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

## Hypotheses

The following hypotheses may be tested:

Where is the true population correlation from which the sample was drawn, and is some value other than zero between -1.00 and 1.00.

## Assumptions

1. The sample has been randomly drawn from a bivariate (two-dimensional) population (Critical)

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

3. The correlation tested represents the degree to which a linear relationship exists between the two variables (Critical)

## Test Statistics

## Output

### Note

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