In our examination of crab sizes before and after molting, we employ statistical analysis. Upon comparing the histograms of pre-molt and post-molt crab sizes, we find that their distributions are quite similar, except for a notable mean difference of 14.6858 units. To ascertain the statistical significance of this discrepancy, we turn to a commonly used method known as a t-test, yielding an estimated p-value of 0.0341998. Since this p-value is less than 0.05, we can confidently reject the null hypothesis that there is no real difference in crab sizes.
The t-test, while a valuable tool, may not always provide a clear understanding of the p-value calculation when comparing means with software. To address this, we employ a Monte-Carlo Procedure. We begin with 472 data points for post-molt crab sizes and another 472 for pre-molt sizes. By combining these sets into a single dataset of 944 points and randomly dividing it into two buckets—Bucket A with 472 data points and Bucket B with the remainder—we can calculate the difference in means between these buckets. We repeat this process N times, recording how often the difference in means equals or exceeds 14.6858. We then compute the probability, denoted as P, as the ratio of these occurrences (n) to the total number of repetitions (N).