Chapter 10--Hypothesis Testing--Categorical Data

We estimate these parameters from the data by x and s

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Unformatted text preview: n this section, we consider a general method of testing for the goodness of ﬁt of a probability model. Example: The frequency distribution of diastolic blood pressure of 14,736 adults ages 30-69 in East Boston, is given below. Group (mmHg) < 50 ≥ 50, < 60 ≥ 60, < 70 ≥ 70, < 80 ≥ 80, < 90 ≥ 90, < 100 ≥ 100, < 110 ≥ 110 Observed Frequency 57 330 2132 4584 4604 2119 659 251 Expected Frequency We wish to test if this data came from a normal distribution. 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 Cont’d... Recall that the normal distribution is indexed by two parameters, µ and σ 2 . ¯ We estimate these parameters from the data by X and S 2 , the sample mean and variance. The expected frequency of the i th class, if the ﬁt is good, is Ei = n × P (Li ≤ X ≤ Ui ) where Li and Ui are the lower and upper class limits of the i th class. In our example, we take L1 = −∞ and U8 = ∞. 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 Cont’d... The agreement between the observed and expected frequencies can be quantiﬁed using g X2 = i =1 (Oi − Ei )2 H0 2 ∼ χg −1−k Ei where g is the total number of classes and k is the number of parameters in the model that had to be estimated. Reject H0 if X 2 > χ2 −1−k ,1−α and g 2 p −value = P (χ2 −1−k > Xcomputed ). g Use this test only if no more than (1/5)th of the expected frequencies are < 5 and none of them are < 1. 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 ×...
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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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