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Howell (1992) pp 410-417 and 542-549 illustrates and recommends the use of the (default) type III sums of squares for looking at sources of variation in an anova where the group sizes differ. This is ''provided the differences in group sizes are independent of the groups''. Howell (1992) pp 410-417 and 542-549 illustrates and recommends the use of the (default) type III sums of squares (termed Method I by Howell) for looking at sources of variation in an anova where the group sizes differ. This is ''provided the differences in group sizes are independent of the groups''.
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The computations for these may be done using either a least squares approach based upon formulating the anova in terms of a linear regression or by using the formulae associated with equal groups as given, for example, [:FAQ/ss here] but replacing the sample sizes of form $$n_text{ijkl}$$ with the harmonic mean of the sample sizes. The computations for these may be done using either a least squares approach based upon formulating the anova in terms of a linear regression or by using the formulae associated with equal groups as given, for example, [:FAQ/ss: here] but replacing the sample sizes of form $$n_text{ijkl}$$ with the harmonic mean of the sample sizes.
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Using type III sums of squares in an anova gives an ''unweighted'' means analysis or more revealingly an ''equally weighted'' means analysis of group means because group means are treated equally irrespective of the size of sample upon which they are based. Using type III sums of squares in an anova gives an ''unweighted'' means analysis or more revealingly called an ''equally weighted'' means analysis of group means because group means are treated equally irrespective of the size of sample upon which they are based.

__Reference__

Howell DC (1992) Statistical Methods for Psychology. Third Edition. Duxbury Press:Belmont, CA.
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  • = A word about unequal group sizes in ANOVA =

Howell (1992) pp 410-417 and 542-549 illustrates and recommends the use of the (default) type III sums of squares (termed Method I by Howell) for looking at sources of variation in an anova where the group sizes differ. This is provided the differences in group sizes are independent of the groups.

The computations for these may be done using either a least squares approach based upon formulating the anova in terms of a linear regression or by using the formulae associated with equal groups as given, for example, [:FAQ/ss: here] but replacing the sample sizes of form $$n_text{ijkl}$$ with the harmonic mean of the sample sizes.

Using type III sums of squares in an anova gives an unweighted means analysis or more revealingly called an equally weighted means analysis of group means because group means are treated equally irrespective of the size of sample upon which they are based.

Reference

Howell DC (1992) Statistical Methods for Psychology. Third Edition. Duxbury Press:Belmont, CA.

None: FAQ/wmeans (last edited 2014-04-30 13:49:02 by PeterWatson)