Pearson Correlation

TEST OVERVIEW & EQUATIONS

The Pearson product-moment correlation summarizes whether two paired variables move together in a linear fashion.

$$\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i \quad \bar{y} = \frac{1}{n} \sum_{i=1}^{n} y_i$$

$$r = \frac{\sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2 \sum (y_i - \bar{y})^2}}$$

$$t = r \sqrt{\frac{n - 2}{1 - r^2}} \qquad df = n - 2$$

$ r $ ranges from -1 (perfect negative association) to +1 (perfect positive association).
The two-tailed p-value comes from the Student's t distribution with $ n - 2 $ degrees of freedom.
Confidence intervals are computed on the Fisher z scale and then transformed back to $ r $.

MARKETING SCENARIOS

Load a marketing use case:

Select a preset to auto-fill inputs and narratives for common marketing analytics use cases (e.g., spend vs. conversions, awareness vs. consideration, or two survey metrics). Each preset can expose the raw CSV so you can inspect the required formatting.

INPUTS & SETTINGS

Select Data Entry / Upload Mode

Drag & Drop raw data file (.csv, .tsv, .txt)

Provide two named numeric columns such as x,y (paired) or 2+ numeric columns with headers for matrix mode. Blank rows are ignored.

We only scan files locally—no uploads leave your browser. Up to 2,000 rows per file.

Type smaller paired datasets directly. Enter Variable X and Variable Y for each row, then set how many rows you need (maximum of 50). For bigger tables, switch to the upload mode.

Row count (max 50)

Need more than 50 rows? Head to the upload mode.

Row	Variable X	Variable Y

Upload a wide file with two or more numeric columns (comma or tab separated). Each column header becomes a variable in the correlation matrix for the summary upload mode.

No summary file uploaded yet.

Upload a file with two aligned columns (e.g., spend and conversions, metric_x and metric_y). Use this when you want to ingest raw paired observations.

No raw file uploaded yet.

Significance level (α):

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.

Pearson product-moment

Tracks linear association and matches the equations above. Works best when both metrics are roughly normal and measured on interval scales.

Spearman rank correlation

Ranks each metric before correlating, surfacing monotonic or ordinal relationships while reducing the influence of extreme points.

This selection drives every card, chart, narrative, and diagnostic once data are provided.

VISUAL OUTPUT

Correlation estimate with confidence interval

Provide data to summarize the correlation estimate and confidence interval.

Scatterplot (X vs Y)

Scatter pair:

Provide paired raw data to explore the scatterplot.

Visual Output Settings

Show regression line on scatterplot Show confidence band (Pearson only) Heatmap color scale

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.

TEST RESULTS

Analysis Status

Enter data to compute the selected correlation.