend + season + residual components

>> COMMENTARY (narration):
    We decomposed the measurement series into three components with STL: trend, the seasonal pattern (period = 7), and
    residual. STL visually and numerically separates a time series' long-term trend, recurring seasonal pattern and
    unexplained fluctuation; this answers "what is the underlying trend, and how much is seasonal?". In the field it is
    fundamental for de-seasonalizing crop/yield series to see the underlying trend and for anomaly detection.

====================================================================================

#96  ARIMA Forecast
    file: 96_arima.xlsx
  >> SCENARIO (narration):
    We model the production series with ARIMA and produce a forecast. For series
    forecasting, ARIMA is appropriate.
  >> VARIABLE SELECTION:
    - Date: date
    - Value: production

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    ARIMA model selected   AIC = 2452.45   forecast + confidence interval

>> COMMENTARY (narration):
    We modeled the production series with ARIMA and produced a forecast (AIC = 2452.45 for model selection). ARIMA
    forecasts the future from the series' own past values (AR), trend (I - differencing) and past errors (MA); on a
    stationarized series it gives strong short-to-medium-term forecasts. In the field it is the most common classical
    method for production/demand forecasting; the confidence interval shows the forecast uncertainty.

====================================================================================

#97  Exponential Smoothing (ETS)
    file: 97_ets.xlsx
  >> SCENARIO (narration):
    We model the sales series with Holt-Winters exponential smoothing. For a
    seasonal trended series, ETS is appropriate.
  >> VARIABLE SELECTION:
    - Date: date
    - Value: sales

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Method: Holt-Winters (seasonal additive, period = 12)   AIC = 842.69

>> COMMENTARY (narration):
    We modeled the sales series with Holt-Winters exponential smoothing: it jointly estimates the level, trend and a
    12-period seasonal component. ETS tracks the series' current level, trend and season by weighting recent
    observations more (exponentially decaying weights); for seasonal and trended series it is a practical alternative
    to ARIMA. In the field it gives fast, reliable results for forecasting production/sales series with regular
    seasonal patterns.

====================================================================================

#98  Mann-Kendall Trend
    file: 98_mann_kendall.xlsx
  >> SCENARIO (narration):
    We test a significant trend in the temperature series without distributional
    assumptions. For robust trend detection, Mann-Kendall is appropriate.
  >> VARIABLE SELECTION:
    - Value: temperature

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    p < .001 ***   significant trend detected   (trend magnitude via Sen's slope)   variable: temperature

>> COMMENTARY (narration):
    We tested whether the temperature series has a significant trend -- without assuming a distribution -- with
    Mann-Kendall: p < .001, a significant trend; Sen's slope gives the robust (outlier-resistant) magnitude of the
    trend. Mann-Kendall is a nonparametric trend test; it requires no normality and is resistant to outliers, hence
    common in environmental and time-series work. In the field/environmental monitoring it is used to robustly detect
    long-term measurement trends (increasing/decreasing).

====================================================================================

#99  Anomaly Detection
    file: 99_anomali.xlsx
  >> SCENARIO (narration):
    We detect unusual observations in multivariate data. For composite outlier
    detection, anomaly detection is appropriate.
  >> VARIABLE SELECTION:
    - Variables: area
    - Variables: yield
    - Variables: fertilizer
    - Variables: irrigation

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Number of anomalies = 14   variables: area, yield, fertilizer, irrigation

>> COMMENTARY (narration):
    We automatically detected unusual observations in multivariate data: 14 plots were flagged as anomalies. Anomaly
    detection finds observations that deviate markedly from normal (erroneous record, exceptional plot) by evaluating
    several variables together; it catches "composite" outliers that univariate thresholds miss. In the field it is
    used for quality control, erroneous-measurement detection and the early detection of exceptional plot behavior.

