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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?

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My choice would be to use regression models for both questions: Ordinal logistic regression for the ordinal variable and "regular" regression for the continuous variable. Group would be an independent variable. This allows you to include control variables (often helpful, even with randomization) and even interactions (should theory dictate any).

It also explicitly treats one variable as the dependent variable and the other as independent; this seems appropriate in your case.

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  • $\begingroup$ Thank you for your rapid response. I tired an ordinal regression but the threshold values on spss seemed to not be that evenly spaced (0.028; 3.9, 5.8). From my basic understanding I was under the impression that this may cause a problem? $\endgroup$ – user49166 Jun 28 '14 at 11:26
  • $\begingroup$ Not necessarily. You need to test the proportional odds assumption (I am not sure how to do this in SPSS). If it is violated, there are alternatives, the easiest to implement is multinomial logistic. $\endgroup$ – Peter Flom Jun 28 '14 at 11:54

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