Hi Hamid: It really depends on you data. You could receive better advice/guidance if you post here (part of) your dataset.

What you are observing is over dispersion (variance >> mean). I would try first to transform to normal e.g. log(X) if you don't have zeroes. Otherwise try other transformations. Alternatively, you could fit your data to a right-skewed distribution and then compare both groups using hypothesis test for that particular model. Or you could use a non-parametric technique. 

PS: I would not remove those observations you call "outliers".

Hope this helps

Dear Dr Edgar Santos-Fernández, Dr Jochen Wilhelm

Thank you very much for your reply

Dear Dr Edgar Santos-Fernández, Dr Jochen Wilhelm

Thank you very much for your reply

Dear Hamid, in biologic experiment, Coefficient of variation (CV %=(sd/mean)*100) must be less than 30% (Standart deviation must be less than 1/3*mean). IF CV more than 1/3*mean, results of study would be misleading. My advice to you increasing the sample size and rewiev the your data (zero, negative).

best regards.

Dear Jochen Wilhelm, i read this information the following sources.I explored a broad time this matter.

M. Mendes, Statistics and Research methods for application science, 2012.Kriter press. İstanbul/Turkey. (Turkish)

Dear Hamid,

The basic check is normality of the variable. If it is basic descriptive, then report median if variable is not normal; otherwise mean (sd) would be fine.

If it is comparing across groups, if normality assumptions violated, non parametric tests would be recommend for univariate analysis. For multivariate a General linear model analysis would suffice.

Dear Dr chan

Thanks a lot. 

CV is not assumption any statistical tests. The standard deviation can be larger than the mean. The range of numbers has to be large for this to occur. One such sample is {0, 0, 1, 15, 20}, where mean= 7.2 and s=8.6. in this situation, we should use median. because the arithmetic mean is influenced by extreme values. large standard deviation indicates that is not homogen data. It may lead to biased estimates. therefore, nonparametric tests are available.

Hamid -

This is not my subject matter area, but have you considered looking at standard errors of the means, in addition to estimating the standard deviations of the populations?   You could find a confidence interval about the difference in estimated means.  If you are concerned that the Central Limit Theorem may not help you enough, you could still use Chebyshev's Inequality.

Cheers - Jim