Bayesian ANOVA
v1.0.2
Sport Sciences context — tests the difference in means among 3+ groups using BF₁₀. It reports directly, as evidence, whether the diyet_tipi (Karbonhidrat, Yüksek Protein, Karma) groups have an effect on dayaniklilik_metre.
🎯 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?
- In Sport Sciences, comparison of 3+ treatments/categories — Carbohydrate vs High Protein vs Mixed
- If there is interaction (2-way) — when the interaction BF₁₀ is greater than the main effect BF₁₀, it changes the direction of interpretation
- Replication: reporting a “no effect” conclusion with evidence
⚙ Assumptions
- Continuous DV (dayaniklilik_metre); categorical factor(s) (diyet_tipi).
- 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 — Sport 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 Sport Sciences:
Spor_Bilimleri/103_bayesian_anova_2yonlu.xlsx
🎬 Scenario
We examine a measurement’s difference across two factors with Bayesian ANOVA.
For the evidential strength of factor effects, this is appropriate.
⚙️ Variable Selection
- Dependent variable: value
- Factor (categorical): factor1
- 2nd Factor: factor2
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: BF10 = 76099 (very strong evidence) outcome: value, factors: factor1, factor2
💬 Interpretation
We examined a measurement’s difference across two factors with Bayesian ANOVA: for factor1, BF10 ~ 76,000, very
strong evidence. Bayesian ANOVA compares the effects of factors and their interactions via Bayes factors; it ranks
probabilistically which model (which effects) best explains the data. Unlike classical ANOVA’s “reject/don’t reject”
decision, it quantifies the relative support among models. In sports science it is used to compare the evidential
strength of factor effects.
⚠ 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.