I would like to raise a problem that bothers me. However, I would like to point out right away that my question is purely theoretical, and the data presented here comes only from a computer experiment and was artificially generated.
Suppose I ran an experiment and collected 750 samples of some parameter (
x1). Then I changed some input conditions twice and collected the same number of samples twice (
Finally, I would like to check whether the changed input conditions had an impact on the tested parameter (variable).
As a result, I got these results.
# A tibble: 3 x 14 # Groups: name  name n min q1 mean median q3 max sd kurtosis skewness SW.stat SW.p nout <fct> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <int> 1 x1 750 -7.28 -1.64 0.0233 0 1.76 7.48 2.50 -0.210 -0.00270 0.999 8.39e- 1 4 2 x2 750 -5.49 -0.780 0.00846 0 0.816 5.90 1.36 1.83 -0.00685 0.980 1.76e- 8 21 3 x3 750 -11.1 -0.762 -0.0266 0 0.719 12.6 1.86 15.5 0.482 0.776 8.59e-31 37
As you can see, the median is "absolute zero" in each of the three repetitions. Mean is not much different from zero either. The first and third quartiles are also very similar.
You could say I got exactly the same answer.
This gives me one answer - in this case there are no statistically significant differences.
However, everyone can see that the answers differ diametrically from each other! If we look at the value of kurtosis, we can see that the kurtosis of the variable
x3 is almost 100 times greater than the kurtosis of the variable
And finally my question. But please forgive me, if statistically it is stupid. I am a statistical self-taught. Is there a statistical test that would answer the question of whether there is a statistically significant difference between the kurtosis value?