The Monte Carlo procedure yields an estimated p-value, which is very close to the p-value obtained from the t-test. The distribution of differences in means from the Monte Carlo procedure is visualized with a histogram.
It shows that the observed difference in means falls within the distribution of differences obtained through random sampling, and concludes that there is strong evidence to reject the null hypothesis (i.e., there is no real difference in means) in favor of the alternative hypothesis (i.e., there is a statistically significant difference in means).
Large Number of Possible Samples: It highlights the enormous number of possible combinations when randomly selecting samples from the data, emphasizing the complexity of exploring all potential samples. In summary, the professor demonstrates that there is a statistically significant difference in the mean sizes of crab shells before and after molting, based on both t-test and Monte Carlo analysis. This difference is observed in the data and is unlikely to occur by random chance. I left with the following questions after class,
- Can the findings of this study be replicated by other researchers using the same dataset and analytical methods?
- Alternative Analytical Approaches: Are there alternative statistical tests or methodologies that could have been employed to analyze this dataset? Exploring alternative approaches can enhance the depth and comprehensiveness of data analysis, potentially providing additional insights or validating the results obtained through the chosen methods.