Chapter 10--Hypothesis Testing--Categorical Data

# Chapter 10--Hypothesis Testing--Categorical Data -...

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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 Stat 491: Biostatistics Chapter 10: Hypothesis Testing: Categorical Data Solomon W. Harrar The University of Montana Fall 2012 Chapter 10: Hypothesis Testing: Categorical Data Stat 491: Biostatistics

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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 Categorical Data Data classified into categories (ordered or unordered). Methods include a. Two-Sample Test for Binomial Distribution b. Tests of Association and Homogeneity c. Goodness-of-Fit Test d. The Kappa Statistic In the first half of the chapter, we focus on the case when the number of categories is two (yes/no, present/Abset, diseased/disease free...). Therefore we consider comparison of two proportions from independent or paired samples. 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 Hypotheses and Tests Assume p 1 and p 2 be the prevalence of the attribute in the populations from which the two samples are drawn. The hypotheses of Interest H 0 : p 1 = p 2 = p vs H a : p 1 6 = p 2 where p is unknown. The test to be used depends on whether the samples are independent or paired. a. Independent Samples i. Normal-Theory Method or Contingency-Table Method ii. Fisher’s-Exact Test b. Paired Samples (McNemar’s Test) i. Normal-Theory Method ii. Exact Test Chapter 10: Hypothesis Testing: Categorical Data Stat 491: Biostatistics

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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 Example A hypothesis has been proposed that breast cancer in women is caused in part by events that occur between the age at menarche (the age when menstruation begins) and the age at first childbirth. The hypothesis is that the risk of breast cancer increases as the length of this time interval increases. If this theory is correct, then an important risk factor for breast cancer is age at first birth. An international study was set up to test this hypothesis. Breast-cancer cases were identified among women in selected hospitals in the United States, Greece, Yugoslavia, Brazil, Taiwan and Japan. Controls were chosen from women of comparable age who were in the hospital at the same time as the cases but who did not have breast cancer. All women were asked about their age at first birth.
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