[R] ANOVA: Does a Between-Subjects Factor belong in the Error Term?

[Peter Dalgaard]

Alex Baugh wrote:
> I am executing a Repeated Measures Analysis of Variance with 1 DV (LOCOMOTOR
> RESPONSE),  2 Within-Subjects Factors (AGE, ACOUSTIC CONDITION), and 1
> Between-Subjects Factor (SEX).
>
> Does anyone know whether the between-subjects factor (SEX) belongs in the
> Error Term of the aov or not? And if it does belong, where in the Error Term
> does it go? The 3 possible scenarios are listed below:
>
>
>
> e.g.,
>
> 1. Omit Sex from the Error Term:
>
>   
>> My.aov = aov(Locomotor.Response~(Age*AcousticCond*Sex) + Error
>>     
> (Subject/(Timepoint*Acx.Cond)), data=locomotor.tab)
>
>   note: Placing SEX outside the double paretheses of the Error Term has the
> same statistical outcome effect as omitting it all together from the Error
> Term (as shown above in #1).
>
>
>
> 2.  Include SEX inside the Error Term (inside Double parentheses):
>
>   
>> My.aov = aov(Locomotor.Response~(Age*AcousticCond*Sex) + Error
>>     
> (Subject/(Timepoint*Acx.Cond+Sex)), data=locomotor.tab)
>
>
>
> 3.  Include SEX inside the Error Term (inside Single parentheses):
>
>
>   
>> My.aov = aov(Locomotor.Response~(Age*AcousticCond*Sex) + Error
>>     
> (Subject/(Timepoint*Acx.Cond)+Sex), data=locomotor.tab)
>
> note: Placing SEX inside the single parentheses (as shown above in #3)
> generates no main effect of Sex. Thus, I'm fairly confident that option #3
> is incorrect.
>
>
>
> Scenarios 1,2, and 3 yield different results in the aov summary.
>
>   
You don't generally want terms with systematic effects to appear as 
error terms also, so 3 is wrong.

In 2 you basically have a random effect of sex within subject, which is 
nonsensical since the subjects presumably have only one sex each. This 
presumably generates an error stratum with 0 DF, which may well be harmless.

That leaves 1 as the likely solution.

You'll probably do yourself a favour if you learn to expand error terms, 
a/b == a + a:b, etc.; that's considerably more constructive than trying 
to think in terms of whether things are inside or outside parentheses.

>
> Thanks for your help!
>
> Alex
>
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