====================================================================================

#100  Variance Components
    file: 100_varcomp_3seviye_h2.xlsx
  >> SCENARIO (narration):
    We decompose measurement variability into nested levels (upper/lower unit). For
    hierarchical variability, variance components is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: value
    - Factor (categorical): upper_unit
    - Factor (categorical): lower_unit (nested)

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Random factors: upper_unit + lower_unit (nested within upper)   % contribution of each component + residual

>> COMMENTARY (narration):
    We decomposed a measurement's variability into nested levels -- upper unit and lower unit within upper: the percent
    contribution of each level and the residual were reported. Variance components analysis answers "how much of the
    variability is between upper units, how much between lower units, how much within unit?". In the field it is used
    in hierarchical structures (region>plot>replicate) to see where uncertainty concentrates and in sampling design; it
    underlies ratio estimates such as heritability (h2).

====================================================================================

#101  Bayesian t-Test
    file: 101_bayesian_t_test_new_old.xlsx
  >> SCENARIO (narration):
    We examine two groups' measurement difference with a Bayesian t-test, expressing
    evidence as a Bayes factor. For an intuitive evidence ratio, this is
    appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: value
    - Grouping (categorical): group

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    BF10 = 3.36e+46   Cohen's d = 3.939   (overwhelming evidence for H1)   outcome: value, group: group

>> COMMENTARY (narration):
    We examined the measurement difference between two groups (new/old treatment) with a Bayesian t-test: the Bayes
    factor is overwhelming (BF10 ~ 3.4e46), the effect very large (d = 3.94) -- the data support the "difference"
    hypothesis over "no difference" by astronomical odds. Unlike a p-value, the Bayes factor gives the RELATIVE
    evidence strength of two hypotheses and can distinguish "no evidence" from "no difference". In the field it is
    preferred when one wants to express the evidential strength of a decision as an intuitive ratio.

====================================================================================

#102  Bayesian Correlation
    file: 102_bayesian_correlation_BF10.xlsx
  >> SCENARIO (narration):
    We evaluate the relationship between two variables in a Bayesian framework. For
    evidential strength, Bayesian correlation is appropriate.
  >> VARIABLE SELECTION:
    - 1st measure / group: X_variable
    - 2nd measure / group: Y_variable

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    r = 0.780 (very strong)   BF10 = 4.50e+14   (overwhelming evidence for a relationship)

>> COMMENTARY (narration):
    We evaluated the relationship between two variables in a Bayesian framework: r = 0.78 and BF10 ~ 4.5e14, i.e. very
    strong evidence for a relationship. Bayesian correlation, instead of a classical p-value, presents the evidential
    strength of the relationship as a Bayes factor and the coefficient's posterior distribution. In the field it is
    valuable for reporting not just whether the relationship between two measurements is "significant" but how strongly
    it is "evidenced".

====================================================================================

#103  Bayesian ANOVA
    file: 103_bayesian_anova_2yonlu.xlsx
  >> SCENARIO (narration):
    We examine a measurement's difference across two factors with Bayesian ANOVA.
    For the evidential strength of factor effects, this is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: value
    - Factor (categorical): factor1
    - 2nd Factor: factor2

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    factor1: BF10 = 76099 (very strong evidence)   outcome: value, factors: factor1, factor2

>> COMMENTARY (narration):
    We examined a measurement's difference across two factors with Bayesian ANOVA: for factor1, BF10 ~ 76,000, very
    strong evidence. Bayesian ANOVA compares the effects of factors and their interactions via Bayes factors; it ranks
    probabilistically which model (which effects) best explains the data. Unlike classical ANOVA's "reject/don't
    reject" decision, it quantifies the relative support among models. In the field it is used to compare the
    evidential strength of factor effects.

