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I've got a mixture of parametric and non-parametric data, with a repeated measures design; measuring animal behaviour in three different treatments. For parametric data, it's simple enough calculating mean difference and 95% confidence intervals. I also want to do the same for the medians of non-parametric data.

For non-parametric data, when looking at differences between treatments I have used Wilcoxon matched-pair signed rank tests. My question is, is there a way to calculate median differences between two treatments +95% confidence intervals for the difference? If not, I've read this page - would the method suggested by Pallant, J. (2007) be a suitable alternative?

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    $\begingroup$ Since you are using SPSS, you may be able to perform quantile regression. With quantile regression at the 50th percentile, you can estimate the median difference and obtain a confidence interval for this difference. $\endgroup$ – Heteroskedastic Jim Jul 27 '18 at 10:57
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First, note that there are no parametric vs. nonparametric data, only parametric vs. nonparametric tests. The distinction relates to the assumptions a test makes on the distribution of the test statistics.

Yes, you can calculate median differences, and you can also calculate confidence intervals for this median. CIs are a Good Thing. CIs for the median are less common and a bit harder to calculate than CIs for the mean. Here Aksakal links to an introduction., However, it's probably easier just to bootstrap it.

The method suggested by Pallant (2007) in the thread you link to is an effect size, not a confidence interval. This can also be informative; in particular, you can compare it between studies. It's just not a CI, and it gives other information than a CI. Use whatever information you want to convey, perhaps even both measures.

(Or do you want a CI for Pollard's effect size? Bootstrap it. When it doubt, bootstrap!)

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  • $\begingroup$ Thanks for the corrections to terminology - I'm new to stats! With confidence intervals for the medians, how would you then use these to calculate the confidence interval of the median difference between the two though? And with effect size, in my mind I thought an unstandardised effect size could be e.g. median/mean differences, whereas the method by Pallant would be a standardised effect size statistic? $\endgroup$ – Bobneedshelp Jul 26 '18 at 16:09
  • $\begingroup$ (1) No, don't calculate CIs for the group medians - take the treatment effects, calculate the median of that, and calculate the CI of that median (e.g., by bootstrapping). (2) Yes, the Pallant proposal is standardized. It's an analogue of Cohen's d. Which makes sense for comparability. $\endgroup$ – Stephan Kolassa Jul 26 '18 at 16:19
  • $\begingroup$ So, using SPSS, I would make a new column of e.g. difference between treatment 1 and 2. Then, use bootstrapping to calculate the median + CIs of this? $\endgroup$ – Bobneedshelp Jul 29 '18 at 13:16
  • $\begingroup$ That's exactly what you want to do. Good luck! $\endgroup$ – Stephan Kolassa Jul 29 '18 at 20:15

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