Bayesian ANOVA
v1.0.2
Health Sciences context — tests the difference of means among 3+ groups with BF₁₀. It reports, directly as evidence, whether the cerrahi_yontem (Klasik, Laparoskopik, Robotik) groups have an effect on iyilesme_suresi_gun.
🎯 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?
- Comparing 3+ treatments/categories in the Health Sciences — Conventional vs Laparoscopic vs Robotic
- When an interaction is present (2-way) — if the interaction BF₁₀ exceeds the main-effect BF₁₀, it changes the direction of interpretation
- Replication: reporting an “no effect” finding with evidence
⚙ Assumptions
- Continuous DV (iyilesme_suresi_gun); categorical factor(s) (cerrahi_yontem).
- Independent observations; groups should be close to balanced.
- Homogeneity of variance — assumed for the pingouin BF computation.
📊 How to Run It in MerQur
Panel assignments (form fields in the program):
- Columns:
{'dv': 'HbA1c', 'factor1': 'ilac', 'factor2': 'cinsiyet'} - Parameters:
{}
📊 Sample Dataset — Health 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 Health Sciences:
Tip/103_bayesian_anova_drug_sex.xlsx
🎬 Scenario
We examine HbA1c’s difference across two factors (drug, sex) with Bayesian
ANOVA. For the evidential strength of factor effects, this is appropriate.
⚙️ Variable Selection
- Dependent variable: HbA1c
- Factor (categorical): drug
- 2nd Factor: sex
Data Preview (First 5 Rows)
| drug | sex | HbA1c |
|---|---|---|
| A | female | 4.85 |
| A | female | 6.61 |
| A | female | 5.67 |
| A | female | 7.02 |
| A | female | 4.18 |
n = 120 · Columns: drug, sex, HbA1c
📈 MerQur Output
─────────────────────────────────────────────
drug: BF10 = 2.59e+08 (very strong evidence) outcome: HbA1c, factors: drug, sex
💬 Interpretation
We examined HbA1c’s difference across two factors (drug, sex) with Bayesian ANOVA: for drug, BF10 ~ 2.6e8, 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 medicine it is used to compare the evidential strength
of factor (drug) 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.