Comparison between bootstrap percentiles confidence interval and BCa confidence interval? I have generated a nonparametric percentiles bootstrap confidence interval ($32.27143, 51.08571$), and a BCA confidence interval ($33.26, 53.49$) with an initial sample size of $n=7$.  Evidently, the BCA interval is larger than the percentiles interval. Shouldn't the BCA interval be better than the percentiles interval (and by "better" I mean "smaller")? I noticed also that when the sample size is larger, for example $n=40$, BCa confidence interval decreases. 
 A: Before using standard bootstrap methods, the data should be tested for bias and skewness beforehand and if they exist, "tricks" should be used to transform the data to correct for this. BCa (bias-corrected and accelerated) bootstrap by Elfron (1987) takes care of these tricks for you.
So, if you have a distribution that has skew and/or bias, you would be able to calculate the true confidence interval. If you randomly drew samples from this distribution and then estimated the confidence interval using the percentile method and the BCa method, the BCa method will tend to be closer to the true confidence interval than the percentile method. The percentile method may worse by underestimating or overestimating the confidence interval. What really matters (although maybe not in the experimenter's mind) is how close the estimate is to the true confidence interval.
As mentioned by @phaneron, you should not simply pick the method that gives you the smaller confidence interval. Doing this would systematically underestimate the confidence interval and make the results invalid.
