I’m shopping for luggage so the thing I care the most about is it breaking the first or second time I use it. I defined 1 or 2 stars as “bad” and 3, 4, or 5 stars as “not bad.” I was comparing two different suitcases that were the same manufacturer, size, and line but one was spinner and one was rollaboard. I preferred the rollaboard, but the reviews were higher for the spinner. The rollaboard had 23 reviews with three 1 star reviews (all of which said it broke the first time they used it). The spinner had 83 reviews with no 1 stars, but one 2 star review. So those probabilities of a negative review are pretty different, but the rollaboard only had 23 reviews so I wasn’t sure. That’s why I did the test.

Before revealing the p-value (which you can now calculate yourself if you feel inclined), what do you guys think? Fisher’s null is that the samples are pulled from the same binomial distribution. What’s your guess before calculating? Do you think we can reject here? I wasn’t sure because of the small sample size - I’m curious about your a priori take.

Is the rollaboard better than the spinner? I’m going to approach this with a little bit of bootstrap.

rollaboard = c(rep(TRUE, 20), rep(FALSE, 3))
spinner = c(rep(TRUE, 80), rep(FALSE, 1))

trials = 100000
n_rollaboard_is_better = 0
for(i in 1:trials) {
  rollaboard_is_better = mean(sample(rollaboard, replace=TRUE)) > 
                         mean(sample(spinner, replace=TRUE))
  
  n_rollaboard_is_better = n_rollaboard_is_better + rollaboard_is_better
}

p_rollaboard_is_better = n_rollaboard_is_better / trials

p_rollaboard_is_better
## [1] 0.02823

The probability that the rollaboard is better ~0.028.