I have multiple paired t$t$-tests, such as one giving results:
t(14)=2.7, p=.017$t_{14} = 2.7,\ p = .017$
althoughAlthough people seem to do effect sizes in different ways in repeated samples, I have taken the mean difference divided by the standard deviation of the differences (I'll call this d$d$, though maybe I should call it something else?) and get 0.70$0.70$. I also have a very strong correlation between the samples, not sure if that is problematic.
I would like to put confidence limits around my effect size estimate. To do so, I randomly resample from the difference scores, compute d$d$ in the same way and repeat 1000 times. My question is whether this is a good approach, rather than, say, just giving confidence limits around the unstandardised difference or resampling from the original samples. My bootstrap gives me a mean d$d$ of 0.79$0.79$ with confidence limits of [0.4, 1.4]$[0.4, 1.4]$. I've tried this on other random data too. Why am I getting a consistently higher d$d$ from bootstrapping, and why are the intervals asymmetric? Is this because of skew in the (difference) scores, and does this make this approach more or less robust?
Thanks!
Edit: here is an example of the data involved. 15 people were sampled atmeasured two times.
TimeA: 1999 1501 1552 2385 2488 1257 1806 1348 2048 1810 1308 2310 1247 1839 1235
MeanAMean A = 1742; SD = 435
TimeB:
2040
1601
1623
2386
2671
1218
1719
1405
2079
2017
1356
2324
1616
1878
1370
MeanBMean B = 1820; SD = 426
Mean
Mean difference = 78, SD of differences = 111, d$d$ = 0.70
A B
1999 2040
1501 1601
1552 1623
2385 2386
2488 2671
1257 1218
1806 1719
1348 1405
2048 2079
1810 2017
1308 1356
2310 2324
1247 1616
1839 1878
1235 1370