# How to test group difference between nominal and ratio data with nonparametric tests?

In my data the dependent variable ‘vocabulary uptake’ is measured as scores ranging from 0-10 and the independent variable is yielded from a ‘reading intervention’ with 4 different reading conditions (glossed, no glosses, etc.). There are about 80 participants in each of the four groups. The data is not normally distributed (I tried to transform the data). Given the fact that there is a natural limit (0), this is probably not surprising. I want to find out what the best way is to determine whether these groups are different or not.

My questions:

1. I am sure that the independent is a ‘nominal’ variable, but I am in doubt about the dependent – I cannot decide whether to treat it as ‘ratio’ data or as ‘ordinal’. The latter would make sense, as the scores can be ranked, but ‘discrete ratio’ makes sense as the values are measured, have numerical value, the difference between, e.g. 1 and 2 is the same as between 3 and 4, and a score of 0 means that there is none of that variable. ‘Ordinal’ data would be easy, but if I categorize the data as ‘discrete ratio’, my problem is that – to my knowledge – the standard nonparametric tests only work with continuous data. What can I do?

2. What test + post-hoc test could I use to find out if there are significant differences between the groups? When working with a nominal dep. and a discrete ratio data indep. variable I would violate the assumptions for most nonparametric standard tests, which assume dichotomous independents and continuous/ordinal dep. variables (Mann-Whitney U, Wilcoxon) or categorical data for the independent variable and continuous/ordinal data for the independent variable (Kruskal-Wallis, Friedman’s test). Also there is a problem with tied values.

I am working with SPSS.

Thanks for any suggestions! Your help would be GREATLY appreciated!

• the standard nonparametric tests only work with continuous data If by nonparametric tests here you mean rank-based tests, they are applicable to both continuous and ordinal data. Recent SPSS versions' "new" nonparametric tests procedure somewhat unresonably demands the analysed variable to be only 'scale level' (at least via menu). Well then, you may safely type your variable as scale rather than ordinal since they "want" so, it will make no difference regarding the results. – ttnphns May 14 '13 at 15:56
• Thanks a lot, ttnphns! Yes, I was referring to rank-based tests. As you wrote, these are applicable to continuous and ordinal data, but my data is neither, I think. The test scores are 0, 1, 2, ... 10, i.e. not continuous. I am worried if any test would still work if my data violate this demand. Any thoughts??? Thanks again. – user25630 May 15 '13 at 9:11
• By "continuous" I meant more generally "scale" = "metric" = "interval or ratio". It can be discrete (after all, any collected data is always more or less discrete) – ttnphns May 15 '13 at 9:17
• And thanks again, ttnphns. I think I will try using a Mann Whitney U test. – user25630 May 16 '13 at 11:45