I am working with biological data. The project is about comparing microbiota composition in different samples who have different type of diet. Here is the experimental design of the project:

1) factor diet -> levels: a) baseline    b) white bread(wb)    c) barley bread(bb)
2) factor responded (if have high blood glucose) -> levels: a) responders   b)non-responders  
sot it would be:    baseline    wb    bb        baseline    wb    bb
               |_____________________|     |_____________________|
                      Responders               non-responders

I have seen big difference between amount of one bacteria in bb-responders and bb-nonResponders. Since the data is not normally districted if I use ttest I will not get any significant value. One suggested me to use Mann Whitney U-test but I am not sure what kind of test I have to use! Could you please help me with that?

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    $\begingroup$ What do you want to find out? $\endgroup$ – Peter Flom Mar 11 '14 at 9:50
  • $\begingroup$ I would like to know if there is a significant difference between bb-responders and bb-nonResponders! $\endgroup$ – Rozita Akrami Mar 11 '14 at 9:58
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    $\begingroup$ "Since the data is not normally districted if I use ttest I will not get any significant value" -- how does the argument behind this assertion go? I'd say something else (that the t-test may be unsuitable for what sounds like 0-1 data, but you should clarify what the response actually consists of). If it is 0-1, the Mann-Whitney may be less suitable even than the t-test. I'd think you would probably look at a model suitable for Bernoulli responses. $\endgroup$ – Glen_b Mar 11 '14 at 9:59
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    $\begingroup$ Significant difference in what? Their mean? Median? Shape of distribution? Some other quantile? $\endgroup$ – Peter Flom Mar 11 '14 at 10:16
  • $\begingroup$ @Glen_b Sorry if I am stating wrong phrases, but based on my poor statistical knowledge I think t-test is commonly used when your data is normally distributed. My data is not 0-1 but is the number of bacteria seen per each sample. $\endgroup$ – Rozita Akrami Mar 11 '14 at 13:15

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