How to Calculate the Significance of a Correlation Coefficient

A correlation coefficient, r, is a number between -1 and +1 that indicates an idea of the strength or degree of a relationship between two variables. -1 is a perfectly negative correlation, 0 is no correlation at all and +1 is a perfectly positive correlation. However, the coefficient of determination -- r2(squared) -- is what best measures the strength of the relationship. This strength is usually expressed in given probability levels, p, such as .05. As Janda.org notes, "this tells how unlikely a given correlation coefficient, r, will occur given no relationship in the population."

Things You'll Need

  • Calculator (statistical model preferred)
  • Level of significance to be tested
  • Critical value table for t, one and two-tailed
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Instructions

    • 1

      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

    • 2

      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.

    • 3

      Calculate the t value:

      t = r√n-2/1-r2(squared)

      Where:

      r = correlation coefficient

      n-2 = degrees of freedom

    • 4

      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.

    • 5

      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.

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