Bayesian t-Test (BEST)
v1.0.2
Natural Sciences & Mathematics context — the posterior-focused version of the classic t-test. With 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 Natural Sciences & Mathematics, it tests whether the Control and Experimental groups differ in terms of elementel_konsantrasyon.
📌 When is it used?
- In Natural Sciences & Mathematics, when comparing two groups (Control vs Experiment) and you also want to test H₀ directly
- Small sample (N<30) — the JZS prior stabilizes the estimates
- In replication studies — seeking evidence for a “no effect” conclusion
- A test of difference from a threshold (reference) value (one-sample mode)
⚙ Assumptions
- The DV is continuous (elementel_konsantrasyon).
- Independence (independent mode): the observations of the two groups are independent.
- Normality is relaxed via the CLT; at 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 — Natural Sciences & Mathematics
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 Natural Sciences & Mathematics:
Fen_Matematik/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 method) 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 lab 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.