# Statistics Dictionary

To see a definition, select a term from the dropdown text box below. The statistics dictionary will display the definition, plus links to related web pages.

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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