Hello everyone!
I need to do a two-way ANOVA on my data (or at least I think it is the best test), but I'm confused about weather to chose repeated measures on just one factor or both.
Experimental design:
3 mice wild type vs 3 mice knockout (different genotype) For each mice, I take a pool of cells and apply 3 different treatments in paralel. I measure a specific gene expression in all treatments for both wild type and knockout mice, only one time point.
My questions:
1) do the different treatments affect the gene expression withing each genotype? 2) do the different treatments affect the gene expression between each genotype?
3) Is the effect of treatment independent or dependent on the genotype?
First, from what I read and could understand, applying different treatments in the same pool of cells simultaneously is considered a repeated measure so I'm assuming this. In this scenario, for question 1, I think a one-way repeated measure ANOVA would be enough to answer.
But for question 2 and 3, I believe I need to do repeated measure two-way ANOVA. Do you agree?
If I have to do repeated measure two-way ANOVA, my MAJOR doubt is:
a) Is the expression of gene A for each treatment the only repeated measure in this two-way ANOVA? And in this case I would do repeated measure two-way ANOVA for one factor (cell treatment).
b) Or is the expression of gene A for each genotype also a repeated measure? And in this case I should do repeated measure two-way ANOVA for both factors?
Thanks in advance for any feedback! If you need any other info, just ask.
Dear Liliana,
the best approach would indeed be a mixed 2-way ANOVA, having “genotype” as between group factor and “treatment” as within group factor (see below my answers to your questions). In this way you can test not only the general effects of treatment and the effect of genotype on gene expression, but also of the effect of the interaction between genotype and treatment. With this design you assume that the different pools of cells from one mouse should indeed be treated as "paired values", i.e. dependent to each other because they have been obtained from the same mouse. Of course, it you should use "blocking", namely randomly assign each cell pool from one mouse to all the different treatments. The problem with this design is that your sample size is equal to 3 for each genotype, meaning that the power of the statistic will be very low and that you can only detect strong effects.
Answering your questions:
a) Is the expression of gene A for each treatment the only repeated measure in this two-way ANOVA? And in this case I would do repeated measure two-way ANOVA for one factor (cell treatment).
Yes, the only repeated measure in your design is the treatment (treatments are applied to different cells from the same mouse/subject)
b) Or is the expression of gene A for each genotype also a repeated measure? And in this case I should do repeated measure two-way ANOVA for both factors?
Genotype is a "between group" factor in your design, because the two genotypes are represented by different animals.
Hope it was of some help. Best regards and good luck with the experiments,
Fabio
Dear Fabio,
Thank you so much for your answer!
You confirmed what I was thinking that the factor genotype would not be a repeated measure since samples are not related. And your explanation was very clear! I'm not very confortable in statistic analysis and even less with 2-way ANOVA, so it was very important to have the feedback from someone else :)
And you are absolutely right about having less power due to the small number of animals per group... It is a limitation that I was not so much aware when I designed the experiment, but I'm "lucky" that the majory of treatments tested induce strong effects on the expression of my genes of interest.
Thank you again for taking the time to answer me!
Best regards and good luck for your work too,
Liliana
Hello Liliana, two-way ANOVA with repeated measures is correct if your variances are equal in all groups (sphericity of data is fundamental for ANOVA and with n=3 might be difficult...). One factor is fixed, the genotype of the cells, the other factor is the repeated one, the treatments. The expression of your specific gene is your dependent variable or your measure, whatever you want to call it. You should have anyway level 2 interactions in your analysis, so to test for between factor effects (effect of genotype on the treatments) and within factor effects (effect of the different treatments within a genotype).
Still, I would have doubts you really need this type of analysis. In the end it's different cells that are subjected to different treatments (not the same cells that undergo in sequence the three treatments), so you can answer your second question by checking if there is a difference in response to each treatment depending on the genotype, that's a simple t-test for each treatment. And you can answer your first question with a simple one-way ANOVA within each genotype (by the way, it would be good in this case to have a non-treated sample as baseline control...). The third question is implicit in the first two, and you might find out that the genotype is relevant in some treatments and not in others... The problem with two-way ANOVA with repeated measures is that significance might arise from wt treatment 1 and ko treatment 3, for example, but this would make no sense in biological terms. You would spot this with post-hoc tests....
Post-hoc tests are always the most complicated story, to find out where the significant differences are, if you have a significance in the ANOVA analysis. The more comparisons you make, the higher the likelihood of finding some stochastic significance (false positive) or missing some difference (false negative), and with repeated measures the number of comparisons tends to be high, so choosing the right test is tricky. Therefore, if you are convinced of the two-way with repeated measures ANOVA approach, I would go for a Tukey's HSD test. Or possibly a Sidak (I think with a Bonferroni you would lose too much power).