I am performing a Wilcoxon signed rank test in R, for two paired samples, where I have used the following:
wilcox.test(abs_error_gics, abs_error_sbp, alternative = "two.sided", mu=0, conf.int=T, conf.level = 0.99, paired = TRUE)
wherein I get the following output:
data: abs_error_gics and abs_error_sbp V = 48485000, p-value = 0.00000002249 alternative hypothesis: true location shift is not equal to 0 99 percent confidence interval: 0.00768364 0.02082407 sample estimates: (pseudo)median 0.01426058
Obviously, I can reject the null hypothesis and say that the difference in medians is not zero. However, from the following table:
what I want to report in my result table, is how much larger the median on average is expected to be for GICS, compared to SBP, in the pairwise difference row. However, I am under the impression that this pairwise difference median, CANNOT exceeed the simple difference of medians? i.e. the simple difference from my table is 0.9%. From the R code I posted, I used paired = TRUE, since both GICS and SBP comes from the same underlying data. Doing this, yielded a pseudo-median larger than the simple difference, which should not be possible in my opinion? However, running it again with paired = FALSE, I get a pseudo-median of 0.89% (i.e. smaller than the simple difference). Can someone explain if my thinking is correct, or?
My data can be found here: