Let R be the ratio of the number of “true relationships” to “no relationships” among those tested in the field… The pre-study probability of a relationship being true is R/(R + 1).
What is the difference between “the ratio of the number of ‘true relationships’ to ‘no relationships’ among those tested in the field” and “the pre-study probability of a relationship being true”?
You could think of it this way: If R is the ratio of (combinations that total N on two dice) to (combinations that don’t total N on two dice), then the chance of (rolling N on two dice) is R/(R+1). For example, there are 2 ways to roll a 3 (1 and 2, and 2 and 1) and 34 ways to not roll a 3. The probability of rolling a 3 is thus (2/34)/(1+2/34)=2/36.
Question re: “Why Most Published Research Findings are False”:
What is the difference between “the ratio of the number of ‘true relationships’ to ‘no relationships’ among those tested in the field” and “the pre-study probability of a relationship being true”?
From Reddit:
You could think of it this way: If R is the ratio of (combinations that total N on two dice) to (combinations that don’t total N on two dice), then the chance of (rolling N on two dice) is R/(R+1). For example, there are 2 ways to roll a 3 (1 and 2, and 2 and 1) and 34 ways to not roll a 3. The probability of rolling a 3 is thus (2/34)/(1+2/34)=2/36.