Bayesian Correlation
v1.0.2
Social, Humanities & Admin Sciences context — reports the relationship between two continuous variables via BF₁₀. Is the egitim_yili ↔ aylik_gelir_bin_TL relationship real or chance? Supports Pearson/Spearman/Kendall.
🎯 What is it for?
Instead of the classical correlation p-value, it reports BF₁₀; it is especially valuable in small samples and replication studies. In the context of Social, Humanities & Admin Sciences, the predicted direction of the relationship (ρ ≈ 0.55) between egitim_yili and aylik_gelir_bin_TL is tested via the Bayes Factor.
📌 When is it used?
- Two continuous variables — to seek direct evidence about direction and strength
- When you want to directly test the “no correlation” hypothesis
- As a replacement for a test that failed with p < .05 at small N
⚙ Assumptions
- Two continuous variables (egitim_yili, aylik_gelir_bin_TL).
- Linear relationship (Pearson) or monotonic (Spearman/Kendall).
- Outlier checking should be done beforehand with Bland-Altman/scatter.
📊 How to Run in MerQur
Panel assignments (form fields in the program):
- Columns:
{'x_col': 'birim_id', 'y_col': 'X_degisken'} - Parameters:
{'method': 'pearson'}
📊 Sample Dataset — Social, Humanities & Administrative 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 Social, Humanities & Administrative Sciences:
Sosyal_Beseri/102_bayesian_correlation_BF10.xlsx
🎬 Scenario
We evaluate the relationship between two variables in a Bayesian framework. For
evidential strength, Bayesian correlation is appropriate.
⚙️ Variable Selection
- 1st measure / group: X_variable
- 2nd measure / group: Y_variable
Data Preview (First 5 Rows)
| unit_id | X_variable | Y_variable |
|---|---|---|
| 1.0 | 25.4 | 38.58 |
| 2.0 | 49.42 | 56.82 |
| 3.0 | 39.88 | 55.51 |
| 4.0 | 35.37 | 51.54 |
| 5.0 | 39.46 | 51.92 |
n = 80 · Columns: unit_id, X_variable, Y_variable
📈 MerQur Output
─────────────────────────────────────────────
r = 0.780 (very strong) BF10 = 4.50e+14 (overwhelming evidence for a relationship)
💬 Interpretation
We evaluated the relationship between two variables in a Bayesian framework: r = 0.78 and BF10 ~ 4.5e14, i.e. very
strong evidence for a relationship. Bayesian correlation, instead of a classical p-value, presents the evidential
strength of the relationship as a Bayes factor and the coefficient’s posterior distribution. In education it is
valuable for reporting not just whether the relationship between two indicators is “significant” but how strongly
it is “evidenced”.
⚠ Common Mistakes
- Pearson is misleading for non-linear relationships — check the scatter plot, and use Spearman if needed.
- Outliers inflate or mask the correlation.
- Correlation ≠ causation (especially in observational studies).
📚 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.