Bootstrap Hypothesis Testing in R with Example | R Video Tutorial 4.4 | MarinStatsLecutres

In this video, Mike Marin introduces a bootstrap approach to hypothesis testing for comparing a numeric variable across two groups using the R programming language. He suggests watching a previous video for a detailed explanation of the concept and approach. The dataset used involves weight gain in chicks on two different diets: casein and meat meal. The video provides a visual comparison through side-by-side box plots and discusses the calculation of two test statistics: the absolute difference in mean weights and median weights. The script includes an alternative test statistic using the 90th percentile of weights. The video also touches on classical hypothesis testing methods such as the two-sample t-test, Wilcoxon test, and Kolmogorov-Smirnov test.

The script proceeds with setting up the bootstrap resampling process in R. It starts by setting a seed for reproducibility and defining parameters such as the number of observations and the number of bootstrap resamples. The variable for resampling is generalized to allow for easy adaptation to different datasets. The code generates 10,000 bootstrap resample datasets with replacement, creating a matrix of 23 rows and 10,000 columns, where each column represents a resample. The script then calculates the test statistics for each resample, initially using a loop to calculate the mean for casein and meat meal observations and storing the absolute differences in means and medians in separate vectors.

The final part of the script involves calculating the p-values for the two test statistics using the bootstrap resamples. The p-value is defined as the proportion of bootstrap test statistics that are more extreme than the observed test statistic under the null hypothesis. The video demonstrates how to calculate this proportion in R and interprets the results, suggesting that a p-value of approximately 8% for test statistic one indicates that if there were no difference in mean weights, such a difference would occur by chance about 8% of the time. The video also discusses the p-value for test statistic two, which is around 26.3%. It concludes by emphasizing the difference between statistical and scientific significance and the importance of considering confidence intervals alongside hypothesis tests. The script includes additional code for plotting the sampling distribution of bootstrap test statistics and exploring hypothesis tests using different percentiles.