# Correlation Tests Two-Sample Dependent Test

Hotelling's Two-Sample Dependent Test for Correlation is used to test if differences exist in correlations from two dependent bivariate populations from which the samples were drawn.

## Hypotheses

The following hypotheses may be tested:

Where and are the population correlations from which the samples were drawn.

## Assumptions

1. The samples has been randomly drawn from two dependent bivariate (two-dimensional) populations (Critical)

2. The populations may be modeled with a bivariate normal distribution (Not Critical, if unimodal)

3. The correlations represent the degree to which a linear relationship exists between two variables (Critical)

## Test Statistics

Where t has n-3 df.

## Output

**Note:** The p-value is flagged with an asterisk (*) when p <= alpha.