CFA (Confirmatory Factor Analysis)
CFA (Confirmatory Factor 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?
CFA (Confirmatory Factor 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 CFA (Confirmatory Factor Analysis).
Panel assignments (form fields in the program):
- factors:
{...} - structural_paths:
None
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/77_cfa_self_academic_social.xlsx
🎬 Scenario
We measured 280 students on twelve indicators of self-concept, four for the academic self, four for the general self, and four for the social self. Unlike an exploratory analysis, here we already have a clear theoretical model: three correlated latent factors with specified item loadings. Confirmatory Factor Analysis is the appropriate method because it lets us test whether this hypothesized three-factor structure fits the observed data, reporting fit indices and factor loadings that confirm or challenge our measurement model.
⚙️ Variable Selection
- Factor 1 (self) items: self_1, self_2, self_3, self_4
- Factor 2 (academic) items: academic_1, academic_2, academic_3, academic_4
- Factor 3 (social) items: social_1, social_2, social_3, social_4
Data Preview (First 5 Rows)
| student_id | self_1 | self_2 | self_3 | self_4 | academic_1 | academic_2 | academic_3 | academic_4 | social_1 | social_2 | social_3 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 2 | 2 | 3 | 2 | 3 | 3 | 2 | 3 | 2 | 1 |
| 2 | 2 | 3 | 3 | 3 | 2 | 2 | 2 | 3 | 3 | 3 | 3 |
| 3 | 5 | 5 | 5 | 4 | 4 | 3 | 3 | 3 | 3 | 3 | 2 |
| 4 | 3 | 2 | 3 | 3 | 3 | 4 | 3 | 3 | 2 | 2 | 1 |
| 5 | 3 | 4 | 3 | 4 | 1 | 2 | 1 | 2 | 3 | 2 | 3 |
n = 280 · Columns (first 12 columns): student_id, self_1, self_2, self_3, self_4, academic_1, academic_2, academic_3, academic_4, social_1, social_2, social_3
📈 MerQur Output
💬 Interpretation
While EFA explores hidden structure, CFA tests a pre-specified theory: here we tested whether three distinct self/competence dimensions — “self”, “academic” and “social” — fit the data. The fit is excellent (CFI = 1.00, RMSEA = 0.000): the items really load onto these three dimensions, the hypothesised scale structure is fully confirmed. CFA is part of structural equation modelling (SEM) and is the strongest way to prove scale validity. It is the standard method for demonstrating the validity of multidimensional educational/psychological constructs like self-concept and self-efficacy.
⚠ 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.
▶ CFA (Confirmatory Factor Analysis) — video walkthrough
This section is part of the Anket Analizleri video (5 analyses in one video). The link below jumps straight to 7:12, 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.