Two-Way ANOVA
Two-Way ANOVA is one of the statistical analyses applied automatically in MerQur. This page illustrates — on a Engineering 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 Engineering 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:
tur - Factor 2:
bolge - Value Column:
DBH_cm
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 — Engineering
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 Engineering:
Muhendislik/07_two_way_anova_type_region.xlsx
🎬 Scenario
We examine the main effects and interaction of type and region on diameter simultaneously. With two categorical factors, two-way ANOVA is appropriate.
⚙️ Variable Selection
- Dependent variable: dbh_cm
- Factor (categorical): type
- 2nd Factor: region
- >> 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)
| tree_id | type | region | dbh_cm |
|---|---|---|---|
| 1 | pine | north | 26.1 |
| 2 | pine | north | 26.5 |
| 3 | pine | north | 29.3 |
| 4 | pine | north | 25.5 |
| 5 | pine | north | 30.2 |
n = 180 · Columns: tree_id, type, region, dbh_cm
📈 MerQur Output
💬 Interpretation
We examined two factors at once: how do type and region affect diameter? Both main effects are significant (type: F(2) = 149.27, eta^2p = 0.64; region: F(2) = 9.56, eta^2p = 0.10). The dominant driver of diameter is type, but region also makes an independent contribution. 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 the field. >> 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 Engineering 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 12:18, where this analysis begins. Narration is in Turkish.
🎓 Education Sciences · 🧪 Natural Sciences & Mathematics · 🏛 Architecture, Planning & Design · 🏥 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.