Chi-Square Goodness-of-Fit Test
Chi-Square Goodness-of-Fit Test 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?
The Chi-Square Goodness-of-Fit Test 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 in 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 Chi-Square Goodness-of-Fit Test.
Panel assignments (form fields in the program):
- Column:
ogrenme_stili - expected_props:
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/22_chisquare_goodnessfit_learning_style.xlsx
🎬 Scenario
Suppose an educational psychologist wants to check whether learning styles are evenly distributed among students. We collected the dominant learning style of 200 students, classified as visual, auditory, kinesthetic, or enrolled. The question is whether the four learning-style categories occur in equal proportions, or whether some styles are clearly more common than others. Since we have a single categorical variable and want to compare observed category counts against an expected distribution, the Chi-Square Goodness-of-Fit test is appropriate.
⚙️ Variable Selection
- Categorical variable: learning_style (visual/auditory/kinesthetic/enrolled)
- >> 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).
Data Preview (First 5 Rows)
| student_id | learning_style |
|---|---|
| 1 | visual |
| 2 | visual |
| 3 | auditory |
| 4 | kinesthetic |
| 5 | visual |
n = 200 · Columns: student_id, learning_style
📈 MerQur Output
💬 Interpretation
We tested whether students’ learning styles (visual, auditory, kinesthetic, reading-writing) are equally distributed with the chi-square goodness-of-fit test. The observed distribution deviates significantly from the equal expectation (chi-square(3) = 17.64, p < .001): some styles are more common than expected, others rare. So learning styles are not balanced in the student population — suggesting instruction should be adapted to the dominant styles. The goodness-of-fit test is the right way to compare an observed category distribution against a theoretical expectation (equal or specific proportions). >> 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).
⚠ 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.
▶ Chi-Square Goodness-of-Fit Test — video walkthrough
This section is part of the Kategorik Veri Analizleri video (7 analyses in one video). The link below jumps straight to 2:06, where this analysis begins. Narration is in Turkish.
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📚 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.