Bayesian ANOVA
v1.0.2
Education Sciences context — tests the difference among 3+ group means with BF₁₀. It directly reports, as evidence, whether the ogretim_modu groups (Face-to-Face, Hybrid, Fully Online) have an effect on matematik_puani.
🎯 What is it for?
Instead of the classic F-test and p-value, it gives a separate BF₁₀ for each effect (main effect + interaction); a direct answer to the question “which effect really matters?”.
📌 When is it used?
- Comparison of 3+ treatments/categories in Education Sciences — Face-to-Face vs. Hybrid vs. Fully Online
- When there is an interaction (2-way) — if the interaction BF₁₀ is larger than the main-effect BF₁₀, it changes the direction of the interpretation
- Replication: reporting a “no effect” conclusion with evidence
⚙ Assumptions
- Continuous DV (math_score); categorical factor(s) (instruction_mode).
- Independent observations; groups should be close to balanced.
- Homogeneity of variance — assumed for the pingouin BF computation.
📊 How to Run in MerQur
Panel assignments (form fields in the program):
- Columns:
{'dv': 'deger', 'factor1': 'faktor1', 'factor2': 'faktor2'} - Parameters:
{}
📊 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/103_bayesian_anova_2yonlu.xlsx
🎬 Scenario
Suppose we want to know whether two instructional design factors jointly
shape a learning outcome. In this study 120 observations were crossed across
factor1, which has three levels A, B and C, and factor2, which has two
levels X and Y, and the continuous outcome is value. We use a Bayesian two-
way ANOVA because we want to compare models with and without each main
effect and the interaction, and report Bayes factors that tell us which
combination of factors the data actually favor. This is more informative
than classical ANOVA when our goal is to weigh competing explanatory models
rather than simply test significance.
⚙️ Variable Selection
- First factor: factor1 (A / B / C)
- Second factor: factor2 (X / Y)
- Dependent variable: value
Data Preview (First 5 Rows)
| factor1 | factor2 | value |
|---|---|---|
| A | X | 49.25 |
| A | X | 58.89 |
| A | X | 45.54 |
| A | X | 45.07 |
| A | X | 51.21 |
n = 120 · Columns: factor1, factor2, value
📈 MerQur Output
─────────────────────────────────────────────
factor1: F(2,117) = 17.91, eta2p = 0.234, BF10 = 76,099 (decisive evidence)
Two-factor design -> score
💬 Interpretation
We examined the effect of two factors on score with Bayesian ANOVA. The first factor’s effect is strong: F(2,117)
= 17.91, effect size eta2p = 0.23, Bayes Factor 76,099 — “decisive evidence”. Bayesian ANOVA gives a separate
Bayes Factor for each effect and interaction, answering “which factor really matters” more informatively than
classic ANOVA — and can even provide “evidence of absence” for non-significant effects. It is a powerful way to
evaluate factor effects with their strength of evidence in educational experiments (such as method x level).
⚠ Common Mistakes
- Use separate Bayesian t-tests for pairwise comparison; do not over-interpret BF₁₀.
- Unbalanced groups affect the BF estimate.
- If there is an interaction, evaluate the main effect interpretation together with the interaction.
📚 MerQur’a Atıf
Örücü, Ö. K. (2026). MerQur: Integrated Academic Data Analysis & Reporting Platform [Computer software] (Version 1.0.0). https://doi.org/10.53463/merqur.2026001
📝 Üretim Notu — Bu sayfadaki örnek veri sentetik olarak üretilmiştir (sabit SEED=42, generator: samples/Ileri_Duzey_v102/_generate_v102_datasets.py). Sayfa içeriği Anthropic Claude desteği ile hazırlanmış, akademik doğruluk yazar tarafından kontrol edilmiştir.