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Bayesian Correlation

Research Disciplines → Natural Sciences & Mathematics → ⚡ Bayesian Correlation

Bayesian Correlation

⚡ Advanced · Bayesian Statistics · Correlation

v1.0.2

Natural Sciences & Mathematics context — reports the relationship between two continuous variables with BF₁₀. Is the sicaklik_C ↔ reaksiyon_hizi relationship real or chance? Supported by Pearson/Spearman/Kendall.

Pearson/Spearman/KendallBF₁₀%95 CrI(r)Posterior dağılım grafik

🎯 What is it for?

It reports BF₁₀ instead of the classical correlation p-value; it is especially valuable in small samples and replication studies. In the Natural Sciences & Mathematics context, the predicted direction of the relationship (ρ ≈ 0.78) between sicaklik_C and reaksiyon_hizi 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

  1. Two continuous variables (sicaklik_C, reaksiyon_hizi).
  2. A linear relationship (Pearson) or a monotonic one (Spearman/Kendall).
  3. Outlier screening should be performed beforehand with a Bland-Altman/scatter plot.

📊 How to Run in MerQur

1
Data tab → load.
2
Analysis → ⚡ Advanced → Bayesian Correlation.
3

Panel assignments (form fields in the program):

  • Columns: {'x_col': 'birim_id', 'y_col': 'X_degisken'}
  • Parameters: {'method': 'pearson'}
4
Prior scale (default stretched-beta, κ=1).
5
▶ Run → r̂, BF₁₀, posterior distribution, 95% CrI.

📊 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/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

BAYESIAN CORRELATION RESULT
─────────────────────────────────────────────

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 the lab it is
valuable for reporting not just whether the relationship between two measurements 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

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.