1. Education 793 Class Notes Cross-tabulations Presentation 3

2. 2 Review Descriptive Statistics Descriptive Statistics we have covered –Central Tendency –Measures of Spread Suppose you have nominal data. 1=Catholic, 2=Jewish, 3=Muslim, 4=Hindu, 5=Protestant, 6=Buddhist Is it meaningful to report a mean as a descriptive measure?

3. 3 One-dimensional: Frequency Tables It is more meaningful to know the percentage of each type. This process divides the sample into subgroups for further study Sample Size=100 –40% Protestant –18% Catholic –10% Jewish –20% Muslim – 6 % Hindu – 6% Buddhist

4. 4 Two-dimensional: Crosstabs With two nominal/ordinal variables we can examine the two, one-dimensional frequency tables and we can examine the joint contingency table to look at the relationship between the two variables. Example: From the 1986 CIRP data –Variable 1: Students views on the statement “Married women are best in the home” –Variable 2: Students’ sex

5. 5 One-dimensional Tables

6. 6 Information to Glean What do we learn from the one- dimensional tables? What types of questions should we raise?

7. 7 Two-dimensional Table Column Percents get file cirp8690.sav. crosstab view8612 by sex86 /cells=count row column. VIEW8612 MARRIED WOMEN BEST IN HOME by SEX86 STUDENT'S SEX SEX86 Page 1 of 1 Count | Row Pct |MALE FEMALE Col Pct | Row | 1 | 2 | Total VIEW8612 --------+--------+--------+ 1 | 762 | 1590 | 2352 DISAGREE STRONG | 32.4 | 67.6 | 55.1 | 36.4 | 73.1 | +--------+--------+ 2 | 889 | 343 | 1232 DISAGREE SOME | 72.2 | 27.8 | 28.9 | 42.5 | 15.8 | +--------+--------+ 3 | 343 | 170 | 513 AGREE SOME | 66.9 | 33.1 | 12.0 | 16.4 | 7.8 | +--------+--------+ 4 | 97 | 72 | 169 AGREE STRONG | 57.4 | 42.6 | 4.0 | 4.6 | 3.3 | +--------+--------+ Column 2091 2175 4266 Total 49.0 51.0 100.0

8. 8 Two-dimensional Table Row Percents VIEW8612 MARRIED WOMEN BEST IN HOME by SEX86 STUDENT'S SEX SEX86 Page 1 of 1 Count | Row Pct |MALE FEMALE Col Pct | Row | 1 | 2 | Total VIEW8612 --------+--------+--------+ 1 | 762 | 1590 | 2352 DISAGREE STRONG | 32.4 | 67.6 | 55.1 | 36.4 | 73.1 | +--------+--------+ 2 | 889 | 343 | 1232 DISAGREE SOME | 72.2 | 27.8 | 28.9 | 42.5 | 15.8 | +--------+--------+ 3 | 343 | 170 | 513 AGREE SOME | 66.9 | 33.1 | 12.0 | 16.4 | 7.8 | +--------+--------+ 4 | 97 | 72 | 169 AGREE STRONG | 57.4 | 42.6 | 4.0 | 4.6 | 3.3 | +--------+--------+ Column 2091 2175 4266 Total 49.0 51.0 100.0

9. 9 Information to Glean What do we learn from the two-dimensional table? Which percents do we want to read? Column percents? Row percents? Defining the population of interest. –Interested in differences between men and women OR –Interested in differences between ageer-ers and disagree-ers

10. 10 Findings The two-way contingency tables are the first step in the process of discovering the factors that determine these proportions. Example: Women are more likely to disagree strongly that “Married women are best in the home” and Men are more likely to disagree somewhat. Thus, we may begin to infer that based on our sample, men in general hold more conservative views on the roles of women. (Sex matters when we consider peoples’ views on women’s roles).

11. 11 Higher Order Tables You can continue to add layers to the tables with 3 or more variables simultaneously examined. Example: Sex and Views on the Roles of Women by Political Beliefs. We will get three separate tables, sex by views for liberals, middle of the road, and conservatives.

12. 12 What do we find?

13. 13 Laptop Exercise Choose two nominal/ordinal variables Formulate a research question about the relationship between the two variables Display frequencies and crosstabs on the two variables Summarize your findings

14. 14 Next Week Normal Distribution: Chapter 5, p 115-136