Minitab printout for the Temperature/Water Example:

**Correlations: Temperature (F), Water Consumption (oz)
**Pearson correlation of Temperature
(F) and Water Consumption (oz) = 0.963

P-Value = 0.001

**Interpretation**

The P-value refers to the *two-tailed correlation test of hypothesis*.

- The null is:
**H**(i.e._{0}: r = 0**no**significant correlation) - The alternative is:
**H**(i.e. a significant correlation)_{a}: r is not equal to 0

r, rho, is the *population correlation
coefficient* for the paired variables.

The test statistic depends on *r, the sample correlation coefficient.*

The test statistic formula is
where the degrees of freedom, *df = n-2* and *n *is the
number of pairs of data.

The P-value is the observed significance level of the test. If the observed significance level is less than the chosen significance level (alpha), then the researcher should reject the null hypothesis in favor of the alternative. Otherwise, there is not enough evidence to reject the null hypothesis.

See the Correlation Terms for review and additional information about correlation coefficient hypothesis testing.