====================================================================================

#104  Bayesian Hierarchical Model
    file: 104_hierarchical_bayesian_LMM.xlsx
  >> SCENARIO (narration):
    We analyze group-nested data with a Bayesian hierarchical model. For stable
    estimates in small groups, this is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: Y_response
    - Cluster: group_id
    - Predictor(s): X_covariate

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    sigma^2_u (group) = 2.90 (8.6%)   sigma^2_eps (residual) = 30.79 (91.4%)   outcome: Y_response, group: group_id

>> COMMENTARY (narration):
    We analyzed group-nested data with a Bayesian hierarchical (multilevel) model: 8.6% of variability is
    between-group, 91.4% within-group (ICC ~ 0.09). The Bayesian hierarchical model is the Bayesian version of LMM -- it
    estimates group effects with posterior distributions and balances small groups via "partial pooling". In the field
    it is powerful for producing stable estimates even in small groups within multilevel (region/plot/replicate) data.

====================================================================================

#105  Spatial SAR
    file: 105_spatial_sar_spatial.xlsx
  >> SCENARIO (narration):
    When modeling a measurement we handle spatial spillover with SAR. For
    neighborhood effects, SAR is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: Y_value
    - Predictor(s): X1
    - Predictor(s): X2
    - Latitude: lat
    - Longitude: lon

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    rho = 0.336   z = 4.94   p < .001 ***   Pseudo R^2 = 0.87   (N = 100, k-NN W, k = 5)
    outcome: Y_value, predictors: X1, X2

>> COMMENTARY (narration):
    When modeling a measurement (Y_value), we handled spatial spillover (the effect of neighboring units) with SAR: the
    spatial lag parameter is significant and positive (rho = 0.34, p < .001) -- a unit's value is related to its
    neighbors' value, a "cluster/spillover" pattern. SAR incorporates spatial dependency into the model; if ignored,
    standard errors are biased. In the field it is the right method for modeling the geographic spread of plot/site
    measurements (neighborhood effect).

====================================================================================

#106  Spatial Error Model
    file: 106_spatial_error_residual.xlsx
  >> SCENARIO (narration):
    We model spatial dependency in the error term. For unmeasured geographic
    factors, SEM is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: Y_value
    - Predictor(s): X1
    - Predictor(s): X2
    - Latitude: lat
    - Longitude: lon

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    lambda = 0.590   z = 6.38   p < .001 ***   Pseudo R^2 = 0.84   (N = 100, k-NN W, k = 5)

>> COMMENTARY (narration):
    This time we modeled spatial dependency in the ERROR term: spatial error autocorrelation is significant (lambda =
    0.59, p < .001) -- the effect of geographic variables omitted from the model makes neighboring errors correlated.
    Unlike SAR, SEM attributes the spread to the error rather than the outcome. In the field, when the source of
    spatial autocorrelation is unmeasured geographic factors (soil, climate, slope), the correct specification is SEM;
    it is chosen by comparison with SAR.

====================================================================================

#107  Geographically Weighted Regression (GWR)
    file: 107_gwr_local.xlsx
  >> SCENARIO (narration):
    Assuming the relationship is not constant in space, we estimate separate
    coefficients per location. For spatial heterogeneity, GWR is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: Y_value
    - Predictor(s): X1
    - Predictor(s): X2
    - Latitude: lat
    - Longitude: lon

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    R^2 = 0.887   local coefficients vary by location   outcome: Y_value, predictors: X1, X2

>> COMMENTARY (narration):
    Assuming the relationship is NOT constant across space, we estimated SEPARATE coefficients for each location (R^2 =
    0.89). Unlike "global" regression, GWR fits a separate model at each point with local overlap/weights; this answers
    "how does this variable's effect vary by region?" and maps spatial heterogeneity. In the field it is powerful where
    the yield-input relationship differs by region.

