Discriminant Analysis
Discriminant Analysis is one of the statistical analyses applied automatically in MerQur. This page illustrates — on a Education Sciences 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?
Discriminant Analysis automatically performs all required assumption checks (normality, homogeneity of variance, etc.) for the relevant data type in the background 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 Education Sciences 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 Discriminant Analysis.
Panel assignments (form fields in the program):
- error:
cats() got an unexpected keyword argument 'max_unique'
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 — Education Sciences
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 Education Sciences:
Egitim_Bilimleri/84_diskriminant_3sinif_5feat.xlsx
🎬 Scenario
Suppose we want to classify students into three achievement levels, low, medium, and high, based on their academic profile. For 105 students we have their math and science scores, GPA, absenteeism days, and weekly study hours. We want both to know which combination of variables best separates the three groups and to build a rule that assigns a new student to a level. We use Discriminant Analysis, which finds the linear combinations of these continuous predictors that maximally distinguish the achievement classes and classifies cases accordingly.
⚙️ Variable Selection
- Grouping variable (target): achievement_class (low/medium/high)
- Predictors: math, science, GPA, absenteeism, study_hour
Data Preview (First 5 Rows)
| student_id | math | science | GPA | absenteeism | study_hour | achievement_class |
|---|---|---|---|---|---|---|
| 1 | 55.4 | 50.4 | 1.44 | 23 | 5.5 | low |
| 2 | 43.2 | 50.1 | 1.69 | 20 | 7.3 | low |
| 3 | 46.8 | 57.4 | 1.84 | 24 | 6.2 | low |
| 4 | 47.3 | 41.9 | 1.35 | 31 | 3.8 | low |
| 5 | 51.2 | 41.0 | 1.24 | 29 | 4.5 | low |
n = 105 · Columns: student_id, math, science, GPA, absenteeism, study_hour, achievement_class
📈 MerQur Output
💬 Interpretation
Discriminant analysis finds the linear combinations of variables that best separate the groups (three achievement classes) — a bit like a classification-focused PCA. Accuracy is 100%: five variables separate the three classes perfectly. Discriminant analysis both classifies and answers “which variables matter most for the separation” (discriminant function loadings). It resembles logistic regression but is the classic choice for multiple groups when variables are normally distributed. It is used in achievement-level classification and for assigning new students to existing groups.
⚠ 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 Education Sciences file.
▶ Discriminant Analysis — video walkthrough
This section is part of the Sınıflandırma video (7 analyses in one video). The link below jumps straight to 11:12, where this analysis begins. Narration is in Turkish.
🧪 Natural Sciences & Mathematics · 🏛 Architecture, Planning & Design · ⚙ 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 →
- 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.