Statistical Learning: 13.6 Resampling Approaches II

TL;DR

Resampling approaches involve shuffling data to generate a null distribution, which can be used to compute p-values and control FDR.

Transcript

and so the way that we're going to do this is by saying well under the null hypothesis there's really no difference between the x's and the y's they all have the same mean under the null hypothesis so i'm just going to scramble them i'm just going to shuffle them together i'm going to permute them i'm going to resample them and i'm going to generat... Read More

Key Insights

• 🔀 Resampling approaches involve shuffling data to generate a null distribution, providing a more robust statistical analysis.
• 💄 Theoretical null distributions may not always be available, making resampling approaches a valuable alternative.
• ☠️ Resampling approaches can be used to compute p-values and control the false discovery rate (FDR).
• ⌛ Computational time is a trade-off for making weaker assumptions in resampling approaches.
• 🛩️ Resampling approaches are particularly useful for small sample sizes or unknown null distributions.
• 🏆 Different test statistics may require unique resampling approaches, requiring careful consideration and customization.
• 😘 Resampling approaches are generally low-cost and can provide additional confidence in statistical analyses.

Questions & Answers

Q: What is the purpose of shuffling the data in resampling approaches?

Shuffling the data under the null hypothesis allows us to simulate the null distribution and generate p-values for hypothesis testing.

Q: How are p-values calculated using resampling approaches?

P-values are calculated by dividing the number of times the test statistic on the shuffled data exceeds the test statistic on the real data by the total number of shuffling iterations.

Q: When are resampling approaches particularly useful?

Resampling approaches are useful when the theoretical null distribution is unknown, the sample size is small, or when assumptions associated with the null distribution are uncertain.

Q: Can resampling approaches be used for other test statistics besides the two-sample t-test?

Yes, resampling approaches can be developed for different test statistics, but it may require careful consideration and customization based on the specific null hypothesis and test statistic.

Summary & Key Takeaways

• Resampling approaches involve shuffling data under the null hypothesis to simulate the null distribution.

• By generating a large number of shuffled datasets and computing a test statistic on each, a p-value can be calculated.

• Resampling approaches are especially useful when the theoretical null distribution is unknown or unavailable.