Hi!

As a Six Sigma resource, i work for a BPO. I have this question on Non parametric testing. Please consider this case:

When we go in for a parametric testing for equality of means for more than 2 populations, we conduct an ANOVA test to find out whether there is a significant difference amongst them or not. Now, if the null hypothesis gets rejected, we go ahead and conduct Tukeys or Scheffé's method to find out which population is significantly different from the others. While if the data is non normal or discrete, we go ahead with the Non parametric ANOVA (Kruskall-Wallis test or others) what happens if the Null gets rejected here, how do we find out the population with a significantly different measure of central tendency.

Could anybody throw light on this and help me with this?
Thanks in Advance!

Regards,
Prateek

Dear Prateek,

You could look at the average rank reported for each of the populations in a Kruskal-Wallis test to get an idea of the relative comparison between the different populations. You could also do a box-plot of the data to visually look at the "mean & spread" in each population.

If you perform a Mood's Median test, then you can look at the confidence intervals for each population to decide which is different. 

SJ.

It depends on the kind of survey to go to this vigorous level. I always differentiate between a statistical decision and business decision. When you reject a null hypothesis itself you have disapproved the claim made by others. Further what is your interest, you can collect more data and plot as suggested Box-plot or ven histogram to decide on your own.

Still if you want ot be perfect, the moment you say non-normal there are methods to make it normal and then proceed for the testing. Use one of that and there itself you will know the difference for e.g, Use Box-Cox transformation which will give you Lambda values for each of the data to make it normal and from that you could make out clear which Lambda you should trust than the other one.