Pearson's Correlation Analysis
Pearson's correlation measures the strength and direction of a linear relationship between two continuous variables. Example: testing whether study hours correlate with exam scores.
Step 1 — Choose the analysis type
Two large cards:
| Card | What it does |
|---|---|
| Single Correlation | Analyse the correlation between two variables (one pair) — full results with statistical inference and scatter plot |
| Matrix Correlation | Compute a correlation matrix for multiple variables at once (many pairs simultaneously) — colour-coded heatmap |
Step 2 — Choose the input method
| Method | When to use |
|---|---|
| Manual entry | Paste or type the values into the relevant columns |
| Excel upload | Import an Excel file with your variables as columns |
Step 3 — Provide your data
For Single Correlation
Enter two columns of values. The Sample Data Generator offers five built-in scenarios:
- Height vs Weight (Height_Weight, Height_BMI)
- Age vs Blood Pressure (Age_SBP, Age_DBP)
- Study Hours vs Exam Score
- Exercise vs Cholesterol
- Screen Time vs Sleep Quality
For Matrix Correlation
Add as many variables as you need with Add Variable / Remove Variable (minimum 2). Each variable needs at least 3 observations. The Matrix Sample Data Generator offers five scenarios:
- Metabolic Panel (Glucose, HbA1c, Insulin, BMI)
- Cardiovascular Risk (SBP, LDL, HDL, TG, CRP)
- Academic Performance (GPA, Study Hours, Sleep Hours, Stress Level)
- Pulmonary Function
- Soil & Crop Analysis
Step 4 — Calculate
Click the calculate button.
Step 5 — Results (Single Correlation)
A Results panel appears with:
-
Correlation coefficient (r) — from −1 to +1
-
Sample size (n) and degrees of freedom (df = n − 2)
-
t-statistic — from
t = r × √(df / (1 − r²)) -
p-value — two-tailed
-
Coefficient of Determination (R²)
-
Interpretation of strength and direction:
| |r| | Strength | |---|---| |
< 0.30| Weak | |0.30 – 0.50| Moderate | |0.50 – 0.70| Strong | |≥ 0.70| Very strong |
A Scatter Plot is rendered below with a Download as JPG button for publication-ready export.
Step 6 — Results (Matrix Correlation)
A correlation matrix where each cell displays the r value between two variables. Cells are colour-coded by |r|:
| |r| value | Tier |
|---|---|
| ≥ 0.70 | Very strong |
| 0.50 – 0.70 | Strong |
| 0.30 – 0.50 | Moderate |
| < 0.30 | Weak |
A Download as Image button exports the matrix. Excel export is also available.
A UniversalChatBot appears after both result types.
Statistical methods used
Correlation coefficient (r)
r = Σ ((xᵢ − x̄)(yᵢ − ȳ)) / ((n − 1) × s_x × s_y)
Hypothesis statement
- H₀: ρ = 0 (no linear correlation)
- H₁: ρ ≠ 0 (two-tailed)
- Significance level: α = 0.05
t-statistic
t = r × √((n − 2) / (1 − r²))
Matrix Correlation
Every pair computed independently using the same Pearson formula. Output is a k × k symmetric matrix.
Minimum sample size: 3 observations per variable for matrix mode.