AND or OR, that’s the question [Power / Sample Size]

posted by Helmut Homepage – Vienna, Austria, 2022-08-10 22:59 (115 d 15:25 ago) – Posting: # 23214
Views: 3,103

Hi Chris,

❝ But this exercise was still helpful since I naively expected the "OR" alternative to result in a smaller sample size compared with the "AND" alternative. I failed to realise that a type I error comes into play for the "OR" alternative, which explains a larger sample size (n=42 vs n=36).


[image]In my workshops I use to give this example:
  1. You toss a single ideal coin once and place a bet on heads (or tails, doesn’t matter). What’s the chance to win? Obviously ½.
  2. You toss it a second time and place the same bet as before. The chance to win this bet is again ½ (coins have a short memory span).
    What is the chance to win at least one of the bets?

❝ Thank you also for modifying the R program. I sincerely appreciate your time and efforts.


Welcome. I would suggest to use the original one because it is more flexible and shows the seed for reproducibility / documentation.



Answers based on the cumulative probability of the binomial distribution (hint: Bernoulli process). In [image]:
  1. pbinom(0, 1, 1/2)
    [1] 0.5

  2. pbinom(1, 2, 1/2)
    [1] 0.75
Trivial: The more often you try, the more likely is the chance to win at least one of the bets. Therefore, coming back to BE: In the OR-conjunction you have to adjust the level of the test.

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