# Paired Wilcoxon signed rank test-compare median

I have been comparing driving behavior before and after a technological intervention for a specific group of people. My data is far from normal hence I have used paired Wilcoxon signed rank test.

If for a specific demographic (such as female), before Median value is 0.5 and after median value is 0.3 and the change is significant at 0.05 level, can I also say that there was 40% decrease in that behavior?

• What is your sample size per group? What is the dependent variable of interest? How is it measured. In general, wilcoxon signed rank doesn’t compare medians. More strict assumptions are required to make this comparison. – LSC Mar 14 at 16:13
• The dependent variable is harsh braking per mile. I have over 30 respondents in all groups. I understand that the Wilcoxon test concludes a significant decrease in the event. But can't I make a statement (without mentioning the significance level) that the data says 40% decrease in harsh events based on median value? – Msilvy Mar 14 at 21:56
• The test is generally used more so to make a claim of different distributions. Unless you know that the distributions are identical in every way except for the median, you wouldn't be able to claim that there is a difference in medians. Hence, the more general claim that the distributions are different in some way is more general but accurate. – LSC Mar 14 at 22:18
• Is there a way to quantify the change with a percent value? – Msilvy Mar 14 at 22:22
• The best way to report the results is to be as precise as possible. That is, I would use the word "median" if I'm looking at the median. Just saying "a 40% decrease" might be misleading, for example, because the percent change might be very different if you were looking at the mean, or maximum, or trimmed mean, or whatever other summary statistic. The reader would probably interpret "40% decrease" as a decrease overall, like maybe the total number of incidents, whereas you are looking at rates. For this reason, also, I would include the units when stating results. – Sal Mangiafico Mar 30 at 14:21