test for not normal data with unequal varience

[#1]

Does anyone can suggest me which test to run for data that are far from normal and variances are not equal. There are 8 treatments (but one treatment does not have data for this particular parameter) and 4 replications in my experiment . This is a field experiment.

[#2]

You have a nonparametric data set, so you need to run a nonparametric test, as you may not be able to use an ANOVA. ANOVA is robust enough to handle deviances from normality and homoskedasticity particularly if the data set is balanced. As you have stated that your data is “far from normal,” so it may be assumed that you cannot use ANOVA.

The Kruskal-Wallis test is what you need to use. See this thread for more information on nonparametric testing.

[#3]

Thank you for your reply. I am a novice with JMP. When I run Wilcoxon test, I got the following output. Level A, B....H are my treatments. I don't know how to interpret my result.Any suggestions will be highly appreciated.

Mean and standard deviations are as follows:

Thanks, Shuresh

[#4]

We all have to start somewhere. I got hit with nonparametric statistics in grad school, so I know how you feel. Operations research masters candidates were required to take a core set of stat courses at my school, but none of us were stat majors and I for one had no statistics background prior to grad school; I actually had to take some entry-level stat courses to get up to speed or risk failing out. Of course, most courses teach statistics as if every data set you will ever encounter will be homoskedastic and normal or near-normal. I am sure that statistics majors get a thorough education in nonparametric statistics, but for the rest of us the response tended to be find a statistician. Of course, when my graduate research required analytics, I was effectively the team statistician so I had to get a crash course on rank sums tests; the project was primarily an engineering/animal science project, but as I was the junior engineer working on an OR degree, all analysis fell to me.

Anyway, you are not running the Wilcoxon Rank Sums test, but instead the Kruskal-Wallis test. The Wilcoxon test is only performed if you have two treatment levels. The Kruskal-Wallis test detected a very significant difference (p < 0.0001), so you need to run pairwise tests if you wish to determine where the differences exist. Please refer to the thread linked in my previous response. You may also want to read up on these tests so that you have a better understanding of how they work.

[#5 · Accepted solution]

Thank you so much for sharing your experience. I am a Ph.D. student in the department of Horticulture, Washington State University at Northwest Research and Extension Center. My Ph.D. project focuses on biodegradable plastic mulches on pumpkin production and quality, as well as mulch biodegradation in the field over time. I am dealing with 6 mulch products. The data set that I am trying to deal with now is percent visual deterioration of mulch measured at every 15 days interval from laying to crop harvest (105 days, 7 - time measurements).

I run pairwise test as you suggested. Now I think I am able to see the differences pairwise.

I highly appreciate your continuous guidance.

Thank you so much. Shuresh

[#6]

For non-parametric data like yours, median tests work well. I particularly like the Mood's Median Test.