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Chapter 10 Notes (1)

Chapter 10 Notes (1) - Fmﬂl Evin Scotch/0n ‘5 Exam...

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Unformatted text preview: / Fmﬂl Evin Scotch/0n ‘5, Exam “Lad Comte/leer Chapter 10 - Comparing Two Groups W est comparisons of groups use independent samples from the groups: > The observations in one sample are independent of those in the other sample I Example: Randomized experiments that randomly allocate subjects to two treatments 0 Example: An observational study that separates subjects into groups according to their value for an explanatory variable Dependent Samples Dependent samples result when the data are matched pairs - each subject in one sample is matched with a subject in the other sample 0 Example: set of married couples. the men being in one sample and the women in the other. 0 Example: Each subject is observed at two times. so the two samples have the same subject How Can We Compare Two Proportions? Standard Error tee.) for Comparing Two Prowrtions > The difference (I51 - 1') j is obtained from sample data > It will vary from sample to sample > This variation is the standard error of the sam lin distribution of ([3. — I32) Confidence Interval for the Diﬂerence between Two Population Promrtions * ~ ‘ . fad-[2,) ,6,(l—[;Z) (pl—P2)iZ(S.€.) ’ (pl—pz)tz _n_l....._+ "2 The z-score depends on the conﬁdence level 0 This method requires: pomi CSi'tmél-l'f, 1: m1, _ - Categorical response variable for two groups - Independent random samples for the two groups - Large enough sample sizes so that there are at least l0 “successes” and at least 10 “failures" in each group Interpreting 3 Conﬁdence IntervaltCI) for a Difference of Proportions Check whether 0 falls in the CI If so. it is plausible that the population proportions are equal If all values in the CI for (pl- p2) are positive, you can infer that (pl- 1);) >0 If all values in the CI for (p]- p2) are negative, you can infer that (p.- p;) <0 Which group is labeled ‘1‘ and which is labeled ‘2' is arbitrary The magnitude of values in the conﬁdence interval tells you how large any true difference is If all values in the conﬁdence interval are near 0. the true difference may be relatively small in practical terms ignificance Tests Comparing Population Proportions Assum tions: 0 Categorical response variable for two groups 0 Independent random samples 0 Signiﬁcance tests comparing proportions use the sample size guideline from conﬁdence intervals: Each sample should have at least about to “successes" and 10 "failures" 0 Two—sided tests are robust against violations of this condition 0 At least 5 “successes" and 5 “failures" is adequate ...
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