# Re: [R] Nested ANOVA models in R

From: <Bill.Venables_at_csiro.au>
Date: Wed, 6 Feb 2008 14:58:52 +1000

Here is a short example:

```		a = rep(letters[1:4], 5),
b = rep(letters[1:5], each = 4))

> summary(aov(x ~ a*b, dat))

Df  Sum Sq Mean Sq
a            3  0.8021  0.2674
b            4  3.7175  0.9294
a:b         12 10.5416  0.8785

> summary(aov(x ~ a/b, dat))

Df  Sum Sq Mean Sq
a            3  0.8021  0.2674
a:b         16 14.2590  0.8912
```

>

So in your nested case you should not get a mean square for 'Female' at all. The interaction sum of squares in the nested case is the sum of the main effect and interaction in the crossed model case, (as are the degrees of freedom).

Although you think of them as different models, in a mathematical sense they are equivalent - you just parcel the degrees of freedom and SSQ a bit differently in the sequential anova.

Bill Venables
CSIRO Laboratories
PO Box 120, Cleveland, 4163
AUSTRALIA

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Hi,

I'm trying to work through a Nested ANOVA for the following scenario: 20 males were used to fertilize eggs of 4 females per male, so that female is nested within male (80 females used total). Spine length was measured on 11 offspring per family, resulting in 880 measurements on 80 families.

I used the following two commands:

summary(aov(Spinelength ~ Male*Female))

and
summary(aov(Spinelength ~ Male/Female))

I get the same mean squares either way, which doesn't seem right to me. In the former case, the mean square for females should be calculated around the overall mean across all females, whereas the mean square in the latter case should be calculated using deviations from the set of 4 females nested within a given male, right?

Of course, it is more appropriate for me to treat each of these as random effects. I know Bates has objections to the SAS-style partitioning variances to obtain F statistics and p-values, and I have read relevant parts of Pinhero and Bates, but how can a specify a nested random effects model that yields p-values for both the males (tested against MS for females) and females nested within males?

Thanks,

Dan Bolnick
Section of Integrative Biology
University of Texas at Austin

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