In today’s discussion, We considered Crab Molt model as an example when independent variables are non-normally distributed. The data contains both pre-molt and post-molt sizes can be used to correlate between a crab’s pre-molt and post-molt size and this correlation can be used to predict a crab’s pre-molt size based on post-molt size. We plot the data using linear model, calculated the Pearson’s R-square value to check the linear model is fit to data.
We plotted histograms for both pre-molt data and post-molt data and compared both plots side by side and found similar in shape, difference in means. We have done the T-test by considering Null Hypothesis(H0): there is no real difference in means, Alternative Hypothesis(Ha): There is a difference in means for pre-molt to post-molt data. Calculated P-value and it is less than 0.05. So, we should reject the null hypothesis.
In some cases, t-test assumptions make the estimate of p-value seems to be unreliable. In this scenario we used Monte-Carlo simulation which itself predicts multiple possible outcomes for an uncertain event.
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