Venturing further into the concept of p-values I found that while p-values are a valuable tool in statistical analysis, they should be interpreted cautiously and in conjunction with other statistical measures. Their reliability depends on various factors, including sample size, study design, and the correct formulation of the null and alternative hypotheses. We studied the pre and post molt data for lab grown crabs today and even though the distribution of the data very closely fit the linear model, both the variables were non-normally distributed, skewed, with high variance and high kurtosis. This gave us a descriptive comparison of the pre and post molt data which showed that shape or pattern of the data were very similar in nature with a small difference in mean. To figure out if there is essentially no real difference in means of pre-molt to post-molt we resorted to a t-test which predicted a very small p- value indicating that the null hypothesis (there is no real difference in means pre-molt to post-molt data) is to be rejected.
However, the t test is based on the assumption that the data fits a normal distribution which is not the case with the pre and post molt dataset. It is hence suggested that we use a Monte-Carlo procedure to estimate a p-value for the observed difference in means, assuming a null hypothesis of no real difference in the pre and post molt of crabs. I did not quite understand why we used the Monte-Carlo test here and will venture more into it and seek the professor’s help on the same.