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 (H 0 is true (H0) is false
Type I error =>
reject H0 when it
is true
Reject null Correct outcome
hypothesis False positive True positive
Falsely
convicting an
innocent person
Type II error =>
failing to reject H0
when its false
Fail to
Correct outcome
reject null True negative
hypothesis 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) - alpha level
- alpha = P(Type I error)
- beta = P(Type II error)
- power: 1 - beta = P(correctly rejecting H0 when it is false)
- can decr. chances of making one error by incr'ing chances of making another
- to lower BOTH chances, INCREASE SAMPLE size (ie. collect more data)
- alpha, beta are used to determine sample size needed
=====================================
WHERE ARE WE GOING?
- the reader can decide on their own whether the results of the study are statistically
signif by examining the study's
- hypo.'s (HA, H0)
- concluions from hypo test, how it relates to context
- pt of this chap: in-depth exmainaiton of hypo tests
main text, p554

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