Pearson correlation
r = --
p = --
95% CI: [--, --]
Pearson Correlation Studio
Correlation tool
Explore how two or more marketing metrics move together with plain-English readouts, interactive outlier sensitivity, and ready-to-share visuals.
QUICK START: Choose Your Path
DATA SOURCE
📚
Use a Case Study
Select a preset to auto-fill inputs and narratives for common marketing analytics use cases (e.g., spend vs. conversions, awareness vs. consideration, NPS vs. retention, or a full-funnel KPI matrix). Each preset exposes the raw CSV so you can inspect the formatting.
📊
Enter Your Data
Drag & Drop raw data file (.csv, .tsv, .txt)
Upload a CSV/TSV with 2 numeric columns for paired correlation, or 3+ numeric columns for a correlation matrix. Blank rows and ID columns are handled automatically.
Type or paste smaller paired datasets directly (up to 50 rows). You can rename Variable X and Variable Y in the table header or paste two columns directly from Excel/Google Sheets into any cell.
Need more than 50 rows? Switch to file upload above.
| Row |
|---|
Upload a wide file with two or more numeric columns (comma or tab separated). Each numeric column becomes a variable in the correlation matrix, and you can also drill down into any single pair below.
No summary file uploaded yet.
Upload a file with two aligned numeric columns (e.g., spend and conversions). If you upload a file with 3+ numeric columns, the tool can automatically build the full matrix or let you pick any X and Y pair.
No raw file uploaded yet.
INPUTS & SETTINGS
Advanced analysis settings
By default we report Pearson’s r for linear, jointly normal relationships. Switch to Spearman’s rho for a rank-based estimate that down-weights outliers and handles ordinal or monotonic trends.
This selection drives every card, chart, narrative, and diagnostic once data are provided.
TEST RESULTS
Analysis Status
Enter data to compute the selected correlation.
Run the analysis to see what the results say in plain language.
💡 How to Interpret These Results
Reading the correlation (r or ρ) and p-value:
- Sign (+ / −): Positive means both metrics tend to rise together; negative means one rises as the other falls.
- p < α (typically 0.05): The correlation is statistically distinguishable from zero. Reject H0 (ρ = 0).
- p ≥ α: Insufficient evidence of a linear (or monotonic) relationship; the observed correlation could plausibly be sampling noise.
Understanding the Fisher-z confidence interval:
- Shows the plausible range for the true population correlation based on your sample size \(n\).
- If the confidence interval excludes zero, the relationship is statistically significant at your chosen confidence level.
- Wide intervals (common when \(n < 30\)) mean the true strength is still uncertain even if \(p < 0.05\).
Effect size benchmarks (Cohen’s |r| and shared variance R²):
- |r| < 0.10 (R² < 1%): Negligible association in practical terms.
- 0.10 ≤ |r| < 0.30 (R² = 1%–9%): Small / weak association—detectable in large lists, but most variation comes from other factors.
- 0.30 ≤ |r| < 0.50 (R² = 9%–25%): Moderate association—meaningful co-movement across campaigns or accounts.
- |r| ≥ 0.50 (R² ≥ 25%): Strong association—substantial shared variation worth investigating further.
Association vs. causation & shape checks:
A strong, significant correlation never proves that \(X\) causes \(Y\)—a third variable (like seasonality or account size) can drive both. Always inspect the scatterplot below for curvature (diminishing returns) and high-leverage outliers (\(|z| > 2.5\)).
Signal details
t(--)=--
R2 = --
Means: --
Overview
n = -- pairs
Mode: Paired upload
APA-Style Statistical Reporting
Summary will appear after analysis.
Managerial Interpretation
Business-facing copy will appear after analysis.
VISUAL OUTPUT
Correlation estimate & confidence intervals (50% / 80% / 95%)
Provide data to summarize the correlation estimate and confidence interval.
💡 How to read the confidence interval chart
- Point & bands: The marker shows the sample correlation (\(r\) or \(\rho\)). In single-pair view, nested bars show the 50%, 80%, and selected \((1-\alpha)\) Fisher-\(z\) confidence intervals; in matrix view, each row shows one variable pair’s \((1-\alpha)\) interval.
- Zero line (\(r = 0\)): If the outer \((1-\alpha)\) interval does not cross the dashed \(0\) line, the correlation is statistically distinguishable from zero at your chosen \(\alpha\).
- Effect-size zones: Shaded background bands mark Cohen’s conventional thresholds at \(|r| = 0.10\) (small), \(0.30\) (moderate), and \(0.50\) (strong).
Scatterplot (X vs Y)
Provide paired raw data to explore the scatterplot.
💡 What to check in the scatterplot
- Shape before number: Check whether the cloud bends (diminishing returns) before trusting a straight-line slope or \(r\).
- High-leverage points (◆): Observations with \(|z_x| > 2.5\) or \(|z_y| > 2.5\) are plotted as highlighted diamonds. Use the Outlier Sensitivity toggle above when it appears to see how much a single point pulls the line.
- Raw vs. Ranks: Switch to Ranks (Spearman view) to see exactly what Spearman’s \(\rho\) correlates after extreme distances are compressed into rank order.
Visual Output Settings
Toggles update immediately once charts are rendered. Confidence bands respect the current alpha setting.
