The error rate data i have has a strong right skewness and therefore violates the assumption of normal distribution for using an ANOVA. I tried transformation by square root and log10. After looking at the histograms it seems like the reason for that is that about half the values are exactly 0%. Is there a way to transform the data to a normal distribution so i can use an ANOVA?
Dear Jonas,
Why do not use nonparametric tests in this case?
Dear Amir,
I am trying to replicate another study and they used an ANOVA. I wanted to use one as well because i thought the results of the original and my replication would be more comparable.
Plus, I thought an ANOVA would have generally more power.
I see, you have a bad/messy data set already. Having tried logrising the data and other failed transformation procedures. I would suggest you use non parametric test that does not bother on normality assumptions. Kruskal-Wallis test is the non parametric version of one way ANOVA
I think the answers to your questions have already been given. ANOVA is a parametric test with lots of assumptions to be tested before you run it. Luckily, its nonparametric equivalent (Kruskal Wallis test) draws on fewer assumptions. It is better to run this non parametric of ANOVA if a key assumption like normality has been violated, although ANOVA can be robust.
Error rates as well as reaction times are typically not suitable for the normal linear model. How does your dependent variable look like? You only said "rates". Are they bounded between 0 and 1 and are continous? Depending on the structure different models are possible, either from the generalized linear model family or maybe a beta-regression.
First of all, thank you for all the answers, they really helped!
I actually would test my hypotheses with a 2 x 3 x 2 rmANOVA if the error rates were distruted normally. That is what i did for reaction time means which are in normal distribution. So i do not think the Kruskall-Wallis-Test is the appropriate test to use but rather the Friedmann-Test, right? I just do jot see if it will work the same way a multi factorial ANOVA does, like testing main effects and interactions. Can you help me out with that?
The error rates are the total amount of errors made in a certain set of conditions divided by the maximum amount of errors possible in that certain set of conditions, so it is a proportion with values between 0 and 1. I have 12 error rates, one for each crossing of the factors of the described ANOVA.
I think the problem is that due to the limited amount of maximum trials for the conditions of one error rate (20), there are many participants that scored an error rate of 0% and the rest of them are distributed among a few other values.
Do these informations help?
I don't think that any ANOVA or typical linear model is appropriate for your design. In my opinion, the boundedness between 0 and 1 is a problem as well es the amount of zeros that you mentioned. The only thing that comes into my mind is a (flexible) beta regression and/or bayesian analysis, where you can flexibly model the outcome variable. Maybe there are other indeas here?
And as far es I know, there is no analog to a 2x3x2 rmANOVA. Maybe have a look at Rand R. Wilcox - Introduction to Robust Estimation and Hypothesis Testing, who has lots of R scripts for robust, parametric analyses basing on ANOVA logic.
Ahh, here something I found last week and havent read it so far, but this may be helpful for you
Article bayes4psy—An Open Source R Package for Bayesian Statistics i...
A R package for bayesian inferencing, which is specifically designed for experimental psychologists and typical designs --> bayes4psy package
https://cran.r-project.org/web/packages/bayes4psy/index.html
https://cran.r-project.org/web/packages/bayes4psy/bayes4psy.pdf
Hope it helps.
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