Hypothesis Testing

Hypothesis Testing

• We talked about this the first day.• Let’s talk more about it now.• Four steps:

– Formulate Null hypothesis and Alternative hypothesis (hypothesis)– Obtain sampling distribution and rejection regions (population)– Calculate test statistic from your data (sample)– Compare the test statistic to rejection regions

(if within rejection region, then significant)

Hypothesis

• Formulate Null and Alternative hypothesis

– Null hypothesis H0 : Population means equal

• If two groups: 1 =

• If three+ groups: 1 = ==

– Alternative hypothesis: H1 : mean NOT equal

• If two groups:: 1 ≠

• If three+ groups: 1 ≠ ≠≠

As a researcher, you want to reject the “null”.

Errors in Hypothesis TestingREALITY

OU

TP

UT

FR

OM

SP

SS

H0 is true (n.s.)

Reject H0

(sig)

H0 is false (sig)

Fail to Reject

H0

(n.s.)

Probability =

Probability = (1 - ) (test statistic is not in

Rejection region)

(test statistic is in

Rejection region)Type I error, or “False Alarm”

Correct Decision

Probability = (1 -

Probability =

Correct Decision

Type II error,or a “miss”

POWER

Factors Increasing Power:

(1) Increasing alpha level (e.g., .05 to .09)

(2) Increasing difference between means

(3) Reducing between-group variation

(4) Increasing sample size