The Correlation Test for Rho = 0 is used to test if a correlation exists between two variables. The correlation represents the degree to which a linear relationship exists between these two variables. If the desired test is for a specific correlation value, other then zero, see the Test for Correlation = .

## Hypotheses

The following hypotheses may be tested:

Where is the true population correlation from which the sample was drawn.

## Assumptions

- The sample has been randomly drawn from a bivariate (two-dimensional) population (Critical)
- The population may be modeled with a bivariate normal distribution (Not Critical, if unimodal)
- The correlation tested represents the degree to which a linear relationship exists between the two variables (Critical)

## Test Statistics

Where t has n-2 df.

## Output

### Note

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