Two-Way ANOVA
Two-Way ANOVA is one of the statistical analyses applied automatically in MerQur. This page illustrates — on a Social, Humanities & Admin 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?
Two-Way ANOVA 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 Social, Humanities & Admin 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 Two-Way ANOVA.
Panel assignments (form fields in the program):
- Factor 1:
cinsiyet - Factor 2:
yontem - Value Column:
puan
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 — Social, Humanities & Administrative 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 Social, Humanities & Administrative Sciences:
Sosyal_Beseri/07_two_way_anova.xlsx
🎬 Scenario
We examine the main effects and interaction of method and sex on achievement simultaneously. With two categorical factors, two-way ANOVA is appropriate.
⚙️ Variable Selection
- Dependent variable: score
- Factor (categorical): method
- 2nd Factor: sex
- >> ADVANCED PARAMETERS (optional in the form — what they do):
- Sum-of-squares type (I/II/III): Type III for unbalanced designs with interaction (SPSS default).
- Post-hoc (Tukey/Bonferroni/Games-Howell) for 3+ level factors.
- Effect sizes: partial eta-squared, eta-squared, omega-squared.
- Levene & residual Shapiro; cell and marginal means tables.
Data Preview (First 5 Rows)
| student_id | method | sex | score |
|---|---|---|---|
| 1 | traditional | female | 81.8 |
| 2 | traditional | female | 72.0 |
| 3 | traditional | female | 66.0 |
| 4 | traditional | female | 74.9 |
| 5 | traditional | female | 58.6 |
n = 150 · Columns: student_id, method, sex, score
📈 MerQur Output
💬 Interpretation
We examined two factors at once: how do instruction method and sex affect the achievement score? The method main effect is very strong (F(2) = 43.85, p < .001, eta^2p = 0.38), while the sex main effect is non-significant (p = 0.52). The decisive driver of the score is method; sex alone contributes nothing notable. The power of two-way ANOVA is that it tests both factors and their interaction in a single model — isolating each factor’s pure effect with the other controlled. It is ideal for answering “which variable really makes a difference?” in education. >> ADVANCED PARAMETERS (optional in the form — what they do): – Sum-of-squares type (I/II/III): Type III for unbalanced designs with interaction (SPSS default). – Post-hoc (Tukey/Bonferroni/Games-Howell) for 3+ level factors. – Effect sizes: partial eta-squared, eta-squared, omega-squared. – Levene & residual Shapiro; cell and marginal means tables.
⚠ 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 Social, Humanities & Admin Sciences file.
▶ Two-Way ANOVA — video walkthrough
A complete end-to-end walkthrough of this analysis in MerQur, narrated on screen. Narration is in Turkish.
🎓 Education Sciences · 🧪 Natural Sciences & Mathematics · 🏛 Architecture, Planning & Design · ⚙ Engineering · 🏥 Health 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.