[R] cross-over designs

[Peter Dalgaard]

Peter Dalgaard wrote:
> Data Analytics Corp. wrote:
>> Hi,
>>
>> I have a dataset from a client where the data is from a cross-over
>> design.  Basically, each subject in a survey was asked to rate two
>> products, A and B.  The subject sampled A first and then after an
>> appropriate wash-out period he/she sampled B.  The next subject did the
>> same, but in a different order.  How can I do an ANOVA analysis on a
>> cross-over design with only two treatments.  This is also a balanced design
>>
>> Thanks,
>>
>> Walt
>>
> 
> The hard bit is often to knock data into the right format. Assuming that
> you have a data in a data frame "mydata" in long format like this
> 
> ID product period score
> 1 A 1 2,3
> 1 B 2 3.4
> ....
> 10 B 1 5.6
> 10 A 2 7.8
> 
> then this should do the trick:
> 
> summary(aov(score~A*B+Error(ID),data=mydata))

Oops, make that product*period, not A*B.

And make sure that ID, product, and period are factors.


> Alternatively, you can do it with t-tests comparing differences within
> ID between the two product orderings. The test for main effect of
> product can be obtained as a test of whether "1st - 2nd" depends on
> whether A or B came first, and vice-versa for the main effect of period.
>  The interaction test (carry-over, etc.) is obtained as a test of
> whether the _sum_ of the two scores is order-dependent.
> 
> (Cynics may point out that it is usually no great loss just to do a
> paired t-test, since period effects are usually weak and interactions
> mostly undetectable in such designs.)
> 


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