Dear, Im having trouble with analyzing data using two-way repeat-measured ANOVA. The reason that I use this technique is that my experiment measure cell survival of the the treated cell with different concentrations of drug at 3 time points, continually. The experiment was repeated for 5 times. Therefore, the time of incubation is the dependent factor since I measured cell survival continually. I found that in some of cell which were treated with one concentration of drug at one time point, the data from 5 experiments aren't distributed normally. I have been trying to find the alternative method like Scheirer-Ray-Hare test but the assumption of this test doens't include data dependency. Moreover, I find the discussion about this problem or similar that some assumption can be violated by ANOVA but those are quite controversial and confusing. Im very novice to statistics. Any suggestion would be humbly appreciated :')
As I understand, you have a Between x Within subjects design.
Between subject factor: 5 experiments.
Within factor: 3 different concentrations at 3 time points.
I suppose you used differents subjects groups for the 5 different experiments.
For this design there is a nonparametric alternative: the ARTool and the f1.ld.f1 form the nparLD R package.
Artool: https://depts.washington.edu/acelab/proj/art/
nparLD: https://cran.r-project.org/web/packages/nparLD/nparLD.pdf
In attachment (between_within.R) an R script for such a design.
Of you used the same subjects for the 5 experiments, you have a Within x Within subjects design. In attachment (within_withinMeier.R) a script for such a design.
Thank you so much for your advice Jos Feys and Jochen Wilhelm . I'll try to look at your method carefully.
Jos Feys I'm a bit confused about concentration, that you said it is the within factor. I understand that drug concentration is the between factor since it was not the same group of cell that had been treated with one concentration, was further used to treat with another concentration. For my understanding, it is still the between x within designing but I just want to clarify my understanding or misunderstanding about the concept. Thank you :)
Hi Wongsakorn Muangsom, If different concentrations were applied to the same cells at different time points, this is a within subjects (cells) factor. If possible, can you send me a copy of the data in Excel format. You could do this on my email address: jos. feys @ telenet. be (remove the blancs).
If your dependent variable (cell survival) is dichotomous response (yes/no) you could consider a logistic regression or a frequency test for dichotomous responses such as the Cochran-Mantel-Haenszel test for the general association between a repeated measures factor (such as time or condition).
If the data violates the assumption of two-way repeated-measured ANOVA, there are other statistical tests that can be used to analyze the data. Some of these tests include Friedman’s test, the Kruskal-Wallis test, and Wilcoxon signed-rank test.
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