I am looking at a monoculture diatom biofilm growth on five different materials measured at 6 different time points.
So my variables are: dependent variable is "cells per mm^2"; independent variables are material (5 different types of silicone rubber) and time point (cells were counted every two days). I had 5 replicates for each material and counted the cells under a fluorescent microscope at 5 different regions on each sample, giving me 25 measurements per material each time.
My data is not normally distributed (according to the Shapiro-Wilk test) and I used the Kruskal-Wallis test to see whther there was a significant difference in cell counts across different materials. I would also like to include time to see whether there was significantly different number of cells at each time. Which test would I use?
Thank you!
You seem to got lost in testing. It would be more enlightning to formulate a resonable growth model and then test meaningful hyopthesis in this model.
You response variable (in cells/mm²) is positive. By definition, this can not be normal distributed, and yourtask is not to demonstrate that you have enough data to show this. So testing the normal distribution is rather useless, to begin with.
Further, the time points are (at least more or less) arbitrary. So testing differences between the materials at these time-points or testing differences between time-points for these materials is testing arbitraty hypotheses. Althogh this is very commonly done, this is not at all smart and usually not very meaningful and hard to interpret (at least in seom consistent way). And it usually comes with a bad of problems, like multiple testing, error-inflation and such - and all that just for a collection of (more or less) arbitrary hypotheses.
A good analysis starts with a good experimental design. In your case this would mean that the time points span a range of exponential growth. In this case you can fit an exponential growth model and infer the growth rates and differences between growth rates on differrent materials. If the growth is up to confluency, you would use a logistic growth model from which you could infer the initial growth rate or the time needed to cover some porportion of the surface and how this depends on the material.
In addition to everything you see and hear, think about the following.
Assumption #5: Your dependent variable should be approximately normally distributed for each category of the independent variable. We talk about the one-way ANOVA only requiring approximately normal data because it is quite "robust" to violations of normality, meaning that assumption can be a little violated and still provide valid results.
https://statistics.laerd.com/spss-tutorials/one-way-anova-using-spss-statistics.php
I think you can get ideas from Repeated Measure analysis.
In this analysis, select Time as Within-Subjects Variables and IV as Between-Subjects Factor.
Follow Prof Wilhelm's advice. You might find this attachment of some help
C R Rao invented all of this. David Booth
This experimental data seems to fit generalized linear models of either the Poisson or the binomial families since it's count data.
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