# STAB22H3 Chapter Notes -Type I And Type Ii Errors, Null Hypothesis, Statistic

CHAPTER 21 - MORE ABOUT TESTS

(HYPOTHESIS TESTS)

=> one-tailed, lower-tailed hypothesis

- INDEPENDENCE ASSUMPTION

- RANDOMIZATION CONDITION

- 10% CONDITION

- SUCCESS/FAILURE CONDITION

- link P-value to decision to H0, and state conclusion in context

- if H0 was true, wouldn't see prop this low, so reject H0

- strong evidence of decline in helmet use

- propose course of a'xn if possible

- ex. Florida legislators should consider change in law

- P-value = probab. that statistic observed is as far, or even farther from hypo val, given

that H0 is true

- P(observed statistic | H0 is true)

- ex. P(we observe 50.7% or less | p = 0.60)

- P-Value NOT equal to

- P(H0 is true | observed statistic)

- when P-value small, H0 is rejected, but doesn't prove it is false

- if P-value v.large, just means that what is observed was v.consistent w/ H0

- alpha-threshold

- P-value has to fall b4 deciding H0

- setting alpha level of the test (aka significance level of the test)

- common alpha levels - 0.05, 0.01, 0.001

- P-values below are said to be signif.

- meant to indicate relative strength against H0

Null hypothesis

Null hypothesis

(H0) is true

(H0) is false

Reject null

hypothesis

Type I error =>

reject H0 when it

is true

False positive

Falsely

convicting an

innocent person

Correct outcome

True positive

Fail to

reject null

hypothesis

Correct outcome

True negative

Type II error =>

failing to reject H0

when its false

False negative

Failing to convict

guilty person

- start by assuming H0 is true

- if error in that case, then thats type I

- other error can only occur if H0 false, and we fail to reject it (type II)

## Document Summary

Chapter 21 - more about tests (hypothesis tests) Link p-value to decision to h0, and state conclusion in context. If h0 was true, wouldn"t see prop this low, so reject h0. Strong evidence of decline in helmet use. P-value = probab. that statistic observed is as far, or even farther from hypo val, given that h0 is true. P(we observe 50. 7% or less | p = 0. 60) When p-value small, h0 is rejected, but doesn"t prove it is false. If p-value v. large, just means that what is observed was v. consistent w/ h0. P-value has to fall b4 deciding h0. Setting alpha level of the test (aka significance level of the test) Common alpha levels - 0. 05, 0. 01, 0. 001. P-values below are said to be signif. Meant to indicate relative strength against h0. Null hypothesis null hypothesis (h0) is true (h0) is false. Type i error => reject h0 when it is true.