Chapter 10--Hypothesis Testing--Categorical Data

chi square distribution is a family of skewed

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Unformatted text preview: tics 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 Normal-Theory Method Fisher’s-Exact Test Yates-Corrected Chi-Square Test Cont’d... Chi-Square distribution is a family of skewed distributions indexed by the degrees of freedom. In R, a 100 × u percentile of a chi-square distribution with d degrees of freedom, denoted by χ2 ,u can be obtained by using d qchisq(u,d) Probabilities (area under the curve) of a chi-square can be obtained using the pchisq command. Compute χ2,0.025 , χ2,0.975 , P (χ2 < 7) and P (χ2 > 10). 9 9 6 9 Returning to Yates-Corrected Chi-Square test, we reject H0 if 2 X 2 > χ2,1−α and p-value is P (χ2 > Xcomputed ). 1 1 This Chi-Square test is always a two-sided test despite using 100(1 − α)th percentile of chi-square. 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 Normal-Theory Method Fisher’s-Exact Test Fisher’s-Exact Test This test is applicable when any of the expected frequencies is less than 5. Example: Suppose a retrospective study is done among men ages 50-54 in a specific county who died over a 1-month period. The investigators try to include approximately an equal number of men who died from Cardiovascular disease (the case) and men who died from other causes (the control). Of 35 people who died from CVD, 5 were on high-salt diet before they died, whereas of 25 people who died from other cause 2 were on such a diet. 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 Normal-Theory...
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