II. Statistical power

to. Define type I and type II error and their relationship to statistical significance and statistical power.

b. The government wants to test the effect of a preventive health program on infant mortality in rural areas. Currently infant mortality is 14/1000 with2 = 0.0003. They are only interested in launching the program if it lowers infant mortality by at least 10/1000 (e.g., because other cheaper interventions are available that achieve that drop). With how many participants would they have to test this program to identify this effect with 5% significance and 80% statistical power? (They can use the critical values of the normal distribution.)

c. Suppose we want to test the effect of 15 different diets (eg 15 small independent experiments and 15 independent t-tests). Suppose there were really no effects, that is, in all 15 tests, the null hypothesis is true. With statistical significance of 5%, what is the probability of having at least one false positive? How can this statistical significance be 'corrected'?

d. Comment on the danger of "cherry picking," and on the protocols in academia for greater transparency in the social sciences.