Bayesian t-Test (BEST)
v1.0.2
Engineering context — the posterior-focused version of the classic t-test. Via BF₁₀, it directly answers the question “how many times more evidence does the data provide in favor of H₁?” Three modes: one-sample/independent/paired. Rouder et al. (2009) JZS Cauchy prior.
🎯 What is it for?
The Bayesian t-Test frees you from the classical p-value dilemma. BF₁₀ > 3: moderate-to-strong evidence for H₁; BF₁₀ < 1/3: moderate-to-strong evidence for H₀. In Engineering, it tests whether the Standard and Improved groups differ in terms of basinc_dayanimi_MPa.
📌 When is it used?
- In Engineering, when comparing two groups (Standard vs Improved) and you also want to test H₀ directly
- Small sample (N<30) — the JZS prior stabilizes the estimates
- In replication studies — searching for evidence of a “no effect” result
- Test of difference from a threshold (reference) value (one-sample mode)
⚙ Assumptions
- The DV is continuous (basinc_dayanimi_MPa).
- Independence (independent mode): the observations of the two groups are independent.
- Normality is relaxed via the CLT; for small N the Bayesian approach is more robust.
- A sensitivity test with JZS scale r ∈ {0.5, 0.707, 1.0} is recommended.
📊 How to Run in MerQur
Panel assignments (form fields in the program):
- Columns:
{'mode': 'independent', 'group_col': 'grup', 'val_col': 'birim_id'} - Parameters:
{'prior_scale': 0.707}
📊 Sample Dataset — Engineering
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 Engineering:
Muhendislik/101_bayesian_t_test_new_old.xlsx
🎬 Scenario
We examine two groups’ measurement difference with a Bayesian t-test, expressing
evidence as a Bayes factor. For an intuitive evidence ratio, this is
appropriate.
⚙️ Variable Selection
- Dependent variable: value
- Grouping (categorical): group
Data Preview (First 5 Rows)
| unit_id | group | value |
|---|---|---|
| 1 | old | 60.02 |
| 2 | old | 54.28 |
| 3 | old | 67.56 |
| 4 | old | 35.73 |
| 5 | old | 42.32 |
n = 80 · Columns: unit_id, group, value
📈 MerQur Output
─────────────────────────────────────────────
BF10 = 3.36e+46 Cohen’s d = 3.939 (overwhelming evidence for H1) outcome: value, group: group
💬 Interpretation
We examined the measurement difference between two groups (new/old treatment) with a Bayesian t-test: the Bayes
factor is overwhelming (BF10 ~ 3.4e46), the effect very large (d = 3.94) — the data support the “difference”
hypothesis over “no difference” by astronomical odds. Unlike a p-value, the Bayes factor gives the RELATIVE
evidence strength of two hypotheses and can distinguish “no evidence” from “no difference”. In the field it is
preferred when one wants to express the evidential strength of a decision as an intuitive ratio.
⚠ Common Mistakes
- In one-sample mode, leaving μ₀ at zero produces astronomical BF values for Likert/score comparisons; enter the correct reference point.
- BF₁₀ > 3 and p < .05 do not always coincide — at small N, p may be significant while BF is weak.
- Do not skip reporting prior sensitivity (r = 0.5/0.707/1.0).
📚 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.