Hi
I'm analysing data coming from a QoL scale where lower scores indicate better quality of life.
As the data in the pre and post intervention reviews is not normally distributed, I've used a Wilcoxon Signed Ranks Test for 2 related samples.
The sample size is not tiny but not very large either (n=51); there is a clear difference in the rankings, with the sum of ranks for negative ranks (which in this case indicate improved QoL) being higher than the sum for positive ranks (598.50 vs 262.50), Z=-2.188 and the p value =.029.
However there is no change in the median values (12 at pre and post).
Would it make sense to report only on the ranks and not the median? Or reporting the median change by ranks (negative, positve, ties)? I'm getting a tad confused.
It is not a test of equality of medians (or more specifically that the median gain score is zero). If you want to test that one option is the sign test on the gain scores. Do you have a scatter plot of post with pre? Also, since you are assuming interval data, which may be fine, it will be worth seeing if the gains are more at one end of the pre-scores.
The sums of ranks aren't always very helpful for the reader because they depend on the sample size of the data analyzed, and aren't in the same units as the original data.
One simple way to express the change in values is to present the median of the differences in scores. Or a five-number summary of these differences. Or a histogram of these differences:
https://rcompanion.org/handbook/images/image064.png
A helpful plot is a bivariate plot of Before and After, with a one-to-one line superimposed. Here, points above and to the left of the line indicate an observation where the value increased.
https://rcompanion.org/handbook/images/image062.png
You could also calculate the number of observations that increased, decreased, or were tied, and express this as a proportion of the total observations.
Another effect size statistic is the matched-pairs rank biserial correlation coefficient. This is a standardized effect size measurement and matches the signed rank test. See: King, B.M., P.J. Rosopa, E.W. and Minium. 2000. Statistical Reasoning in the Behavioral Sciences, 6th. Wiley.
As an additional comment: Note that the signed rank test works only with a single vector of the differences between the paired observations. The first step in the test procedure is to take these differences. So the test doesn't look at the before and after data per se except to take these differences.
That being said, there's no reason why you can't present summary statistics for each of before and after.
Grazie Sal Mangiafico - I hadn't thought of looking at the median of the differences. What I was looking at yesterday was to visualise the median score for negative ranks, positive ranks and ties and show the difference (but that becomes a difference between the median of a subgroup, rather than the median of the differences).
I'll work a bit more on that today (I wouldn't go for scatter plots simply because I need to make a report in as plain English as possible). Thanks
You might look at the distribution of the differences in QoL scores. It might make sense to report the mean decrease in scores. e.g. "The average change in scores was a 13 point decrease."
It also might make sense to report e.g. "25% of scores decreased between 0 and 10 points, 20% decreased between 11 and 20 points, ...., 10% neither increased nor increased, and 15% increased (with a range of 1 to 12 points)." This would make an simple table.
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