Counting the Significant Findings

Hypothesis TestingHard+30 XP+30

A screening lab runs $20$ independent hypothesis tests, each at significance level $\alpha = 0.05$ .

Unknown to the lab:

in $12$ of the tests the null hypothesis is genuinely true — there is no real effect;
in the remaining $8$ tests a real effect is present, and at that effect size each of those tests has power $0.80$ .

A test is called statistically significant when it rejects $H_0$ .

What is the expected number of the 20 tests that come out statistically significant?

Select all that apply.

Type I / II Errors and Power

Effect Size (d):2.0

Significance (α):

Type I Error (α): 0.05

Type II Error (β): 0.361

Power (1 - β):

63.9%

Type I Error (α) is rejecting H₀ when it is true.
Type II Error (β) is failing to reject H₀ when it is false.
Power (1 − β) is the probability of correctly rejecting H₀. Increasing sample size or effect size increases power.