Statistics Dictionary

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Mean Square

A mean square is an estimate of population variance. It is computed by dividing a sum of squares (SS) by its corresponding degrees of freedom (df), as shown below:

MS = SS / df

The term "mean square" is probably used most often in analysis of variance. For example, in one-way analysis of variance, we are interested in two mean squares:

  • Within-groups mean square. The within-groups mean square ( MSWG ) refers to variation due to differences among experimental units within the same group. It can be computed as follows:

    MSWG = SSW / dfWG

  • Between groups mean square. The between-groups mean square ( MSBG ) refers to variation due to differences among experimental units within the same group plus variation due to treatment effects. It can be computed as follows:

    MSBG = SSB / dfBG

See also:  One-Way Analysis of Variance