# Difference between skewed continuous variable and/ or ordinal variable by their binary group allocation

I need to select the most appropriate hypothesis test to answer: "whether there is any difference between variable 1 (ordinal) and/or variable 2 (continuous) by group (binary)". This is a randomised study of just over 500 individuals.

Variable 1 is an ordinal scale of severity for the first event that occurred to each individual (0 = no event, 1 = mild, 2 = severe, 3= extremely severe). The data is positively skewed with 45 % being 0, 52 % being 1, 2% being 2 & <1% being 3.

Variable 2 is the total number of events that each individual experienced over one year (ranges from 0 to 12). 45% of individuals had no event. There is a strong positive skew (0 = 241, 1= 120, 2 = 84, 3 = 33, 4=18, 5= 9...etc until only 2 individuals had 12 events).

The individuals are randomised to one of two groups (placebo vs intervention)

I have so far done two separate Mann-Whitney U tests (one each for variable 1 and variable 2 - each by group i.e.placebo and intervention). I have also used SPSS to calculate Kendall's tau and Spearman's rho correlation coefficients, which are negative. I have little experience of using these but I understand that Spearman's is ok for continuous data such as variable 2 and and Kendall's tau is ok for ordinal data such as variable 1. However I am not sure that it is appropriate to use this correlation to compare variables 1 or 2 with the binary grouping variable?

Does anyone have any suggestions on whether this seems appropriate or is there a better way of doing this?