How to Find the Variance in an ANOVA Test

When performing an Analysis of Variance (ANOVA) test, there is a load of information that you must handle. Among this large set of information are important variance statistics. In total, there are three variances in an ANOVA test, represented by the terms SSB, SSW and SST. These terms stand for the sum of squares between groups, the sum of squares within groups and the sum of squares total, respectively. You can calculate all of these variances directly from the summary statistics in an ANOVA test.

Instructions

  1. SST

    • 1

      Calculate the total of your data points. Sum all the data points in the study together. Call this value "T."

    • 2

      Count the number of data points in the study. Call this number "N."

    • 3

      Calculate the mean correction. The calculation for the mean correction is to square "T" and divide by "N." Call the mean correction "C."

    • 4

      Compute the total of squared data points. Square all the data points in your study. Then add all of the squared data points together to arrive at a total. Call this total "T2."

    • 5

      Find SST. SST is found by subtracting "C" from "T2."

    SSB

    • 6

      Sum the data points for each group in your study separately. Label the sums as "x1, x2, ..." for as many groups as are in your study.

    • 7

      Square the sums. Go back to the numbers you just found and square them separately. Label the results "sx1, sx2, ..." for all the groups in your study.

    • 8

      Find the number of data points in each group separately. Label these numbers "n1, n2, ..." for all the groups.

    • 9

      Calculate SSB. Divide each "sx" value by its corresponding "n" value. Sum all of the resulting numbers and subtract the mean correction, "C," from the final result.

    SSW

    • 10

      Find SST. Use the method described in the section for SST.

    • 11

      Find SSB. Use the method described in the section for SSB.

    • 12

      Calculate SSW. Subtract SSB from SST.

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