Chapter 20 Learning Objective 1 Explain the purpose and importance of cross tabulation. Cross tabulation is the most commonly used multivariate technique. Its purpose is to study the relationships among and between categorical variables. Learning Objective 2 Describe how percentages should be calculated for a two-way cross tab. In a two-way cross-tab analysis, percentages should be calculated using the marginal totals for the independent variable as the denominator. Thus, percentages are calculated in the direction of the causal variable. Learning Objective 3 Describe how one determines if there is a statistically significant relationship between two categorical variables in a cross-tabulation table. The Pearson chi-square test of independence is used to determine whether or not two categorical variables are independent of one another. Cramer’s V is used to obtain an indication of the strength of the relationship between the categorical variables. Learning Objective 4 Discuss two techniques for examining associations among ordinal variables. When there are only two ordinal variables, the Spearman rank-order correlation coefficient is appropriate for assessing the degree of association between the rank order variables. Spearman’s rho can range from _1 to _1. When there are three or more ordinal variables, Kendall’s coefficient of concordance provides a measure of association between the ordinal variables; its value can range from 0 to 1. Learning Objective 5 Explain two techniques for comparing groups on dependent variables assessed on continuous measures. When there are only two groups, the independent samples t-test is used to determine if the mean score on the dependent variable for one group is significantly different than the mean score for the second group. If there are more than two groups, the analysis of variance technique, which compares the variance in dependent variable scores within groups with the variance in dependent variable scores between groups, is appropriate. Learning Objective 6 Explain the difference between an independent sample t-test for means and a paired sample t-test for means. In the independent samples t-test, mean scores on the dependent variable are compared for different groups of respondents. In a paired sample t-test, mean scores on two different variables (measured on similar scales) are compared across a single group (i.e., all respondents provide scores on both variables). Learning Objective 7 List three advantages of using analysis of variance versus conducting a series of ttests to examine differences across groups. The ANOVA technique (a) would be more efficient, requiring fewer computations; (b) would decrease the likelihood of a Type I error; and (c) would consider the joint effects of different independent variables. Learning Objective 8 Discuss two techniques for determining the degree of association between two continuous measures. One approach is to calculate the Pearson product moment correlation coefficient, which assesses the degree of linear association between the variables. Another approach is to use simple regression, a technique in which a mathematical equation is derived that relates a dependent variable to an independent variable. Learning Objective 9 Describe how multiple regression differs from simple regression. Simple regression and multiple regression differ in that only one independent variable is used to predict the dependent variable in simple regression, whereas more than one independent variable is included in multiple regression.