[R] Asking, are simple effects different from 0

[Chuck Cleland]

On 3/5/2008 3:19 PM, jebyrnes wrote:
> Indeed, but are not each of the cell means also evaluations of the effect of
> one factor at the specific level of another factor?  Is this an issue of
> "Tomato, tomahto".

   I don't think it is "tomato, tomahto".  Say the grand mean is around 
100 and the within cell standard deviations are around 10.  You could 
easily have a situation in which all of the cell means are significantly 
different from 0, but there is nothing at all interesting going on with 
the two explanatory factors.  In other words, the cell means can be very 
different from 0 with no explanatory variable effects of any kind, based 
only on the overall location of the response.

> I guess my question is, if I want to know if each of those is different from
> 0, then should I use the 48df from the full model, or the 9 for each cell?

> Chuck Cleland wrote:
>>    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, Ph.D.
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