Normality Tests
Normality Tests 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?
Normality Tests automatically applies all necessary assumption checks (normality, homogeneity of variance, etc.) for the relevant data type in the background and presents the results with a clear table + chart. Automated 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 Normality Tests.
Panel assignments (form fields in the program):
- Column:
GPA - Significance (α):
0.05
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/02_normality_GPA_study_motivation.xlsx
🎬 Scenario
Many of the parametric tests we plan to use assume that continuous variables are normally distributed. So before choosing between parametric and nonparametric approaches, we check that assumption directly. With 200 students measured on GPA, weekly study hours, and motivation, we want to know whether each of these variables departs from a normal distribution. A normality test such as Shapiro-Wilk is appropriate here because it formally evaluates the distributional assumption for each continuous variable rather than relying on eyeballing a histogram.
⚙️ Variable Selection
- Variables to test: GPA
- Variables to test: study_hour
- Variables to test: motivation
Data Preview (First 5 Rows)
| student_id | GPA | study_hour | motivation |
|---|---|---|---|
| 1.0 | 3.1 | 5.0 | 3.79 |
| 2.0 | 2.3 | 5.7 | 3.92 |
| 3.0 | 2.62 | 7.0 | 3.9 |
| 4.0 | 2.51 | 2.4 | 3.34 |
| 5.0 | 2.62 | 9.8 | 3.38 |
n = 200 · Columns: student_id, GPA, study_hour, motivation
📈 MerQur Output
💬 Interpretation
We tested whether three variables — GPA, study hours and motivation — are normally distributed. The result differs by variable: GPA is normal (p = 0.068 > 0.05; grades symmetric, bell-curve-like), but study hours and motivation deviate significantly from normality (p < .001). This is typical in educational data — study hours are usually right-skewed (most study little, a few a lot), and motivation may be an ordinal/bounded scale. The practical takeaway: we can safely use parametric tests (t-test, ANOVA, Pearson) on GPA; for study and motivation, nonparametric methods (Mann-Whitney, Kruskal-Wallis) or a transform are more appropriate. The normality check is a critical pre-step that decides, for each variable separately, which test family is appropriate.
⚠ 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.
▶ Normality Tests — video walkthrough
This section is part of the Veriye İlk Bakış ve Parametrik Testler video (14 analyses in one video). The link below jumps straight to 2:54, 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.