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
