I am comparing length of stay after laparoscopic and open appendectomy in over 160000 patients. LOS is typically a skewed variable so I use the median and interquartile range and ranksum test to describe the result, which is 2, IQR 2-3 and 2, IQR 2-4, p<0.0001. So there is a highly significant difference but it does not show that well in the median and IQR.
The difference in length of stay is very small. This finding is a negative finding but still interesting as it goes against what most people think about LOS after laparoscopic appendectomy. That is why I want to report on the difference in LOS which is not evident if I only report median and IQR with p-value.
The arithmetic mean (3.1 vs 2.8 and a difference of 0.3 days) is not recommended as the distribution is skewed. I wonder if any other measure could be used like, geometric mean (2.5 vs 2.3, difference 0.2 days) or harmonic mean (2.1 vs 1.9 days, difference 0.2 days)? When can I use geometric mean or harmonic mean?
I am inclined to use the harmonic mean which comes closest to the median and gives a difference of 0.2 days. Is this incorrect?