We are analyzing whether there is a significant difference between pre-molt and post-molt crab sizes as part of our research. The data show a huge variation in the values of kurtosis, with post-molt kurtosis rise to an astonishing 13.116 and pre-molt kurtosis being relatively low at 9.76632. The two groups have surprisingly similar shapes when we compare the actual sizes of the crabs; the main difference between the two groups’ means is a difference of 14.6858.
Determining whether the observed difference in mean size is a real phenomena or just a statistical aberration is our main challenge. Our first inclination is to use the tried-and-true T-test to answer this question.The T-test, however, is predicated on the notion that data follow a normal distribution, which is dubious in our case given the high values of kurtosis. In light of this, we suggest the Monte Carlo permutation test as an alternate strategy that can gracefully accommodate the non-normality of our data. In order to determine whether the size of pre-molt and post-molt crabs differs significantly, we converge the two datasets. Ten million times, randomly split the combined data into two groups of equal size.For each division, determine the mean differences.The mean differences should be distributed. Use this distribution to comprehend how likely it is, under the null hypothesis, to observe a mean difference as extreme as the difference in our actual data. This will be shown as a curve of the permuted mean differences (p) in relation to the total number of permutations (N).