Re: basic question about anova

On Aug 6, 7:40 pm, Ray Koopman <koop...@xxxxxx> wrote:
On Aug 6, 10:03 am, amorphia <spam.onto...@xxxxxxxxx> wrote:





Hi all,

I have a one-way ANOVA with N=16 for each of two factor levels. The
factor is just significant (p = around 0.04). There is another two-
level factor which I can add, making a balanced 2x2 ANOVA with N=8 in
each cell. This factor was not expected to be a significant predictor
and indeed it is not. However, adding in this second factor has the
effect of slightly increasing the p value for the first factor to
around 0.05.

I'm trying to understand how this can happen. I can think of two
reasons which kind of make sense to me but I'm not sure. Perhaps the
interaction term explains a little bit of the variance that the first
factor was previously explaining? It can't be the second factor,
because it is orthoganal to the first, right?

Or maybe, I wonder, does a two-way ANOVA inherently have a little less
power than a one-way?

Cheers,

Ben

The sum of squares (and hence the mean square) for the first factor
does not change when the analysis is changed from one-way to two-way.

In order for the p-value for the first factor to be the same in the
two-way analysis, the sum of squares for the error term would have
to diminish slightly more than proportionally to its df, so that the
mean square would be slightly smaller than in the one-way analysis,
in order to make up for the slight widening of the F-distribution
with fewer denominator df (28 vs 30).- Hide quoted text -

- Show quoted text -

Thanks Ray!

Cheers,

Ben

.

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