[Lign251] HW4: Q3 c-ii

[Roger Levy]

Hi Alex,

Yes, I think you're on the right track -- and doing this kind of 
simulation is a perfectly good way to sharpen your intuitions!

The other kind of simulation that could be useful is to generate pairs 
of vectors from underlyingly correlated distributions, and compare the 
results of paired versus unpaired t-tests.

Good work!

Roger

Alex Del Giudice wrote:
> After careful thought I think I'm capable now of answering my own 
> question (hopefully correctly and without totally giving away the 
> answer... which may be completely wrong)
> 
> A high correlation does have implications for the variance of data which 
> can be captured by one type of t-test but not the other.
> 
> Is this right?
> 
> (I hope the following isn't cheating wrt developing intuitions), but the 
> following bit of code was the first step to jarring my brain into a new 
> intuition mode (and making me realize that the intuitions I had in my 
> previous e-mail were totally incorrect):
> 
> corrs = NULL
> pvalues = NULL
> for (x in 1:1000){
> pop1 = rnorm(10,0,1)
> pop2 = rnorm(10,1,1)
> pvalues[x]=(t.test(pop1,pop2,paired=T)$p.value)-(t.test(pop1,pop2,paired=F)$p.value)
> corrs[x]= cor.test(pop1,pop2)$estimate[[1]]
> }
> plot(corrs,pvalues)
> corpval <- lm(pvalues ~ corrs)
> abline(corpval)
> 
> Alex
> 
> 
> Alex Del Giudice wrote:
>> I'm having a hard time coming up with any intuitions regarding 
>> correlations and the statistical power of paired/unpaired t-tests.
>>
>> I think this is because it seems to me that you can hold one constant 
>> and vary the others wildly (e.g. invent pairs of data sets that 
>> correlate very well but have drastically different results for p values 
>> of paired and unpaired t-tests - which is something I think I've done 
>> with the help of R).
>>
>> Can anyone maybe give me a hint which may lead me to better intuitions?
>>
>> Alex
>>
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-- 

Roger Levy                      Email: rlevy at ucsd.edu
Assistant Professor             Phone: 858-534-7219
Department of Linguistics       Fax:   858-534-4789
UC San Diego                    Web:   http://ling.ucsd.edu/~rlevy