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Unformatted text preview: CHAPTER 8: CHI-SQUARE TESTS 8.1 INTRODUCTION The Chi-square ( 2 ) test may be used when we want to investigate if there exists an association between two categorical variables or one qualitative variable and one quantitative variable . The symbol 2 is often used rather than the term chi-square . The Greek letter is pronounced chi . The first chi-square procedure studied here is the chi-square goodness-of-fit test . The chi-square goodness-of-fit test can be used when one is testing to see whether a frequency distribution fits a specific pattern . For example, to meet customer demands, the Baylor University bookstore manager may wish to see whether buyers show a preference for some specific brands of hand calculators than others, so that she can increase orders of those items accordingly. If there is no preference, it means that each brand of hand calculator is bought with the same frequency. The second procedure studied is the chi-square independence test . It is a hypothesis test used to decide whether an association exists between two characteristics of a population. For instance, we could apply that test to a sample of U.S. adults to decide whether an association exists between annual income and educational level for all U.S. adults. The third procedure studied is the chi-square homogeneity of proportions test . The homogeneity of proportions test is used when samples are selected from several different populations and the researcher is interested in determining whether the proportions of elements that have a common characteristic are the same for each population. The sample sizes are specified in advance, making either the row totals or column totals in the contingency table known before the samples are selected. For example, a researcher may select a sample of 80 freshmen, 80 sophomores, 80 juniors, and 80 seniors and then find the proportion of students who own domestic cars. The researcher might then use the homogeneity of proportions test to compare the proportions for each grade level in order to see whether they are equal or not. 8.2 THE CHI-SQUARE DISTRIBUTION A variable is said to have a chi-square distribution if its distribution has the shape of a special type of right-skewed curve called a chi-square ( 2 ) curve . The following is the plot of the chi-square probability density function for 4 different values of the shape parameter. Dr. LOHAKA QBA 2305 CHAPTER 8: CHI SQUARE TESTS Page 1 Properties of the chi-square ( 2 ) distribution The distribution of the 2-statistic has some of the following basic properties: Its density curve (total area under the curve) is equal to one (1). Its curve is always right skewed....
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