1
$\begingroup$

I'm looking into comparing charge/cost (economics) data among paired samples (i.e pre vs post). The sample size is about ~150 paired samples, where charge/cost is highly skewed with a long tail.

I'm concerned about using a paired t-test as it violates the assumption of normality, and I've been looking into using the coin package in r for its implementation of the fisher-pitman permutation test. Upon doing some research, I've also read about possibly doing a bootstrapped hypothesis test? Would a wilcoxon signed rank test be appropriate in this case? What would be most appropriate in this situation?

$\endgroup$
1
$\begingroup$

Wilcoxon is indicated for what you describe.

[Edit] as @greenparker said this needs some explaining.

t-test assumes equal standard deviation and that a fitted normal describes the data.

If those assumptions are not suitable, or at least, if a plot shows that can be a very bad assumption, then use a method that does not make the assumptions or transform the data (e.g. applying logs)

Wilcoxon is the distribution-free version of t-test for paired data.

$\endgroup$
  • $\begingroup$ According to Wikipedia in German and in Catalan, Wilcoxon test assumes symmetrical distribution. Answers to stats.stackexchange.com/questions/14434/… give somehow conflicting statements about it. Therefore, is skewness a problem for Wilcoxon text? If it were, it would be less suitable for this question. $\endgroup$ – Pere Jul 29 '16 at 12:19
  • $\begingroup$ I agree with commenting and discussing details but it seems that Wikipedia is not a right source. My stats professor edited Wikipedia adding intentional errors to make us thinking about what can be a "correct" or a "bad" solution. Please check this from Northwestern University basic.northwestern.edu/statguidefiles/… $\endgroup$ – pachamaltese Jul 29 '16 at 20:41
0
$\begingroup$

If you just want to compare the means, the t-test can be used since it is robust to departures of normality. See my previous answer: Hypothesis testing options on non-normal populations

Alternatively, you can compare them using nonparametric approaches such as the one proposed here, where the authors calculate $P(X<Y)$ for paired observations in order to assess discrepancies between $X$ and $Y$. Alternative parametric approaches using skewed dependent distributions have also been studied here

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.