Calculate the correlation coefficient for your data set.
r = N'xy - ('x) ('y) / √[N'x2 - ('x)2] [N'y2 - ('y)2]
Where:
N = number of pairs of scores
'xy = sum of the products of paired scores
'x = sum of x scores
'y = sum of y scores
'x2 = sum of x scores squared
'y2 = sum of y scores squared
Assume the test is against the null hypothesis: r xy(subscripts) = 0.0. This allows you to determine which table to correctly use when evaluating significance.
Calculate the t value:
t = r√n-2/1-r2(squared)
Where:
r = correlation coefficient
n-2 = degrees of freedom
Using a statistical table for t critical values, find the value of t required to be significant. Use the first column, degrees of freedom or n-2, to find your correct row. Use the heading across the top signifying the percentage of probability you chose earlier to find the correct column. The intersecting box is your critical t value.
Compare your calculated t value to the critical t value. If your calculated value is less than the table value then the null hypothesis -- that there is no relationship in the population -- cannot be rejected. If your calculated value is greater than the critical table value, then you can conclude only a 5% probability that r would occur given no relationship between the two variables in the population.