The "likelihood of missing an association" refers to Type II error. The risk of Type II error is represented by beta. This could be confused with power, which is 1 - beta.

Type II error (β) Stating that there is not an effect or difference when one exists (null hypothesis is not rejected when it is in fact false).

β is the probability of making a type II error. β is related to statistical power (1 – β), which is the probability of rejecting the null hypothesis when it is false.

Increase power and Decrease β by: Increased sample size Increased expected effect size Increased precision of measurement

Also called false-negative error. β = you blindly let the guilty man go free.

If you increase sample size, you increase power. There is power in numbers.

This figure helps a lot! https://stats.stackexchange.com/questions/7402/how-do-i-find-the-probability-of-a-type-ii-error

null hypothesis is divided into two type, true or false

null hypothesis is true-> H0, null hypothesis is false-> H1, when you accept H1, it is β error, when you reject H1(false), it is true(=power=1-β )

so, no association between caffeine and pancreas cancer, it is H0(-> all H0 are no association, no difference in default).

an association between caffeine and pancreas cancer, it is H1 -> missing in H1-> β error