Paired or unpaired data and questions about test with >2 groups

#1
Hi guys!
I am here for some help with my statistics. I am currently working on a small project involving the expression of surface markers on cells in donated blood from different individuals. Basically, for each individual, I will keep a part of the blood untreated and apply two different treatments to the rest. What I was advised was to perform a test comparing all three groups and if it turns out significant, to test just two groups against each other with a Bonferroni correction. Unfortunately this came from a fellow student of mine who can’t explain it much further so I have a few questions:

I measure surface marker expression on the cells from each blood donation without a treatment and with two different treatments. I assume that this is paired data since I measure those markers for the same person with and without treatments. Is this correct? I keep on seeing a lot of papers which have a very similar setup to mine but use Mann-Whitney U tests, which Graphpad tells me is for unpaired data…

I have heard that the Shapiro-Wilk test would be a good test to assess normality but my sample size (in some cases only 4 individuals) is too small… The current opinion in the lab seems to be that flow cytometry data is rarely normally distributed and that I should just assume non-normal distribution but I would nevertheless like to test it. Are there any easy-to-execute alternatives?

Also I struggle with the distinction of test comparing three or more data sets from the tests which only compare two data sets. If I do a Friedman test (this is what Graphpad comes up with when I want it to compare more than two data sets which are paired and non-normally distributed) and get a p-value of 0.047 what does that mean? Would I even need that? I didn’t quite understand why I couldn’t just test treatment one against the control and then treatment two against the control…

If anyone would take the time to answer any of those questions I would be very grateful! :tup:
 

Karabiner

TS Contributor
#2
I assume that this is paired data since I measure those markers for the same person with and without treatments. Is this correct?
It very much seems so.
I have heard that the Shapiro-Wilk test would be a good test to assess normality but my sample size (in some cases only 4 individuals) is too small…
You will use a test that doesn't assume normality.
If your data is interval scaled, then the Friedman
test for a global comparison of all 3 conditions,
and/or Wilcoxon signed rank test for pairwise
comparisons of conditions.

Would I even need that? I didn’t quite understand why I couldn’t just test treatment one against the control and then treatment two against the control…
Personally, I would just perform the 2 pairwise comparisons
(if you aren't interested in the comparison of the 2 treatments),
and leave out the Friedman. But this is to a large degree a
matter of convention in one's respective ecological niche.


With kind regards

K.
 
#3
Thank you so much for taking the time to help me, Karabiner!
It seems that what I did until now works pretty well with what you told me. The comparison of the control with the two treatments together is of no interest in my case so I will just start with the pairwise comparison straight away...

The question with the Shapiro-Wilk test was whether there is something else I could use instead. The tests I have used until now to assess significance were for non-normally distributed data because it seems that flow cytometry data is usually not normally distributed. But I'd still like to test the distribution (and would obviously use other tests if it ended up being normal) so I can properly justify why I used those tests instead of just saying 'Well, I assume the distribution wouldn't be normal...'