Bayesian ANOVA
v1.0.2
Agriculture, Forestry & Aquatic context — tests the difference among 3+ group means with BF₁₀. It reports directly, as evidence, whether the cesit (A, B, C) groups have an effect on taze_agirlik_g.
🎯 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 Agriculture, Forestry & Aquatic — A vs B vs C
- When there is an interaction (2-way) — if the interaction BF₁₀ is greater than the main-effect BF₁₀, it changes the direction of the interpretation
- Replication: reporting a “no effect” result with evidence
⚙ Assumptions
- Continuous DV (taze_agirlik_g); categorical factor(s) (cesit).
- Independent observations, with groups kept 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 — Agriculture, Forestry & Aquatic
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 Agriculture, Forestry & Aquatic:
Ziraat_Orman_Su/103_bayesian_anova_2yonlu.xlsx
🎬 Scenario
We examine the effect of two factors (factor1, factor2) on an outcome (value) with a Bayesian two-way ANOVA. Classical ANOVA
gives F and p; Bayesian ANOVA compares which model (main effects, interaction) best explains the data using Bayes factors: is
there evidence for an interaction, and which effect is most strongly supported?
⚙️ Variable Selection
- Dependent (continuous): value
- Factor 1: factor1
- Factor 2: 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
─────────────────────────────────────────────
Bayesian ANOVA | factor(s): factor1 | model comparison (Bayes factors)
value ~ factor1 (+ factor2)
💬 Interpretation
We examined the effect of factor(s) on an outcome with a Bayesian ANOVA. Classical ANOVA gives F and p; Bayesian
ANOVA compares which model — main effects only, or also the interaction — best explains the data using Bayes
factors. This gives a direct answer to “is there evidence for an interaction”; in the classical approach a
“non-significant” interaction does NOT prove its absence, whereas the Bayes factor can measure evidence for H0 too.
The practical value of Bayesian ANOVA is expressing model selection in the language of probability: being able to
say “the data most support this model” is more informative for decision-making than classical p-value thresholds.
⚠ 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.