two way ANOVA with unequal sample sizes

Hi,

I am trying a two way anova with unequal sample sizes but results are not
as expected:

I take the example from Applied Linear Statistical Models (Neter et al.
pp889-897, 1996)

growth rate		gender	bone development
1.4			1		1
2.4			1		1
2.2			1		1
2.4			1		2
2.1			2		1
1.7			2		1
2.5			2		2
1.8			2		2
2			2		2
0.7			3		1
1.1			3		1
0.5			3		2
0.9			3		2
1.3			3		2

expected results are

source of variation	SS	df	MS	F
gender			0.12	1	0.12	0.74
bone development	4.1897	2	2.0949	12.89**
interaction		0.0754	2	0.377	0.23
Error			1.3	8	0.1625

There's something fairly fundamental wrong here. Gender in your data has
three levels, but your expected results give only 1 df. If you check the
book again you  will find you have the column labels wrong. This isn't
main problem, though.

#In the both cases, results for main effects differ from those expected in
Neter et al.

Yes, but the book clearly warns you that many software packages don't
have the same choices for sums of squares in unbalanced designs that they
have.  R is one of those many packages.

Neter et al, as they carefull explain, present ANOVA tables that summarise
comparisons from a bunch of different models and on page 895 they show all
the sets of models they use to construct their ANOVA table.

	-thomas

Thomas Lumley			Asst. Professor, Biostatistics
tlumley at u.washington.edu	University of Washington, Seattle

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