Piotr Wi�niewski wrote: > I am to decide whether there is a statistical difference between two > groups concerning variable X. > > Variable X distribution is not normal, it is right-skewed. > Log-transformed X distribution is normal (it's histogram looks normal, > it mathces Kolmogorov-S. and Lillefors statistics) > > I compared results from Mann-Whitney test and t-Student test on > log-transformed data. > > Here are the results: > > > Mann-Whitney U test > raw data > ------------------- > n mean SD median min-max > X1 30 1.43 0.7 1.21 0.26-4.02 > X2 6 1.00 0.2 1.0 0.78-1.28 > > p=0.014 > > > > t-Student test > log-transformed data > ------------------------ > n mean SD > X1 30 0.26 0.46 > X2 6 -0.11 0.17 > > p=0.17 > > > The conclusions seem to be diverse. Nonparametric test shows that the > difference between groups is significant, and parametric test on > log-transformed data shows that there is no such difference. > > I am not skilled enough (yet) to interpret these results. Which result > should i trust?
Possibly neither ... the standard deviations for the two groups seem moderately different: if there is a possibility that the standard deviations really are different then you should not use the simple two-sample Student-t test. This effect would not be important for the non-parametric test, providing that you understand what it is (ie. which parameter (median)) you are testing. Other choices would be to look for changes in both location and scale, or to use a nonparametric test which is sensitive to both location ans scale differences. In general you should aim for some conclusions about possible differences that will encompass both location and scale: part of this should take into account what the data-values actually represent and what type of differences might reasonably be expected. David Jones . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
