PCA (Principal Components Analysis)

Boyut İndirgeme

PCA (Principal Components Analysis) is one of the statistical analyses applied automatically in MerQur. This page illustrates — on a Architecture, Planning & Design sample dataset — how the analysis is run, what the MerQur output looks like, and how the result is reported in APA 7 format.

🎯 What is it for?

PCA (Principal Components Analysis) automatically applies in the background all the assumption checks required for the relevant data type (normality, homogeneity of variance, etc.) and presents the results with a clear table + chart. Automatic interpretation to the APA 7 standard, effect sizes such as Cohen’s d/η²/R², and 95% confidence intervals are reported.

📌 When is it used?

Statistical analysis of measurements in the Architecture, Planning & Design domain
To produce APA 7-compatible result tables for academic publications
Hypothesis testing and decision-making processes
Undergraduate / master’s / PhD theses after the appropriate method has been selected

📐 Assumptions

Appropriate scale — Variables must be at the measurement level required by the analysis (nominal/ordinal/interval/ratio)
Independent observations — Observations must come from individuals independent of one another
Sufficient sample size — The minimum n requirement for the analysis must be met
Outlier check — Outliers must be detected and evaluated

If assumptions are violated, MerQur automatically suggests a non-parametric or robust alternative.

🛠 How to do it in MerQur

Load the data. Select the sample file from File → Open. MerQur auto-detects column types.

Select the analysis. From the left side select PCA (Principal Components Analysis).

Panel assignments (form fields in the program):

Columns: [alan_m2, yesil_orani, agac_sayisi, ... +3 adet]
Bilesen sayisi: 3
Missing strategy: drop

Optional settings. Effect size ✓ · 95% confidence interval ✓ · Assumption checks (automatic).

▶ Run — click the button. Results are produced automatically as a table + chart.

📄 Export to Word. APA 7-formatted report with italic statistical symbols.

📊 Sample Dataset — Architecture, Planning & Design

ℹ Note: The scenario, MerQur output and interpretation below were produced by actually running the real example dataset in MerQur. Numeric results on your own data will differ; the goal is to show how the analysis is set up and interpreted end-to-end.

🎬 Example File

This analysis is demonstrated on the following example dataset for Architecture, Planning & Design:

Peyzaj_Mimarligi/69_pca_park_6ozellik.xlsx

🎬 Scenario

We reduce six park features to a few summary axes and reveal hidden dimensions with PCA.

⚙️ Variable Selection

Variables: area_m2, green_ratio, tree_count, path_length_m, water_area_pct, satisfaction

Data Preview (First 5 Rows)

park_id	area_m2	green_ratio	tree_count	path_length_m	water_area_pct	satisfaction
1.0	2231.0	0.424	35.0	585.0	5.3	2.91
2.0	3458.0	0.643	78.0	710.0	19.6	3.52
3.0	4182.0	0.631	98.0	1088.0	26.9	3.6
4.0	3180.0	0.571	69.0	985.0	23.7	4.14
5.0	1414.0	0.371	31.0	518.0	6.8	2.76

n = 180 · Columns: park_id, area_m2, green_ratio, tree_count, path_length_m, water_area_pct, satisfaction

📈 MerQur Output

PCA (PRINCIPAL COMPONENTS ANALYSIS) RESULT ───────────────────────────────────────────── PC1 = 87.5% (the first component alone explains most of the variance) 6 park features (area, green ratio, tree count, path length, water area, satisfaction)

💬 Interpretation

We reduced six park features to a few summary axes with PCA. The first component alone explains 87.5% of the variance — strikingly high. The meaning: these features are very highly correlated, all measuring a single “park size/richness” dimension (large parks generally have many trees, long paths, higher satisfaction). PCA is the basic tool for summarising multivariate park data, reducing collinearity and revealing hidden dimensions (like general park quality). One component being this dominant suggests a composite park-quality index could be built.

⚠ Common Mistakes

Misidentifying the data type (e.g., loading a categorical variable as numeric)
Skipping assumption checks and going straight to the p-value
Failing to report effect size — APA 7 requires both p and effect size
Failing to apply a Type I error correction (Bonferroni/Tukey) in multiple comparisons
Not switching to a non-parametric alternative when n is insufficient

📹 Video Walkthrough

Watch the video below for an end-to-end walkthrough of this analysis on a Architecture, Planning & Design file.

▶ PCA (Principal Components Analysis) — video walkthrough

This section is part of the Kümeleme ve Boyut İndirgeme video (7 analyses in one video). The link below jumps straight to 4:59, where this analysis begins. Narration is in Turkish.

▶ Watch this analysis (4:59) 📺 All videos

🔀 The same analysis in other disciplines:
🎓 Education Sciences · 🧪 Natural Sciences & Mathematics · ⚙ Engineering · 🏥 Health Sciences · 📊 Social, Humanities & Admin Sciences · 🏃 Sport Sciences · 🌾 Agriculture, Forestry & Aquatic

📚 If You Used This Analysis, Cite MerQur

If you performed this analysis using MerQur in a scientific study, please use the citation below as part of your academic citation obligations (APA 7):

Örücü, Ö. K. (2026). MerQur: Integrated Academic Data Analysis & Reporting Platform [Computer software] (Version 1.0.0). https://doi.org/10.53463/merqur.2026001

For BibTeX, RIS, EndNote and the English citation form: all citation formats →

Sources:

American Psychological Association. (2020). Publication manual of the American Psychological Association (7th ed.).
Field, A. (2018). Discovering statistics using IBM SPSS Statistics (5th ed.). Sage.
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum.