Two-Way ANOVA
Two-Way ANOVA 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?
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 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 Two-Way ANOVA.
Panel assignments (form fields in the program):
- Factor 1:
cinsiyet - Factor 2:
yontem - Value Column:
basari
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/07_two_way_anova_method_sex.xlsx
🎬 Scenario
Here we ask two questions at once: does teaching method affect achievement, does sex affect achievement, and do the two interact? We have 150 students crossed by instruction method, with levels traditional, project, and mixed, and by sex, female and male, with achievement recorded for each. A two-way ANOVA is the right design because we have two categorical factors and we want to estimate their main effects as well as their interaction on a continuous outcome.
⚙️ Variable Selection
- Factor 1: method (traditional, project, mixed)
- Factor 2: sex (female, male)
- Dependent variable: achievement
- >> 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 | achievement |
|---|---|---|---|
| 1 | traditional | female | 80.8 |
| 2 | traditional | female | 77.1 |
| 3 | traditional | female | 63.0 |
| 4 | traditional | female | 64.3 |
| 5 | traditional | female | 69.7 |
n = 150 · Columns: student_id, method, sex, achievement
📈 MerQur Output
💬 Interpretation
We examined achievement with two factors — instruction method and sex — together. The method effect is very strong (F = 42.24, η²p = 0.37), while the sex effect is significant but very small (F = 4.61, p = 0.033, η²p = 0.03). So the main determinant of achievement is instruction method; sex contributes minimally. Two-way ANOVA’s strength is seeing both factors’ effects — separately and jointly (interaction) — at once. This answers questions like “is the method effect similar for both sexes” and reveals for whom educational interventions work best. >> 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 Education Sciences file.
▶ Two-Way ANOVA — 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 13:06, 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.