Hypothesis Testing

H0

is trueH0

is false

Fail to reject H0

Reject H0

3/22/11Review:

A Type I error occurs when H0 is true but we reject it.

A Type II error occurs when H0 is false, but we fail to reject it.

3/22/11Goal: Be able to• understand the relationship between α, β, power, and effect.

H0

is trueH0

is false

Fail to reject H0

Reject H0

The probability of rejecting H0 is determined by the α-

levelIt’s also the probability

of a Type I error occurring.

The probability of failing to reject H0 is is called β.

You won’t need to calculate it for the AP exam.

The probability of NOT committing a Type II error is 1

– β.This is called the power of

the test.

Power and effect

Suppose we test the effect of a new running shoe.

Bob currently sprints 28 feet/sec without the new shoes. With the new shoes, he sprints 28.6 feet/sec.How many trials would you need to make that difference clear?

Suppose he sprints 56 ft/sec with the new shoes.How many trials would you need to make that difference clear?

With a small effect, you would want a larger sample.With a large effect, you could use a smaller sample.

Sample size and effect are the key elements of power.

3/22/11Homework:

#15 - 23 odd