Chapter 10--Hypothesis Testing--Categorical Data

# For one sided test replace 2 with chapter 10

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Unformatted text preview: ation of Sample Size and Power R × C Contingency Tables Chi-Square Goodness-of-Fit Test The Kappa Statistic Independent Samples Suppose it is anticipate that k times as many people as in group 1 will be enrolled in group 2. 2 n1 = 1 pq 1 + ¯¯ z1−α/2 + k p2 q2 p1 q1 + z1−β k /∆2 where ∆ = |p1 − p2 |, p = (p1 + kp2 )/(1 + k ), q1 = 1 − p1 , ¯ q2 = 1 − p2 and q = 1 − p . ¯ ¯ Power Achieved Power = P Z ≤ ∆ p1 q1 /n1 + p2 q2 /n2 − z1−α/2 p q (1/n1 + 1/n2 ) ¯¯ p1 q1 /n1 + p2 q2 /n2 where p = (n1 p1 + n2 p2 )/(n1 + n2 ), ∆, q , q1 and q2 are as ¯ ¯ deﬁned before. For one sided test, replace α/2 with α. Chapter 10: Hypothesis Testing: Categorical Data Stat 491: Biostatistics Introduction Two-Sample Test for Binomial Proportions McNemar’s Test Estimation of Sample Size and Power R × C Contingency Tables Chi-Square Goodness-of-Fit Test The Kappa Statistic Examples: Cancer, Nutrition Suppose we know from Connecticut tumor-registry data that the incidence rate of breast cancer over a 1-year period for initially disease-free women ages 45-49 is 150 cases per 100,000. We wish to study whether ingesting large doses of vitamin E in capsule form will prevent breast cancer. The study is set up with (1) a control group of 45- to 49-year-old women who are mailed placebo pills and are expected to have the same disease rate as indicated in the Connecticut tumor-registry data and (2) a study group of similar-age women who are mailed vitamin E-pills and are expected to have a 20% reduction in risk. How large a sample is needed if a two-sided test with a signiﬁcance level of .05 is used and a power of 80% is desired? Chapter 10: Hypothesis Testing: Categorical Data Stat 491: Biostatistics Introduction Two-Sample Test for Binomial Proportions McNemar’s Test Estimation of Sample Size and Power R × C Contingency Tables Chi-Square Goodness-of-Fit Test The Kappa Statistic Otolaryngology Suppose a study comparing a medical and a surgical treatment for children who have an excessive number of episodes of otitis media(OTM) during the ﬁrst 3 years of life is planned. Success rate of 50% and 70% are assumed in the medical and surgical groups, respectively, and the recruitment of 100 patients for each group is realistically anticipated. Succ...
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## This note was uploaded on 02/03/2014 for the course STAT 491 taught by Professor Solomonharrar during the Fall '12 term at Montana.

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