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Chapter 10--Hypothesis Testing--Categorical Data

# The hypothesis is that the risk of breast cancer

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Unformatted text preview: 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. 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 Example Cont’d... We have two independent samples here. Let p1 be the probability that age at ﬁrst birth is ≥ 30 in case women with at least one birth. Let p2 be the probability that age at ﬁrst birth is ≥ 30 in control women with at least one birth. The hypothesis of interest is then H0 : p1 = p2 = p vs Ha : p1 = p2 . The null hypothesis says,to be over 30 at ﬁrst birth is equally like in the two groups. There are two approaches: 1 2 Approximate Methods (Normal-Theory or Contingency-Table Methods) Fisher’s-Exact Method 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 Normal-Theory Method The best estimator of p1 − p2 is p1 − p2 , the diﬀerence in the ˆ ˆ sample proportions. The large-sample sampling distribution of p1 − p2 when H0 is ˆ ˆ true is 1 1 · (ˆ1 − p2 ) ∼ N 0, p (1 − p )( + )...
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