Bayesian Correlation
v1.0.2
Agriculture, Forestry & Aquatic context — reports the relationship between two continuous variables with BF₁₀. Is the yaprak_alan_indeksi_LAI ↔ biokutle_kg_ha relationship real or just chance? Supported by Pearson/Spearman/Kendall.
🎯 What is it for?
Instead of the classic correlation p-value, it reports BF₁₀; particularly valuable in small samples and replication studies. In the context of Agriculture, Forestry & Aquatic, the predicted direction of the relationship (ρ ≈ 0.82) between yaprak_alan_indeksi_LAI and biokutle_kg_ha is tested with 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 (yaprak_alan_indeksi_LAI, biokutle_kg_ha).
- Linear relationship (Pearson) or monotonic (Spearman/Kendall).
- Outlier checks 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 — 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/102_bayesian_correlation_BF10.xlsx
🎬 Scenario
We examine the relationship between two continuous variables (X_variable, Y_variable) in a Bayesian way. Classical correlation
gives an r and a p; Bayesian correlation provides the posterior distribution of r and the Bayes factor (BF10): how strong is the
evidence for “a relationship exists” against “no relationship”, and what is the credible interval for r?
⚙️ Variable Selection
- Variable 1: X_variable
- Variable 2: 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 = 4.5 x 10^14 (decisive: relationship exists) (X_variable, Y_variable)
💬 Interpretation
We examined the relationship between two continuous variables in a Bayesian way. Classical correlation gives an r
and a p; Bayesian correlation provides the posterior distribution of r and the Bayes factor. The result is very
strong: r = 0.78 and BF10 = 4.5 x 10 to the 14. So “a relationship exists” is supported over “no relationship” by
a fourteen-zero ratio — decisive evidence. The advantage of the Bayesian approach is answering not just “is it
significant” but “how strong is the evidence” and “what is a reasonable range for r” directly. In a very strong
relationship like this, the Bayes factor makes the result indisputable: there is a real, strong connection between
the two variables.
⚠ 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.