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Meaning of ANOVA Sum of Squares Values


Summary Table for ANOVA
Source DF SS MS F
Between Groups 2 943,6 471,8 0,986
Within Groups 12 5744,00 478,66667
Total 14 6687,6

Calculation Scheme:

  • Calculate standard deviation for all observations.
  • Calculate the Standard Deviation for each group of subjects
    • Convert the SD of each group to a SS.
    • Add the group SS's together to get Within Groups SS
    • DF is one less than the number of groups of subjects.
  • Subtract Within Groups SS from Total SS to get Between Groups SS
    • DF is the difference in DF for Total SS less DF for the Within Groups SS
  • Mean Square (MS) is a SS divided by its DF.
  • The value of F is the MS Between Groups divided by MS Within Groups

Snapshot of the datum_by_datum calculation of an ANOVA

Each picture is a snapshot of the way the RippleSoftware tool "Teaching Statistics" shows the meaning of the ANOVA Sum of Squares

Calculation of the Total Sum of Squares

To determine the Total SS in an ANOVA: (1) find the mean of all the scores; (2) find the deviation of each of the scores from the overall mean; (3) square each of the deviation scores; and (4) add them up.

Calculation of the Within Groups Sum of Squares

To determine the Within Groups SS in an ANOVA: (1) for each level of the independent variable, find the group mean; (2) find the deviation of each of the scores in a group from that group's mean; (3) square each of the deviation scores; and (4) add them up.

Calculation of the Between Groups Sum of Squares

To determine the Between Groups SS in an ANOVA: (1) find the mean of all the scores; (2) find the mean of each of the groups; (3) calculate the difference between each of the group means and the overall mean; (3) write down each of the group-mean-deviations the same number of times as there were subjects in the group; (4) square the deviations and then add up the squared deviations.


Calculating the Sum of Squares from a Standard Deviation.


©2004-2006 by Burrton Woodruff. All rights reserved. Modified 9/26/06