PCA (Principal Components Analysis)
PCA (Principal Components 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?
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 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 PCA (Principal Components Analysis).
Panel assignments (form fields in the program):
- Columns:
[ogrenci_id, matematik, fen, +3 daha] - n_components:
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 — 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/69_pca_academic_6ders.xlsx
🎬 Scenario
Let’s say we measured students across six subjects and suspect these scores share a few underlying dimensions of ability. For 180 students we have math, science, language, reading_comprehension, logic, and art scores. Principal Component Analysis is well suited here because it reduces these six correlated subjects into a smaller set of uncorrelated components, revealing for instance a general academic factor and perhaps a verbal-versus- quantitative contrast, which simplifies interpretation and visualization.
⚙️ Variable Selection
- Variables: math
- Variables: science
- Variables: language
- Variables: reading_comprehension
- Variables: logic
- Variables: art
Data Preview (First 5 Rows)
| student_id | math | science | language | reading_comprehension | logic | art |
|---|---|---|---|---|---|---|
| 1.0 | 69.5 | 72.9 | 72.0 | 66.0 | 80.7 | 76.6 |
| 2.0 | 62.5 | 69.3 | 67.5 | 69.2 | 62.4 | 68.4 |
| 3.0 | 63.9 | 69.8 | 67.9 | 62.7 | 68.5 | 69.0 |
| 4.0 | 65.2 | 65.5 | 72.8 | 69.2 | 75.2 | 70.3 |
| 5.0 | 69.4 | 71.1 | 63.9 | 73.4 | 66.4 | 66.3 |
n = 180 · Columns: student_id, math, science, language, reading_comprehension, logic, art
📈 MerQur Output
💬 Interpretation
We reduced six subject scores to a few summary axes with PCA. The first component alone explains 87.5% of the variance — strikingly high. The meaning: subjects are very highly correlated, all measuring a single “general academic ability” dimension (g-factor-like). So a student good at math is generally good at science and language too. PCA is the basic tool for summarising multivariate data, reducing collinearity and revealing hidden dimensions (like general ability). One component being this dominant is the educational reflection of the “general intelligence/ability” debate.
⚠ 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.
▶ PCA (Principal Components Analysis) — video walkthrough
This section is part of the Kümeleme ve Boyut İndirgeme video (4 analyses in one video). The link below jumps straight to 0:00, 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.