One way ANOVA or two way ANOVA? + non-parametric equivalents

New Member

I am unsure about the choice of statistical test for my experiment design.

I have four experimental groups, devided by two factors: disease (disease/healthy) and genotype (wild-type/knockout). Groups: wild-type & disease, wild-type & healthy, knockout & disease, knockout & healthy. I am measuring different parameters characteristic for the disease (continuous numerical variables - the disease affects bone, so I measure bone density, numbers of cells, ...). We hypothesised amelioration of the disese parameters in the knockout group when compared to wild type group with disease. The control groups are included to show the values of measured parameters in healthy subjects.

Until now, I used one-way ANOVA or Kruskal Wallis as a non parametric equivalent when necessary, plus a post hoc test. I was recently suggested that two-way ANOVA would be the choice of test in this type of design. I ultimately want to show that the disease parameters are increased in wild-type group with the disease, but not in the knockout group with the disease. I also wish to compare the healthy groups (wild-type&healthy and knockout&healthy) to observe if there is a change in parameters in healthy subjects.

So my question is: one-way ANOVA or two-way ANOVA? Is two-way ANOVA a must in two-factorial designs even though some of the comparisons it offers are of no significance in my case?
Also, if two-way ANOVA is the way to go in this case, what is the non-parametric equivalent (some of my data do not follow normal distribution)? I found that Friedman and Quade test are recomended, but it seems that this can be applied to variables from groups measured at different occasions?
What about the post hoc test in for non-parametric equivalent?

I would appreciate any input on this.



TS Contributor
The 2-way ANOVA would be the appropriate parametric test. During the analysis, you can test the specific contrast in which you are interested and not test those that are not of interest. Don't worry about the distribution of the raw data. The distribution of the residuals is what is important.

Regarding the Friedman and Quade tests, I have not used these. I understand that the Friedman test is a non-parametric version of a repeated measures ANOVA, so it may not be appropriate. A quick search on Quade shows it is used for randomized complete block designs, so that may be better suited. However, I have no knowledge of any potential drawbacks of these. ANOVA is remarkably robust against deviations from normality, so I would at least try it.