Hypothesis testing and Decision Making Formal aspects of hypothesis testing

Null and Alternative Hypotheses Null hypothesis (H 0 ) sets the ‘what if’ for calculating probabilities Alternative hypothesis (H a ) sets the rejection region. Oddly enough, the alternative is usually what you have in mind to prove during the study.

Tails The rejection region can fit into 1 or 2 tails of the sampling distribution of means. The RR is determined by the alternative hypothesis. Two TailsOne Tail

Tails illustrated Two tails. One tail. Note 1.96 vs. 1.65

Example of 2 tails Suppose: Then: Note 5 percent is split into two tails.

Example of 1 tail Suppose: Note all 5 percent is at the top tail.

Review Suppose Draw sampling distribution of means.  What is the shape of this distribution?  What is the mean of this distribution?  What is the standard deviation of this distribution? Draw RR if

Statistical Decision Making Must decide how to act even if uncertain (developed by Fisher for agriculture) Make decisions like bets in gambling (null is false if null is improbable) If we do this, some times we will be right; sometimes wrong. We can calculate probabilities of mistakes and correct decisions. Some have names.

Decisions Null true Null False Accept Null Right, but… Beta (type II error) Reject Null Alpha (type I error) Correct rejection (power) Population Condition Sample Decision Fire alarmNo fireFire Alarm silent Right, but… Beta Alarm sounds AlphaCorrect rejection Three named probabilities: Alpha, beta, and power.

Researcher’s Choice We can pick alpha (but usually.05) We can improve power by  Good alternative hypothesis  Good design (minimize error)  Large samples

Review Define the following  Alpha  Beta  Power Why is it good to have alpha be a small number? Why is it good to have power be a large number?

Definition The alternative hypothesis sets the placement of the _____.  1 alpha  2 omega  3 rejection region  4 standard error

Definition Alpha refers to what kind of error?  1 descriptive  2 primary  3 type I  4 type II

Application A researcher can increase the _____ to increase the power of a study.  1 number of outcomes  2 sample size  3 standard error  4 study duration