1Bivariate Analysis - Crosstabulation• One of most basic research tools –shows how x varies with respect to y• Interpretation of table depends upon “direction of percentaging”•exampleRow vs. Column Percents119. A. The United States Supreme Court has ruled that no state or local government may require the reading of the Lord's Prayer or Bible verses in public schools. What are your views on this--do you approve or disapprove of the court ruling? 100.00 100.00 100.00 100.00 100.00 100.00 21.95 52.11 5.44 13.88 6.62 100.00 Total 5,468 12,980 1,355 3,457 1,649 24,909 72.71 63.04 58.01 43.82 35.48 60.40 26.43 54.39 5.22 10.07 3.89 100.00 DISAPPROVE 3,976 8,183 786 1,515 585 15,045 27.29 36.96 41.99 56.18 64.52 39.60 15.13 48.63 5.77 19.69 10.79 100.00 APPROVE 1,492 4,797 569 1,942 1,064 9,864 SCHOOLS LT HIGH S HIGH SCHO JUNIOR CO BACHELOR GRADUATE Total PUBLIC RS HIGHEST DEGREE PRAYER IN BIBLE column percentage row percentage frequency Key . tab PRAYER DEGREE, row colRow vs. Column Percents 100.00 100.00 100.00 100.00 100.00 100.00 Total 32.87 51.14 5.36 7.46 3.17 100.00 78.56 74.29 72.93 68.65 58.88 74.71 DISAPPROVE 34.56 50.85 5.23 6.86 2.50 100.00 21.44 25.71 27.07 31.35 41.12 25.29 APPROVE 27.87 51.99 5.74 9.25 5.15 100.00 SCHOOLS LT HIGH S HIGH SCHO JUNIOR CO BACHELOR GRADUATE Total PUBLIC RS HIGHEST DEGREE PRAYER IN BIBLE column percentage row percentage Key -> RACE = B 100.00 100.00 100.00 100.00 100.00 100.00 Total 20.08 52.64 5.38 14.78 7.10 100.00 71.61 61.70 55.57 41.53 34.09 58.41 DISAPPROVE 24.62 55.60 5.12 10.51 4.15 100.00 28.39 38.30 44.43 58.47 65.91 41.59 APPROVE 13.71 48.49 5.75 20.79 11.26 100.00 SCHOOLS LT HIGH S HIGH SCHO JUNIOR CO BACHELOR GRADUATE Total PUBLIC RS HIGHEST DEGREE PRAYER IN BIBLE column percentage row percentage Key -> RACE = W . by RACE, sort : tabulate PRAYER DEGREE, column nofreq row2Reading Tables - Basics•What’s the difference between 20% and 30%?•What do row, column, and total percents tell you?•Why are percent distributions more informative than distributions of raw numbers?•Always best to either show or mention your numbers – two forms of info clearer than one.ExampleAttitudes towards Women's Work10.430.559.211.53751.5010203040506070WORK FULL-TIME WORK PART-TIME STAY HOMEPercentMen WomenExample before recodingAttitudes toward Women's Work, by Education020406080100Work Full-Time Work Part-Time Stay HomePrecent0 1 3 4 5 6 7 8 9 10 11 12 13 14 1516 17 18 19 203Example after recodingAttitudes toward Women's Work, by Education103259123058103951123751010203040506070Work Full-Time Work Part-Time Stay HomePercent0-11 12 13-15 16-20Extensions• Three-way crosstabulations– Web: use the “control” option– Stata: use “by” or “table”• Crosstabulations for subsample– Web:use the “filter” option– Stata: use the “if” option• Example: Educational differences in attitudes toward women’s roles – could do either way(wrkbaby x educ x sex or wrkbaby x educ if sex=male).Chi-square statistic –Introduction• Chi-square statistic is useful for testing statistical significance of relationships in crosstabulations, or contingency tables. • Contingency tables: tables cross-classifying categoricalvariables. • 2-way and 3-way (involving two or three variables.4Chi-square statistic• Chi-square statistics reported by a cross-tabulation tests the hypothesis that the row variable and the column variable are independent of each other. If they are independent, joint probabilities can be determined by marginal probabilities. –(Ni+/N++) x (N+j/N++) • For a two-way contingency table of dimension IxJ, the degrees of freedom are (I-1)(J-1). • A large chi-square rejects the hypothesis. Larger the chi-square => the stronger the evidence against independence => the stronger the relationship. • Example of religious homogamy.Chi-square statistic Pearson chi2(16) = 1.7e+03 Pr = 0.000 741.0 344.0 33.0 106.0 28.0 1,252.0 Total 741 344 33 106 28 1,252 20.1 9.3 0.9 2.9 0.8 34.0 OTHER (SPECIFY) 11 7 0 3 13 34 50.9 23.6 2.3 7.3 1.9 86.0 NONE 19 19 4 41 3 86 16.6 7.7 0.7 2.4 0.6 28.0 JEWISH 1 2 22 2 1 28 196.5 91.2 8.8 28.1 7.4 332.0 CATHOLIC 51 256 4 19 2 332 456.9 212.1 20.3 65.4 17.3 772.0 PROTESTANT 659 60 3 41 9 772 PREFERENCE PROTESTAN CATHOLIC JEWISH NONE OTHER (SP Total RS RELIGIOUS RS SPOUSE'S RELIGION expected frequency frequency Key . tabulate RELIG RELIGSP, chi2 expectedComparison of means• Like crosstabulations but better for continuous (i.e., interval) variables.• Example: Mean age at first marriage by sex and race (agewed x sex x race)5Comparison of meansMean age at Marriage, by Sex and Race23.621.023.820.525.121.915171921232527MALE FEMALEAge at marriageWhite Black OtherRegression: Concepts• In
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