====================================================================================

#108  Nested Mixed Model
    file: 108_nested_lmm_R_P_F.xlsx
  >> SCENARIO (narration):
    We model a value in a nested design (upper>lower>block). For nested hierarchies,
    nested LMM is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: value
    - Factor (categorical): lower_group_no
    - Factor (categorical): upper_group
    - Factor (categorical): block

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    upper_group (P) effect: F = 27.44, p < .001 ***   lower_group_no (R) effect: F = 6.11, p < .001 ***
    nested variance components (block within P)

>> COMMENTARY (narration):
    We modeled a value in a nested design (upper group > lower group > block): both the upper level (F = 27.44, p <
    .001) and the lower/replication level (F = 6.11, p < .001) make significant contributions. Nested LMM correctly
    handles hierarchies where sub-units are nested within super-units (each block belongs to only one group); by
    partitioning variance into levels it shows each layer's share. In the field it is used to correctly separate
    effects in plot/block/replicate hierarchies.

====================================================================================

#109  Crossed Mixed Model
    file: 109_crossed_lmm_A_B.xlsx
  >> SCENARIO (narration):
    We model a design where two random factors are crossed. For two independent
    classification axes, crossed LMM is appropriate.
  >> VARIABLE SELECTION:
    - Dependent variable: value
    - Factor (categorical): factor_a
    - 2nd Factor: factor_b

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    A x B interaction: F = 14.67, p < .001 ***   main effects ns (A: p=0.767, B: p=0.480)   outcome: value

>> COMMENTARY (narration):
    We modeled a design where two random factors are crossed rather than nested (each level of A pairs with each level
    of B): while the main effects are non-significant (A: p=0.77, B: p=0.48), the A x B interaction is very strong
    (F = 14.67, p < .001) -- so the effect depends on the COMBINATION of factors. Crossed LMM, unlike nested, handles
    two independent grouping axes (e.g. method x block, each method in each block) at once. In the field it is the
    right choice for jointly analyzing the effects and interaction of two independent classification axes.

====================================================================================

#110  Kernel Density (KDE) Map
    file: 110_KDE_traffic_density.xlsx
  >> SCENARIO (narration):
    We produce a continuous density surface from measurement-point locations. For a
    density map, KDE is appropriate.
  >> VARIABLE SELECTION:
    - Value: traffic_density
    - Latitude: lat
    - Longitude: lon

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    n = 95 points   measurement-weighted spatial density surface (continuous heat map)

>> COMMENTARY (narration):
    Using measurement-point locations (n = 95) we produced a continuous density surface (a KDE heat map): the point
    distribution was turned into a smooth "density" surface. KDE answers "where is it dense?" from scattered point data
    as a continuous map; it shows the trend rather than individual points. In the field/infrastructure it is the core
    spatial tool for visually mapping measurement/density distributions and identifying empty/dense zones.

====================================================================================

#111  Hexbin Density Map
    file: 111_Hexbin_measurement_noktalari.xlsx
  >> SCENARIO (narration):
    We aggregate measurement points into hexagonal cells to show density. For the
    over-plotting problem, hexbin is appropriate.
  >> VARIABLE SELECTION:
    - Latitude: lat
    - Longitude: lon

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    n = 150 points   spatial density via aggregation into hexagonal cells

>> COMMENTARY (narration):
    We colored measurement points (n = 150) by counting within hexagonal cells. Hexbin aggregates many overlapping
    points (the over-plotting problem) into a regular hexagonal grid to show density clearly; compared with squares it
    carries less directional bias. In the field/infrastructure it is used to turn dense point clouds
    (measurement/sensor locations) into a readable density map and to compare spatial concentrations.

====================================================================================

#112  Moran's I
    file: 112_Morans_I_structure_quality_autocorrelation.xlsx
  >> SCENARIO (narration):
    We test whether structure quality is distributed randomly or in clusters across
    space. For spatial autocorrelation, Moran's I is appropriate.
  >> VARIABLE SELECTION:
    - Value: structure_quality
    - Latitude: lat
    - Longitude: lon

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Moran's I = 0.765   z = 13.52   p < .001 ***   (k-NN neighbors, k = 6)   variable: structure_quality

>> COMMENTARY (narration):
    We tested whether structure quality (structure_quality) is distributed randomly or in clusters across space with
    Moran's I: I = 0.77, z = 13.52, p < .001 -- very strong positive spatial autocorrelation, i.e. similar quality
    values cluster geographically. Moran's I quantifies "Tobler's first law" (near things are similar). In the
    field/infrastructure it is the first test for detecting the geographic clustering of measurements and for deciding
    whether a spatial model is needed.

