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

Hi Chris,

In my workshops I use to give this example:

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 :

❝ 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 :

`pbinom(0, 1, 1/2)`

[1] 0.5

`pbinom(1, 2, 1/2)`

[1] 0.75

**OR**-conjunction you have to adjust the level of the test.—

Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

Science Quotes

*Dif-tor heh smusma*🖖🏼 Довге життя Україна!_{}Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

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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

- AND or OR, that’s the question chrisk 2022-08-12 16:02

- AND or OR, that’s the question Helmut 2022-08-11 15:25

- AND or OR, that’s the question chrisk 2022-08-10 22:00

- AND or OR, that’s the questionHelmut 2022-08-10 20:59

- AND or OR, that’s the question chrisk 2022-08-10 17:46

- AND or OR, that’s the question Helmut 2022-08-10 15:58

- Sample size for 3-way crossover chrisk 2022-08-10 15:24

- Sample size for 3-way crossover Helmut 2022-08-10 11:30