Chapter 10--Hypothesis Testing--Categorical Data

Assess whether this dierence is signicant or simply

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Unformatted text preview: d that among women with at least one birth: 683 of 3220 (21.2%) women with breast cancer (case women) and 1498 of 10,245 (14.6%) women without breast cancer (control women) had an age at first birth ≥ 30. Assess whether this difference is significant or simply due to chance. State your conclusion. (2) Cardiovascular Disease. A study looked at the effects of OC use on heart disease in women 40 to 44 years of age. The researchers found that among 5,000 current OC users at baseline, 13 women developed a myocardial infarction (MI) over a three-year period, where as among 10,000 non-OC users, 7 developed an MI over a 3-year period. Assess the statistical significance of the results. 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 Contingency-Table Method The data for the cardiovascular example can be presented as follows: OC use status User Non user Total MI status Yes 13 7 20 over 3 years No 4987 9993 14980 Total 5000 10000 15000 This table is known as a 2 × 2 contingency table. The row totals (row margins) are fixed and known. 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 Yates-Corrected Chi-Square Test Let Oij be the observed frequency of cell (i , j ). Under H0 , the expected cell frequencies, denoted by Eij , are E11 = n1 p , ˆ E12 = n1 (1−p ) ˆ E21 = n2 p ˆ and E22 = n2 (1−p ) ˆ The test statistic is X2 = (|O11 − E11 | − 0.5)2 (|O12 − E12 | − 0.5)2 + E11 E12 (|O21 − E21 | − 0.5)2 (|O22 − E22 | − 0.5)2 + + E21 E221 For large n1 and n2 , more specifically expected cell frequencies H0 at least 5, X 2 ∼ χ2 . 1 Chapter 10: Hypothesis Testing: Categorical Data Stat 491: Biostatis...
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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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