How to Test for Population Variances

For many statistical procedures, the assumption that the variances of the populations or subdivisions of populations in the study are equal is essential. Therefore, before employing such statistical analyses, statisticians and researchers will test the variances in the population or populations to determine whether the assumption of homogeneity of variances (whether the variances are equal) is valid. This test requires two samples, one from each population or subdivision.

Things You'll Need

  • An F-Table (found is most basic and advanced statistical textbooks)
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Instructions

    • 1

      Calculate the sample variances for the samples from each population separately. Begin with one sample, taking the mean of the data points for that sample. Subtract this mean from all of the data points in the sample. Square the resulting values. Sum these values. Divide the sum by the number of data points in this sample. This is the sample variance for the first sample. Do the same for the second sample.

    • 2

      Divide the larger sample variance by the smaller. Call this value "F." It represents the F-statistic that you will use in the test of homogeneity of variances.

    • 3

      Compute the degrees of freedom for the F-statistic. The F-statistic has two degrees of freedom: "df1," which represents the degrees of freedom for the larger sample variance, and "df2," which represents the degrees of freedom for the smaller sample. Compute df1 by subtracting 1 from the number of data points in the sample with the larger variance. Computer df3 by subtracting 1 from the number of data points in the sample with the smaller variance.

    • 4

      Find the critical value for the F-statistic. Use the F-table in a statistics textbook to find the critical F-value for your calculated df1 and df2. This table will use df1 as the row and df2 as the column. Follow the corresponding row and column along to the number that represents the critical F-value. Call this number "F-crit."

    • 5

      Compare "F" to "F-crit." If "F" is larger than "F-crit," then the result of the test is to reject the hypothesis that the variances are equal. That is, it is unlikely that you have homogeneity of variances and thereby should not use the statistical procedures that rely on this assumption. Otherwise, you are good to go.

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