[Lign251] HW4: Q3 c-ii

[Alex Del Giudice]

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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