I'm doing research on a pest insects and I want to see which leaf of a crop they like te most. Each plant has 8 leaves and I counted the insects on each leaf of 172 different plants. (a lot of these leaves had 0 insects on them)
I now want to see if there is a significant difference between the amount of insects feeding on the different leaves AND I want to see between which leaves these differences are found.
I was thinking about simply ANOVA but my results aren't normally distributed.
You said your sample is not normally distributed. Fine! Check, do you at least 30 sample size in each of the comparison groups? If yes, then you can go ahead with ANOVA even if the overall sample is not normally distributed.
IF otherwise, then use non-parametric test (Kruskal Wallis test)
Hope this helps.
In my opinion you must use the plant as a plot, and not the leaf. In this way you can analyze the average of insects per leaf in each plant. This data will be better behaved and, probably, better adherent to the assumptions of the analysis of variance (central limit theorem can be applied in this case).
Other problem resolved in this approach is the relation between the number of insects in the leaves of the same plant. In example, 0 insect in one leaf can be explained by a lot of insects in one softer adjacent leaf.
Remember to test the adherence of the error to the gaussian distribution and you can solve problems trying to adjust a model that do not assumes normal distribution using a generalized linear mixed model or in a older method, try to transform the data using, in example, the box-cox method.
Count data -> count model.
I suggest a negative binomial or a zero-inflated Poisson model.
It might be interesting to see if the insects clump (more than expeced under the assumption of an independent distribution). Another possibly interesting aspect or covariable is the size of the leafs.
I agree both with Marcelo and Jochen. Your data are clustered by each plant. Forgetting the within plant variability you can average the number of insects per leaf but you loose then some information. The best is to carry out a GLM with Poisson or BN model.
If leafs are scaled on the plants you should treat them as a stratum, (fixed effect) if they are taken randomly in each plant, it must be treated as a random effect.
Dear Dr. Verlinden, The scientists above have each their solution. Mine opinion is that the best (because permitting to use your quantitative data that you obtained, without tranforming them into a Poisson or a binomial negative distribution) should be to use non-parametric multiple statitic. Try the test of Krukal-and-Wallis or this of Kolmogrov-Smirnov for instance. Sincerely yours. André Panis Associated Scientific at French Research Institute for Agriculture, Sophia-Antipolis (Alpes-Maritimes, France).
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