[R] Asking, are simple effects different from 0

[Chuck Cleland]

On 3/5/2008 1:32 PM, jebyrnes wrote:
> Ah.  I see.  So, if I want to test to see whether each simple effect is
> different from 0, I would do something like the following:
> 
> cm2 <- rbind( 
> "A:L" =  c(1, 0, 0, 0, 0, 0), 
> "A:M" = c(1, 1, 0, 0, 0, 0), 
> "A:H" = c(1, 0, 1, 0, 0, 0), 
> "B:L" =   c(1, 0, 0, 1, 0, 0), 
> "B:M" = c(1, 1, 0, 1, 1, 0), 
> "B:H" = c(1, 0, 1, 1, 0, 1))

   That does not corresponds to what I think of as the simple effects. 
That specifies the six cell means, but it does not *compare* any cell 
means.  I think of a simple effect as the effect of one factor at a 
specific level of some other factor.

> summary(glht(fm, linfct = cm2), test = adjusted(type="none")) 
> 
> Correct? What is the df on those t-tests then?  Is it 48?

   Yes, df = 48 for each contrast.

> Interestingly, I find this produces results no different than
> 
> fm2<-lm(breaks ~ tension:wool+0, data=warpbreaks) 
> summary(fm2)

   Yes, but those are not what I would call the simple effects.  Those 
are essentially one-sample t-tests for each of the 6 cell means.

> Also, here, it would seem each t-test was done with the full 48df.  Hrm.

   The df are based on the whole model, not the 9 observations in one cell.

> Chuck Cleland wrote:
>>
>>    Each column corresponds to one of the coefficients in the model, and 
>> each row specifies a particular contrast.  The numbers in the matrix 
>> indicate how the model coefficients are combined to indicate a 
>> particular difference in means.
>>    For example, the first row indicates that the third coefficient 
>> (woolB) is multiplied by -1.  The baseline categories are A and L for 
>> the wool and tension factors, so the woolB effect in fm is the simple 
>> effect of B vs. A in the baseline category of the tension factor. 
>> Multiplying this coefficient by -1 produces an A vs. B comparison in the 
>> baseline category of the tension factor. 

-- 
Chuck Cleland, Ph.D.
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