# Wilcoxon Signed Rank vs Bootstrapping for Skewed Cost Data

I'm currently looking at non parametric cost data (highly skewed to the right), and I'm trying to compare cost data pre and post intervention.

Traditionally I've been taught that due to the non parametric nature of the data, the traditional t-test would not be feasible, as it violates the assumption of normality. A non parametric test would be recommended such as the Wilcoxon's Signed Rank test (due to the paired nature of my data).

I've also recently heard about using bootstrapping as a method to compare cost data, however most of what I have read involved bootstrapping confidence intervals.

Can anyone shed some light on which is the prefer method in comparing skewed cost data, and methodology on using bootstrapping for hypothesis testing. I'm currently using R and is reading up on the boot package.

Thank you

• Data are neither parametric nor nonparametric; those are adjectives that apply to models or techniques. If you mean "not normally distributed" that's not at all the same thing as "nonparametric" and similarly "parametric" is not at all the same thing as "normally distributed" -- one can fit parametric non-normal models and correspondingly, one can happily use nonparametric procedures on data drawn from normal distributions. Please amend your post to more clearly express the actual situation. Jun 16, 2016 at 23:24

If you want to find out, whether costs are increased or decreased, use a signed-rank-test. The latter is well established, any reader knows it and you don't have to argue how many samples you took and why you decided to use parametric or non-parametric bootstrap and so on. The t-test is probably the most used single test and normality assumptions become less and less important the more the sample number increases. It is advantageous if you want to compare means as more recipients know about the mean than rank sums. Also, power analysis, if needed, is easier with the t-test.

Bootstrapping is great for confidence intervals and if you want to compute some self-made statistic instead of a standard like the mean or the rank sum. It is more complicated and you have more researcher's degrees of freedom, thus more to report, which will distract your readers from the content. If there is a simple and well established method, don't do complicated things. If not, bootstrapping is great to tailor make a test/statistic for your special needs.