ANOVA or Kruskal Wallis

Dear Stats experts here...

I have a question:

I am counting cells in histology slides of certain timepoints after a treatment.

day 0, day 1, day 5, day 10, day 20, day 30, day 60, day 90

for each time points I have 3 histology slides of three independent individuals.
each individual has only one slide for one time point and not for another.

therefore I assume it is a non-repeated measurement.

my question: to find out if there is a significant difference between timepoint 0 versus any other timepoint, I may either use a 1-way anova or a non-parametric Kruskal Wallis test.

As there are only 3 subjects per time-point (very small sample size) - I am not sure, if I am allowed to use a 1-way-ANOVA with DUnnet-post hoc testing (to compare all time points vs. baseline timepoint of day 0) --- or if the small sample size forces me to use a non-parametric test, in this case a Kruskal Wallis test...

what do you suggest?
1. I am not sure, if a QQ-plot helps... with a sample size of n=3 a qq-plot will not reveal any hint for or against normal distribution, I suppose, or am I wrong. Furthermore, I am using graphpad prism, doesn't support QQ-plots as far as I know, and normal distribution testing gives an error message, sample size too low...
2. are there cases when I may assume normal distribution, just as I am dealing with "biological" data... cells in a tissue after a treatment... from a rational point of view, they should be normal distributed


Less is more. Stay pure. Stay poor.
An n-value > 30 is sometimes used for normal assumption. Doesn't help you much.

Your design still complexes me. You have 8 time points with three unique individuals each time point? Equaling 240 unique individuals?? What is suppose to happen over time (more or less cell counts)???
cell count goes down (cell death) and then goes up (regeneration) at later time points. a biopsy (histology) for legal reasons has only been performed once in each indivuum. therefore, we have no repeated-measurements, but only 3 values for each time point, with different individuum for every time point. hope you understand what I mean.

with non-parametric testing, I have nearly no significant results, with parametric ANOVA I have fascinating nice significancies... as I am dealing with biological data, may I assume normal distribution and use ANOVA, or is there no way to procede like this?
Or do I have to admit in the methods section: Due to the small sample size for each time point, no assessment of normal distribution was possible (and therefore parametric statistical tests not useable) and non-parametric tests not adequate due to underassessment of statistical significance?


TS Contributor
... as I am dealing with biological data, may I assume normal distribution and use ANOVA,
Just out of curiosity, is this a common assumtion and common
practice in your field? Has this been done in other studies in your

With kind regards

Difficult to tell... I just was thinking that the amount of cells in a tissue should follow Gaussian distribution (but I might be wrong)...


Less is more. Stay pure. Stay poor.
Still confused by the design. For clarification you have three slides for three different individuals at every time point for 8 time points. So you have 240 unique slides? Correct or not?

If so these individuals are independent. You are looking for decrease then increase, etc. But you don't know the previous cell counts for any of these individuals. There is no direct link or causal relationship, you can't connect these cell counts. This is like an observational study where perhaps a hypothesis could be generated but absolutely no relationship can be established or hypothesis tested. That is if I understand the design correctly. You may have a bunch of cross-sectional data - hard to make founded conclusions with. Not trying to be a pessimistic, all data is information.
Thank you very much for your reply!

yes, at each time point, I have three (new) individuals (independent). Therefore, at each time point I have one histology slide for one (new) individual.
Also, prior to treatment, a slide of three unique individuals (normal / control group) has been obtained.

As for each time point, sildes from new individuals are taken (each individual has only one slide at one timepoint), we are dealing, with non-repeated and independent measurements.

Mean cell count in a certain layer decreases after treatment and then increases afterwards. SD is quite low. I just would like to find out, if the decrease compared to baseline (before treatment) is significant at certain timepoints. And for doing that I have planned to perform an ANOVA or a Kruskal Wallis. However, with Kruskal Wallis everything seems to be non-significant, although on the figure, the decrease in cell count seems quite impressive. With ANOVA the decrease is highly significant, however as mentioned above, I am not sure, if I am allowed to perform an ANOVA analysis (and due to small sample size, testing for normal distribution is impossible).

A dilemma :)
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I am not sure if I am understanding you right, but for ANOVA or kruskal wallis I am defining each time-point with three cell counts of three independent individuals as one group.


Less is more. Stay pure. Stay poor.
So you potentially have 8 groups in the ANOVA or Kruskal that you are comparing. I get that, now I understand what you are trying to do.

However, you still just have cross-sectional groups from different individuals. I don't think there is much you can do with these data (that I can think of). Once again the difference is that you don't know how many cells each individual had at each time point, so you can't show an increase or decrease. Perhaps you could have randomly selected the individual for these three time points, than you would hope they were reflective of each other by chance.

The only thing that I can think that may, and I say with a tremendous amount of apprehension, do would be to plot the averages with whiskers on a charter and disclose that they are unique individuals and actual changes or fluctuations are hypothesized but cannot be determined with this dataset.