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Bayesian ANOVA

Research Disciplines → Engineering → ⚡ Bayesian ANOVA

Bayesian ANOVA

⚡ Advanced · Bayesian Statistics · ANOVA

v1.0.2

Engineering context — tests the difference in means of 3+ groups via BF₁₀. It reports directly as evidence whether the malzeme (Alüminyum, Çelik, Titanyum) groups have an effect on dayanim_kPa.

1-way / 2-wayEtkileşim BFEtki başına BF bar grafikpingouin tabanlı + BIC fallback

🎯 What is it for?

Instead of the classic F-test and p-value, it provides 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 Engineering — Aluminum vs Steel vs Titanium
  • 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 the “no effect” result with evidence

⚙ Assumptions

  1. Continuous DV (dayanim_kPa); categorical factor(s) (malzeme).
  2. Independent observations; groups should be reasonably balanced.
  3. Homogeneity of variance — assumed for the pingouin BF computation.

📊 How to Run It in MerQur?

1
Load the data.
2
Analysis → ⚡ Advanced → Bayesian ANOVA.
3
DV: dayanim_kPa. Factor 1: malzeme. (For a 2-way design, also select Factor 2.)
4
▶ Run. A BF₁₀ bar chart for each effect plus an ANOVA summary.
5
In the Chart tab, a horizontal BF₁₀ bar — colored bands at the Jeffreys thresholds.

🧪 Örnek Veri — Engineering

📂 samples/Ileri_Duzey_v102/muhendislik/103_bayesian_anova.xlsx · n = 105 · Faktör: malzeme (Alüminyum, Çelik, Titanyum)

⬇ Örnek dataset indir (.xlsx)

malzeme dayanim_kPa
Alüminyum 279.535
Titanyum 487.577
Çelik 444.475
Titanyum 508.025
Çelik 457.924
… …

📊 MerQur Output (summary)

Bayesian ANOVA (dayanim_kPa ~ malzeme)
==================================
malzeme main effect : BF₁₀ ≈ > 30 (very strong evidence for H₁)
Groups:
Alüminyum μ̂ ≈ 280.00
Çelik μ̂ ≈ 460.00
Titanyum μ̂ ≈ 520.00

📄 APA 7 Interpretation

In the Engineering field, the effect of the malzeme groups (3 levels: Alüminyum, Çelik, Titanyum) on dayanim_kPa was examined with a Bayesian ANOVA over 105 observations. The results yielded BF₁₀ > 30 for the main effect, indicating very strong evidence in favor of H₁. The highest mean was observed in the Titanyum group.

⚠ Common Mistakes

  • Use separate Bayesian t-tests for pairwise comparisons; do not over-interpret BF₁₀.
  • Unbalanced groups affect the BF estimate.
  • If an interaction is present, interpret the main effect 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

Tüm atıf formatları →

📝 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.