Observations:
- Data Collection: Collect data on crab sizes before and after molting.
- Kurtosis Assessment: Recognize that both groups have high kurtosis, indicating non-normal data distributions.
- Hypothesis Testing Challenge: Due to data non-normality, traditional t-tests aren’t suitable. An alternative approach is needed.
- Monte Carlo Test:
Data Pooling: Combine data from both groups into one dataset.
Random Sampling: Randomly split the combined dataset into two groups numerous times (e.g., 10 million).
Calculate Mean Differences: For each split, compute the mean difference between the two groups.
Distribution of Mean Differences: Aggregate mean differences to create a distribution representing what’s expected under the null hypothesis (no real difference).
Compare Observed Difference: Compare the observed mean difference in the actual data to the distribution of permuted mean differences.
Calculate p-value: The p-value is the proportion of permuted mean differences as extreme as or more extreme than the observed mean difference. A low p-value suggests the observed difference is likely not due to chance, supporting null hypothesis rejection.
This Monte Carlo permutation test is a robust way to assess the significance of the observed mean difference while accommodating non-normal data. If the calculated p-value is below your chosen significance level (e.g., 0.05), it implies a significant difference between premolt and postmolt crab sizes.
Overfitting:
Overfitting is when a model fits the training data too closely, capturing noise and leading to excellent training performance but poor generalization to new data. It happens when the model is overly complex or flexible. To counter overfitting, one can simplify the model, use regularization, cross-validation, more data, early stopping, or ensemble methods to ensure better predictive performance on unseen data.