I want to analyze the quantitative data between two independent groups. The number of samples in each group is 6 . Between these 6 samples, I have two extreme values that affect the data . If I take the average between 4 samples and then use this average for the 2 samples, then I take mean and median and perform a Mann-Whitney test, is this right? If I use trimmed mean my sample size will become too small, but if I use it without any change it will affect the u test.
Hi Brishna! In this case, I would rather consider a mixed model or recursive partitioning. Removing outliers and using a non-parametric test is good start though. Be careful you've a very small sample size. I'm also facing a similar issue. What do you think?
I think another way. If i accept that the data which are out of the four samples are not true and the data occur in the four samples is true then i can find the sensitivity and specifity as percentage then i can compare this percentage with non parametric test. But i am not sure . Is it a good way
If the "extreme" values are obviously wrong measurement/observations, then remove them and to the analysis as usual for the remaining data. If you are not sure and you want to use their information at least partly, then do a weighted analysis and use some sensible weights. If these values are simple extreme but possible and if they could also be sensible, then you should think harder what these values might try to tell you (wrong model? wrong assumptions? missing predictors? ...).
Keep them in and accept the data
You should have a very good reason ( biological) to exclude one
perform a MWU test on the n=6,6
Extreme values are not bad unless those values had been influenced by other values, if were obtained at same conditions than the rest of values, you should keep it, Mann-Whitney U test assign ranges of which those extreme values will be standardized
Perhaps the Dixon Q test will help
http://en.wikipedia.org/wiki/Dixon's_Q_test
When dealing with outliers you should take into account the problem context. Sure they will affect the analysis. If you replace them by an average or median, the variance will be reduced and probably you will get statistical difference for this reason. You should take into account that very time you do an imputation you are "guessing" the value. In your case, you have very few data and that is a problem with outliers
Hi Brishna, when dealing with extreme observations you could either remove the observations or winsorize it. I prefer winsorize the data because no data will be removed.
You need to get back to us on what you think caused the outliers. If you don't have a biologically plausible explanation for why they're errant, I'd advise keeping them and either accept the insignificant result (and rerun the experiment with a larger sample if possible, first doing sample size calculations that account for the variation you expect to see), or at most winsorize them and then run a MWU test.
Brishna. Use the two extreme values plus the average of the 6 datapoints of your sample. Forget about normality in this case. If you give me media U and two extreme values, I can obtain a plausible continuous solution for distribution that fits perfect to extreme values. I would give two graphs: cummulative distribution function, and Lorenz curve. This is a theme I researched recently but is has not been published at academic level.
I may also create the 3 data values from imagination. Suppose Kmax=220, Kmin=40, and U=100 measuring units. The obtained curves do not have anything to do with premises nor shapes of normal curves.
OK, best wishes, Emilio
Here it is the spanish version of paper (15 pages) taken to Cuba event two weeks ago, about extreme values and some critiques to normal curves theory.
INDUCCIÓN PARAMÉTRICA APLICADA A MUESTRAS PEQUEÑAS -MÉTODO Y MODELO CON FUNCIÓN INVERSA-
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