The relationship between the pre-molt and post-molt sizes of crabs using
statistical analysis. When we compare the histograms of crabs’ sizes pre-molt and post-molt side by side, we observe that the shape of the distributions is quite similar. The only notable distinction is a mean difference of 143.898 – 129.212=14.6858. The question is this difference in means statistically significant, To tackle this issue, we could employ a common statistical method known as a t-test. The estimated p-value, p = 0.0341998. With a p-value <0.05, we can conclude that we reject the null hypothesis that there is no real difference.
The primary use of a t-test is to assess whether there is a significant difference in the means of two populations. Furthermore, applying a t-test to compare two means using suitable software may not inherently provide a clear understanding of how the p-value was computed, For these reasons we carry out a Monte-Carlo Procedure to calculate a p-value for the observed difference in means while considering a null hypothesis that assumes no real difference. 472 post-molt data points and another set of 472 pre-molt data points. If we combine these two sets into one, resulting in a combined dataset of 944 points, and then randomly divide it into two separate buckets, namely Bucket A with 472 data points and Bucket B containing what remains, we can proceed to calculate the difference in means between these buckets. This process is repeated N times, and we keep a record of how many times n the difference in means is greater than or equal to 14.6858. The probability, denoted as P, is then calculated as P = n/N.