Further Stats- Quality of tests

Type I error

Ho incorrectly rejected.

Type I error is same as

Significance level of test. Usually small.

Type II error

Ho is incorrectly accepted. Actual value of parameter p is required.

Type II error same as

Acceptance region for true parameter. Usually larger.

Type I error for continuous distribution

Equal to significance level

Size of a test

Probability of rejecting Ho, when true. Same as Type I error.

Power of a test

Probability of rejecting Ho when false. Equal to 1-P(Type II)

Power when correct decisions are being made more often than not

Power > 0.5

What increases power?

Increasing sample size and significance level

Power function of a test

Function of parameter p, which gives probability that test statistic fill fall in critical region of test, if p is true value of parameter.

Which power is better

Test with a higher power is better.