Which test to use?!


I'm having to use nonparametric methods to analyse some data owing to an abnormal distribution which results from a disprortionate number of zero's in the results. These zero's are extremely meaningful to the point of the study and thus I don't think can be removed or transformed (unless anyone has any other ideas?!) I'm now struggling to know which analysis to perform. Individuals were assigned one of 3 treatments which they were subjected to 4 times over. i.e. a given individual was only ever subjected to one type of treatment. Therefore I don't think that the data are matched - leading to a Friedman test being the option and I'm concerned that if I simply carried out a Kruskal-Wallis they'd be issues of pseudoreplication. Is there a way of sorting this problem?! I'd be very grateful for any advice as I am new to statistics!


TS Contributor
Maybe if we understood why the individuals were subjected to the treatment 4 times we could help point you in the right direction. If you could simply take the average of the 4, then the analysis would be very easy (Kruskal-Wallis). However, if the variation between observations is important, then maybe Friedman's test is the way to go.
Hi John,

Many thanks for your reply. The original reason for replicating with an individual was to examine the idea of individual variability, i.e. whether a given individual would always respond in the same way to a given treatment. Time constraints meant that this was only feasible 4 times over. I'm a bit concerned now because what I'm reading statistics wise seems to suggest that I can't use Freidman because the data are not matched - i.e. a given individual did not experience all 3 treatments. Is this right or could I still use it? Hope this makes sense!
Many thanks, Rachel.


TS Contributor
I'm quite the pragmatist when it comes to deciding between parametric and nonparametric, and notions of normality and violations of the ANOVA assumptions. I think it's best to try a couple of different methods if you're concerned about normality, but then couple the data analysis with what you know about your field of study...

I'm inclined to recommend computing the average for each person and then do a Kruskal-Wallis (rank the averages) and one-way ANOVA on the averages - see if you get similar results.

Then take the variance of each person and use that in a one-way ANOVA. If you want, go ahead and rank the variances and do a KW - see what you get.

Also, I would create a plot showing each person and to see if their scores systematically increase / decrease with each subsequent treatment.
Hi John,

Thanks for that - I've now tried the ANOVA and KW on the averages of the 4 repeats and in both get highly significant differences (Tukey and Nemenyi test show that they lie between each of the treatments still - so that's cool!) Would you agree then that the Freidman test is out of the qustion as a result of the experimental design?

Thanks very much for your time.