Bioequivalence and Bioavailability Forum • AND or OR, that’s the question

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

posted by Helmut – Vienna, Austria, 2022-08-10 22:59 (617 d 04:26 ago) – Posting: # 23214
Views: 4,877

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).

In my workshops I use to give this example:

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.
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]

pbinom(0, 1, 1/2) [1] 0.5
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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Helmut Schütz

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Complete thread:

Sample size for 3-way crossover chrisk 2022-08-09 18:55 [Power / Sample Size]
- Sample size for 3-way crossover Helmut 2022-08-10 11:30
  - Sample size for 3-way crossover chrisk 2022-08-10 15:24
    - AND or OR, that’s the question Helmut 2022-08-10 15:58
      - AND or OR, that’s the question chrisk 2022-08-10 17:46
        
        AND or OR, that’s the questionHelmut 2022-08-10 20:59
        
        AND or OR, that’s the question chrisk 2022-08-10 22:00
        
        AND or OR, that’s the question Helmut 2022-08-11 15:25
        
        AND or OR, that’s the question chrisk 2022-08-12 16:02
        
        The unknown ρ Helmut 2022-08-17 15:04