Chapter 10--Hypothesis Testing--Categorical Data

# We reject h0 if x 2 2r 1c 11 and 2 p value p 2r 1c

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Unformatted text preview: able using the expected frequencies. 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 Test for Homogeneity of Proportions cont’d... We compare the observed table with the expected table. The more diﬀerence between the tables, the more evidence against H0 . Let R and C represent the number of rows and columns (R = 2 and C = 5 in the previous example). The chi-square statistic R C X2 = i =1 j =1 (Oij − Eij )2 H0 2 ∼ χ(R −1)×(C −1) Eij when no more that (1/5)th of the expected frequencies are < 5 and none of the expected frequencies is < 1. We reject H0 if X 2 > χ2R −1)×(C −1),1−α and ( 2 p −value = P (χ2R −1)×(C −1) > Xcomputed ). ( 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 Test for Homogeneity of Proportions: Rcode There are two ways of conducting the chi-square test. Entering the frequencies as a matrix freq<-matrix(c(320,1206,1011,463,220,1422,4432, 2893,1092,406),nrow = 2, ncol = 5, byrow = TRUE) HT<-chisq.test(x=freq) HT HT\$expected We can also have x as a vector containing age at ﬁrst birth and y as a vector of indicators of case-control status. Example: Assess the statistical signiﬁcance of the data for the case-control study. 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 Chi-Square Goodness-of-Fit Test In Chapters 6, 7 and 8, we assumed that the data came from an underlying probability model. I...
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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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