SUMMARY STATISTICS
Summary Statistics
Variables in analysis
| Variable | Mean | Median | Std. Dev. | Min | Max |
|---|---|---|---|---|---|
| Provide data to see summary statistics. | |||||
DIAGNOSTICS & ASSUMPTIONS
Diagnostics & Assumption Tests
After you run an analysis, this panel summarizes sample size, variance, skew, outliers, and whether Pearson or Spearman best fits the relationship.
OVERVIEW & WHAT THIS TOOL SOLVES
Before building a complex regression or allocating budget to a marketing driver, analysts need to know which metrics actually move together—and whether an apparent relationship is real or just a mirage caused by a single extreme outlier or a curved saturation pattern. Pearson Correlation Studio measures the strength, direction, and statistical significance of linear association between two continuous variables (or across an entire multi-variable correlation matrix), while automatically pairing it with rank-based Spearman correlation and one-click outlier sensitivity checks.
🎯 Questions It Answers
- How strongly and in what direction do two continuous marketing metrics (e.g., ad spend and signups) co-move?
- Is the observed correlation statistically distinguishable from zero at our chosen confidence level?
- Is our correlation being distorted by a single extreme outlier or a monotonic curve that Spearman rank correlation would catch?
📂 What Data You Need
- Single-Pair Mode: Two numeric columns measured on the same N observations (paired rows)
- Matrix Mode: Three or more numeric columns to inspect all pairwise correlations simultaneously
- Sample Size: At least N ≥ 4 paired observations (N ≥ 30 recommended for stable confidence intervals)
💡 What You'll Discover
- Parametric & Nonparametric Readout: Pearson r, R² shared variance, Fisher-z confidence interval, and Spearman ρ
- Outlier What-If Toggle: Instant comparison of r with and without extreme leverage points
- Raw vs. Rank Scatterplot & Heatmap: Visual inspection of linearity, confidence ellipses, and multi-metric clusters
📐 Under the Hood: Model Equations & Variable Definitions
1. Sample Means & Pearson Product-Moment Correlation (r)
\[ r = \frac{\sum_{i=1}^{n}(x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=1}^{n}(x_i - \bar{x})^2}\,\sqrt{\sum_{i=1}^{n}(y_i - \bar{y})^2}}, \qquad R^2 = r^2 \]
💬 Read it in plain English: Pearson r divides the shared co-movement of X and Y around their averages by the product of their individual spreads, producing a scale-free number between −1 and +1 whose square (R²) tells you the share of variance explained linearly.
r
Pearson Correlation CoefficientOUTPUT ⓘ
Dimensionless measure of linear association ranging from −1 (perfect negative) to +1 (perfect positive).
R2
Shared Variance (Coefficient of Determination)OUTPUT ⓘ
Proportion of variance in Y linearly associated with X (and vice versa): R² = r².
xi, yi
Observed Paired ValuesYOUR DATA ⓘ
Values of variable X and variable Y for observation i (i = 1, …, n).
x̄, ȳ
Sample MeansESTIMATED ⓘ
Arithmetic averages of X and Y across all n paired observations.
n
Paired Sample SizeYOUR DATA ⓘ
Total number of complete (non-missing) observation pairs.
2. Hypothesis Test (t), Fisher z Confidence Interval & Spearman Rank Correlation (ρ)
\[ t = r\sqrt{\frac{n - 2}{1 - r^2}} \;(\text{df} = n - 2), \qquad z_r = \tfrac{1}{2}\ln\!\left(\frac{1+r}{1-r}\right), \qquad \rho_s = \text{corr}\bigl(\text{rank}(x), \text{rank}(y)\bigr) \]
💬 Read it in plain English: The t-statistic tests whether r is significantly different from zero, Fisher's z-transform bends skewed correlations into a symmetric bell curve to build accurate confidence intervals, and Spearman's ρ runs the exact same correlation on rank-ordered data to capture curved monotonic trends and resist outliers.
t
Correlation Test StatisticINFERENCE ⓘ
Student t-statistic with df = n − 2 testing the null hypothesis H₀: ρ = 0.
zr
Fisher z-Transformed CorrelationINFERENCE ⓘ
Variance-stabilizing transformation with standard error SE_z = 1 / √(n − 3) used to compute the CI for r.
ρs
Spearman Rank CorrelationOUTPUT ⓘ
Pearson correlation computed on the within-variable ranks rank(x_i) and rank(y_i); robust to outliers and monotonic curves.
df = n − 2
Degrees of FreedomINFERENCE ⓘ
Effective sample size after estimating the two means x̄ and ȳ.
🔍 Key Nuances & Common Traps to Watch For
- Correlation ≠ Causation: A strong r = 0.75 between loyalty app opens and monthly spend does not prove that push notifications forcing app opens will cause spend—an unobserved third variable (brand enthusiasm) may drive both.
- Zero Linear Correlation ≠ No Relationship: Pearson r only detects straight-line relationships. An inverted-U curve (like ad frequency vs. brand favorability, where too many ads cause fatigue) can yield r ≈ 0 even when the relationship is strong. Always check the scatterplot!
- Pearson vs. Spearman Gap: When Pearson r and Spearman ρ disagree sharply, inspect the scatterplot and toggle Exclude Extreme Outliers—either one leverage point is pulling Pearson r, or the relationship is monotonic but curved.