I am looking for a straighforward alternative to analyze 2x2x2 mixed exerimental design (two within and one between-subject factors) with highly skewed data.
What I was able to find are ranking approaches, which I find not very elegant. I have also used log-tranformation which is just a little bit better.
Any ideas? How to deal with such data?
Hi Wojtek,
have you considered applying Box-Cox transformation and then, when reducing the skewness, employ ANOVA?
BoxCox transformation is far more efficient in reducing skewness than log-transformation, as the parameter is data-driven.
you might wish to read the following:
Sakia, R. M. (1992). The Box-Cox transformation technique: a review. The statistician, 169-178.
Article The Box-Cox Transformation Technique: A Review
Hi Michał!
Perfect! Good idea. I will try to use it straightaway :)
Dear Wojciech,
I am posting a article & attaching a file, might it'll help you.
Article:
Does Box-Cox Always Work?
The Box-Cox power transformation is not a guarantee for normality. This is because it actually does not really check for normality; the method checks for the smallest standard deviation. The assumption is that among all transformations with Lambda values between -5 and +5, transformed data has the highest likelihood – but not a guarantee – to be normally distributed when standard deviation is the smallest. Therefore, it is absolutely necessary to always check the transformed data for normality using a probability plot.
Additionally, the Box-Cox Power transformation only works if all the data is positive and greater than 0. This, however, can usually be achieved easily by adding a constant (c) to all data such that it all becomes positive before it is transformed. The transformation equation is then:
Y’ = (Y+C)l
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