====================================================================================

#113  Getis-Ord Gi*
    file: 113_Getis_Ord_traffic_hotspot.xlsx
  >> SCENARIO (narration):
    We map locally where traffic density clusters high/low. For hot/cold spots,
    Getis-Ord is appropriate.
  >> VARIABLE SELECTION:
    - Value: traffic_density
    - Latitude: lat
    - Longitude: lon

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Hot spots = 31   Cold spots = 27   n = 68   (k-NN k = 8, binary weights)   variable: traffic_density

>> COMMENTARY (narration):
    We mapped locally WHERE traffic density (traffic_density) clusters high/low with Getis-Ord Gi*: 31 significant hot
    spots (high-density clusters) and 27 cold spots (low-density clusters). While Moran's I states the overall
    clustering, Gi* shows its location -- for each point it tests "is the surrounding area high or low?". In the
    field/infrastructure it is used to pinpoint high/low-value zones (hot/cold spots) for targeted planning.

====================================================================================

#114  DBSCAN Spatial Clustering
    file: 114_DBSCAN_structure_kumeleri.xlsx
  >> SCENARIO (narration):
    We cluster structure/measurement locations with density-based DBSCAN. For
    spatial clusters and outlier locations, DBSCAN is appropriate.
  >> VARIABLE SELECTION:
    - Latitude: lat
    - Longitude: lon

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Clusters = 4   Noise (outliers) = 10   n = 115   (location: lat, lon)

>> COMMENTARY (narration):
    We clustered structure/measurement locations (n = 115) with density-based DBSCAN: 4 natural geographic clusters and
    10 "noise" (scattered, cluster-less) points. DBSCAN does not require the cluster count in advance, finds clusters
    of any shape, and separates sparse points as outliers -- ideal for spatial clustering. In the field/infrastructure
    it is used to detect region-level natural concentrations (structure/measurement clusters) and to isolate isolated
    locations; it completes our descriptive spatial analysis series.

====================================================================================

#115  Mixed-Design (Split-Plot) ANOVA
    file: 115_mixed_anova_tensile_strength_MPa.xlsx
  >> SCENARIO (narration):
    We follow 40 specimens measured at three aging levels (0h, 100h, 200h); each belongs to one of two alloy groups (alloy_A / alloy_B). A mixed (split-plot) design tests the between-subjects
    main effect, the within-subjects main effect and their interaction on tensile strength.
  >> VARIABLE SELECTION:
    - Dependent variable: tensile_strength_MPa
    - Subject ID: specimen_id
    - Between-subjects factor: alloy
    - Within-subjects factor: aging

  ----- RESULT & COMMENTARY -----
>> RESULT (screen):
    Between (alloy): F(1,38) = 32.51  p < .001  np2 = 0.461
    Within (aging):  F(2,76) = 96.84  p < .001  np2 = 0.718
    Interaction:         F(2,76) = 4.70  p = 0.012  np2 = 0.110
    Mauchly W = 0.999  p = 0.980   n_subjects = 40   n_obs = 120

>> COMMENTARY (narration):
    In a alloy x aging mixed design we analyzed tensile strength for 40 specimens (120 observations). The interaction is significant (F(2,76) = 4.70, p = 0.012, np2 = 0.110) * -- the two groups' change across aging differs in magnitude. The between-subjects main effect (alloy_A vs alloy_B) is F = 32.51, p < .001; the within-subjects main effect (0h/100h/200h) is F = 96.84, p < .001. Mauchly's test p = 0.980, so sphericity holds, so uncorrected within p is read directly. Read the interaction first: when it is significant the group effect must be interpreted separately at each aging level. In engineering, the mixed design is the standard analysis for comparing alloys under accelerated aging cycles.

====================================================================================
