Boot War

Boot War is a card game designed to enhance one's understanding of the nonparametric bootstrap test with pooled resampling methods. By diving deep into various game settings, players can derive rich insights. Let's break down the basic gameplay:

1. Select a Mode

Choose 't' for the independent t-test or 'pt' for the paired t-test. In the independent t-test, the effect size is derived from the mean difference between the player's cards and the computer's cards. For the paired t-test, the effect size is calculated as the mean of round-by-round differences between the player and the computer.

2. Define the Deck

Default: A standard 52 card deck with ranked suits. For a twist, employ the R anonymous function to craft an "anonymous deck". The game even supports a bring-your-own-deck feature, known as an "interleaved deck" in Boot War, where different decks are set for the player and the computer.

3. Select a Confidence Level

Set your desired confidence level for the test statistic and effect size. While the default is set at 0.95 (for 95% confidence intervals), it's a crucial component to experiment with.

4. Choose the Number of Bootstrap Resamples

Decide on the count of bootstraps for analysis, integral to the nonparametric bootstrap test with pooled resampling.

5. Select the Number of Rounds

 Opt for any round count between 1 to 26. However, a word of caution: selecting 1 to 3 rounds may lead to crashes. My personal recommendation lies between 5 to 12 rounds, especially if you're interested in observing outcomes in smaller sample sizes.

6. Set a Seed

Consistency is key. By setting a similar random number seed, expect consistent outcomes for identical inputs.

7. Play out the Rounds

Simply hit the 'Deal Card' button to progress through the rounds.

8. Score the Game

When you finish playing out the rounds, the game will employ the nonparametric bootstrap test with pooled resampling to compute the final score, which includes effect size and confidence interval, and to determine the winner.

Final Thoughts

For an enriching experience, I advise players to experiment with an anonymous deck (e.g., function(x) { rpois(20, 15) }) or an interleaved deck (e.g., function(x) { list(rpois(10, 15), rpois(10,10)) }). Once you've set your deck, play around with the mode, confidence level, number of bootstrap rounds, and total rounds to glean insights into the chosen distribution's performance. You might also find it enlightening to think about the side-by-side comparison of the bootstrap p-value and Welch's p-value as you play with the settings.

A tip for enthusiasts: Repetitively playing the game with consistent settings (except for the seed) mimics a manual simulation study, which can offer profound insights if you set the deck up to sample from a distribution that is meaningful to you.