Matching Appropriate Procedures and Test Statistics with Appropriate Levels of Measurement for Bivariate Analyses.* Independent Variables Nominal Ordinal Interval/Ratio Dependent Nominal Crosstabs Crosstabs with with Chi-square Variables • Chi-square • Chi-square • Lambda. • Lambda Ordinal Crosstabs Crosstabs with with • Chi-square • Chi-square • Lambda • Lambda • Gamma • Kendall’s tau • Sommers’ d Means with Means with Interval/ Correlate Ratio • t-test • t-test • Pearson’s r • ANOVA • ANOVA • Regression (R) * This is not an exhaustive table of possible relevant tests. It has been adapted from Babbie and Benaquisto (2002).
Matching Appropriate Procedures and Test Statistics with Appropriate Levels of Measurement for Multivariate Analyses. Independent Variables Multiple Independent Variables (Including Both Interval/Ratio Variables, and Categorical Variables Coded as binary dummy variables: 0 or 1.) Dependent Categorical where • Logistic Regression. Variables number of categories = 2 Categorical where number of • Multinomial Logistic Regression. categories > 2 Interval/ • OLS Multiple Regression. Ratio
Example: Crosstabulation with Chi-square (Two Nominal Variables). Table 1. Employment Status By Gender (in Percentages for Women and Men). Gender Women Men Full Time 43.2 65.9 Part Time 27.2 8.2 Employment Status Unemployed 3.7 2.4 Other 2.5 4.7 Retired 23.5 18.8 Total 100 100 N 81 85 � = 13.64, df = 4, p. < .01
Example: Intercorrelation Matrix (Three Interval/Ratio Level Variables). Table 2: Correlations Among Age, Education, and Personal Income. (N in parentheses.) Age Years of Personal Education Income Age ----- .23** .26** (177) (159) .23** ----- .42** Years of Education (177) (160) .26** .42** ----- Personal Income (159) (160) * p. � .05, ** p. � .01.
Example: Difference in Means with t-test (one nominal variable, three interval/ratio variables). Table 3. Means for Men and Women: Years of Experience, Years of Education, and Personal Income. Women Men Mean 8.90** 13.77** Years of Experience Standard Deviation 7.84 11.16 N 58 68 Years of Education Mean 14.95* 15.74* Standard Deviation 2.12 2.17 N 94 86 Personal Income Mean 24, 268** 46,968** Standard Deviation 19,098 26,451 N 82 80 Observed significance values associated with t-tests of differences in means: * p. � .05, ** p. � .01.
Example of Frequencies and Percentages (Ordinal Variable). Table 4. Frequencies and Percentages for Political Efficacy Item #1: Sometimes Politics and Government Seem So Complicated that a Person Like Me Can’t Really Understand What’s Going On. Frequency Percentage Strongly Disagree 7 35.0 Disagree 2 10.0 No Opinion 2 10.0 Agree 4 20.0 Strongly Agree 5 25.0 Total 20 100.0
Example of Means, Standard Deviations, and N (Interval/Ratio Variables). Table 5. Means, Standard Deviations, and N. Variable Mean Standard N Deviation Years of Experience 11.53 10.04 126 Years of Education 15.36 2.17 183 35,478 25, 620 162 Personal Income
Example of Percentages (Several Ordinal Variables) Table 6. Percentages for Responses to Political Efficacy Items. Strongly Disagree No Agree Strongly Disagree Opinion Agree 35 10 10 20 25 Item #1: Sometimes politics and government seem so complicated that a person like me can’t really understand what’s going on. Item #2: The political parties are 30 20 5 15 30 so big that I doubt I could influence them even if I were active in them. 25 20 10 20 25 Item #3: I believe that I can help to change the minds of public officials. Item #4: People like me don’t 35 15 0 20 30 have any say about what the government does. 35 15 5 20 25 Item #5: Generally, those elected to Parliament soon lose touch with people. 35 15 0 20 30 Item #6: So many other people vote in elections that it doesn’t matter much whether I vote or not. Item #7: I don’t think that the 35 15 0 10 40 government cares much what people like me think.
Example of Multiple Regression Analysis with Standardized Regression Coefficients. Table 7. Standardized Regression Coefficients for Models Predicting Environmentally Friendly Behaviour: Entire Sample . Independent Variables Model 1 Model 2 Model 3 Model 4 Model 5 Gender (1= male) - .11* - .12* - .12* ---- ---- Age - .23*** - .22*** - .14* - .24*** - .16** Education (squared) .20*** .19*** .14* .20*** .15* Income (log) - .08* - .08 - .11+ - .09 - .12* Parent (1 = parent) ---- .07 .07 ---- ---- Gendpar (female parent = 1) ---- ---- ---- .12* .12* Post Materialist Values Index ---- ---- - .01 ---- - .03 Frequency of Communication (log) ---- ---- .20*** ---- .19*** Activism ---- ---- .19*** ---- .18*** 2 R .09*** .09*** .19*** .11*** .20*** 2 Adjusted R .07*** .08*** .17*** .09*** .12*** + � .10 * p. � .05 ** p. � .01 *** p. � .005 N=254 N=254 N=254 N=257 N=257 --- Variable not included in equation.
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