Hi there,
I've hit a statistical wall and can use all the advice I can get. My dataset is not normal. not homogenous and has a lot of zeros. My project is comparing dominant and subordinate, male and female hamsters with and without drug for three agonistic behaviors (I know...it's a lot).
The nature of the design lends itself to a lot of zero scores (e.g. dominant animals show a lot of aggression while most subordinates show none; vice versa with submission).
Initially I tried to do a Kruskal-Wallis test with post-hoc Mann-Whitney U, but I was advised that rank ordered tests are sensitive to lots of zeros.
I also tried doing ANOVA with post hoc MWU even though the data is non-normal, but ANOVA is not robust against violations to homogeneity of variance, even though it can handle violations to normality.
I'm not sure how to move forward and don't have an intimate enough understanding of stats to make a judgement call on which violations are more acceptable than others or what type of analysis would be best for this interesting (**frustrating**) dataset.
Hi Dene,
As you know, unlike ANOVA test which compares the means of different groups Kruskal Wallis test uses the median values of the groups to perform the test. When the distributions of the groups are approximately normal, both methods give you similar results. However, the median method is usually preferred for the data sets with outliers.
I am not familiar with the nature of your dataset, but I have a few suggestions that may help you handle your data:
1) Perform both ANOVA and Kruskal Wallis tests with considering and without considering the zeros. You may define a rank when you are not considering the zeros. Then compare the results of both scenarios to see how much the zeros affect your stats.
2) You may also classify your data sets via other methods, such as Jenks Natural Breaks. This method will minimize each group's average deviation from the class mean while maximizing the deviations between classes.
3) Estimate the variance of the residuals via the least-squares optimization and perform the statistical tests on the residuals.
Hope this helps!
Best regards,
Ebrahim
Although you write a lot, you miss to give the most relevant information:
what's the nature of the response variableyou are analyzing? How it ismeasured?
You wrote tht it is "aggression", but this needs to be operationalized somehow, an there are many different wayshow such a property can be operationalized. And this will eventually determine the characteristic of the valiable you are goind to analyze.
Depending on the properties of this variable you can look for zero-inflated models or hurdle models, and -assuming that your variable is non-negative and right-skewed- these may be Poisson-, negative binomial-, gamma- or log-normal models. If your variable hat a lower and upper bound, a beta-model may be appropriate. The "quasi-models" (like quasi-Poisson and quasi-binomial) would give evenmore flexibility to model the relationshipbetween mean and variance, but I am not aware if such models are available as hurdle or zero-inflated models.
https://fromthebottomoftheheap.net/2017/05/04/compare-mgcv-with-glmmtmb/
Dear Denè my suggestion is 'go discrete' you can use a k-means algorithm to subdivide your fata into (few) homogeneopus cluster (even simply 0 > 0 if this is the best clusterization in terms of variance explained) and then simply perform the myriads of tests (e.g. Chi-square, Fisher exact test..) to study departures from randomness of any association you wish to study between aggression and external variables...
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