Re: interpretting F & t-vals from regression

Rob Campbell wrote:
Hi,

I think this probably a silly question but I've been confused about this for
a while.

I fit a linear model in R and obtain an ANOVA table with the anova command.
*All the factors explain a significant proportion of the variance according
to the table. *
So I want to see what the coefficients are for one of my factors and whether
or not they are significant. I therefore use the summary command. This
shows me values for the coefficients, which look sensible and I can
understand them, and their associated t-values and p-values. Now, say
factor X was significant in the ANOVA table but when I look at the
coefficients for the levels of X it turns out that none of them are
significantly different from 0. Factor X seems to explain a significant
proportion of the variance in the data but coefficients, which are the
interpretable bit, show no significance. Does that make sense? Is this
situation fairly common?

You say you are testing for differences from zero. However, it is the pairwise comparisons among the levels of your factors (k) that is tested by the F test. The number of comparisons is actually: k(k-1)/2. If I have a factor with 4 levels, then I have 6 possible comparisons.

For example, if the mean of one level is above zero and that of another is below zero, it is easy to see how differences from zero could be rejected, though a significant difference could exist.

It all depends on how your contrasts are coded in R. I think the default for linear models is treatment coding, so one of your factor levels is a reference category, and all of the tests represent differences from that one group. There may also be interactions among your factors.
.

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