My question has three parts (the method and results for my experiment follow the questions):
If I have three groups of non-parametric sample data, can I use the Mann-Whitney U test to test the Null Hypothesis for group 1 against 2, then 1 against 3, then 3 against 2? Or do I need to use the Kruskal-Wallis test? GraphPad states that sequential testing using the Mann-Whitney U against each group is not appropriate but I cannot logically think why that would be the case and the Kruskal Wallis won't tell me which group is different or not, only if there is a difference somewhere between all three: https://www.graphpad.com/guides/prism/7/statistics/stat_checklist_mannwhitney.htm
Do I need to test whether my data is normally distributed, or can I assume it isn't based on what I expect given my experiment and results (details below).
Is it even appropriate to do any stats hypothesis testing on my data at all, given the method I used to obtain the data means that the samples in each group are not going to follow data distributions of the same shape (GraphPad says I cannot do this: https://www.graphpad.com/guides/prism/7/statistics/stat_checklist_mannwhitney.htm). If I cannot use the Mann-Whitney U or Kruskal-Wallis, is there any stats test I can use?
My method is as follows:
I used three different bioprinters to print a series of patches with three different materials. I then monitored them for how long it took for each patch to disintegrate and recorded this duration in days. The median (and IQR) time to disintegrate results are in the table at the bottom which might give a clearer idea of what I would like to ask. I used 3 different materials and 3 different bioprinters for each material so I would ideally like to test for a difference between the bioprinters as well as a difference between the materials.
The group sizes were between 4 and 11 patches, all printed in one discrete session (or print run) on any given occasion when I printed them. I then recorded how many days it took for each patch to disintegrate up to a max of 28 days.
Given that the data obtained from my experimental print runs would have varied a lot due to practical factors (eg how the print run went on the day), is it appropriate to do stats testing on this data at all?
If it is not appropriate to do stats testing, how to I present that in a publication article? Just not mention it?
Any advice you could give me would be greatly appreciated. Thanks!