1. In the Lab: Working With Crosstab Tables Lab: Association and the Chi-square Test Chapters 7, 8 and 9 1

2. Constructing Crosstab Tables Analyze | Descriptive Statistics | Crosstabs Rule of Thumb: – independent variable is column variable – dependent variable is row variable 2

3. Creating a Crosstab Table 3

4. Creating Crosstab Table and Adding Cell Percents 4

5. Describing Relationships Using Crosstab Tables Does what category a case is in on the independent variable make a difference for what category it will be in on the dependent variable? – Does the percent of cases in a particular category of the dependent variable change as you move through the categories of the independent variable? 5

6. Crosstabs Output with Column Percents for HAPPY by HEALTH for 1980 GSS Young Adults 6

7. Layering (for control) Lets you examine the relationship between the independent and dependent variables for separate groups of cases by adding another variable to the analysis A way of introducing a control variable into the analysis. 7

9. Association Is there an association between highest educational degree and overall happiness with life? How strong is the association? What is the pattern or direction – Nominal: What is the pattern of % – Ordinal: Is it a positive or a negative association? 9

10. About Measures of Association Purpose of measures of association Level of measurement 10 pair of variablestype of measure of association nominal & nominalnominal measure of association nominal & ordinalnominal measure of association nominal & interval/rationominal measure of association ordinal & ordinalordinal measure of association ordinal & interval/ratioordinal measure of association interval/ratio & interval/ratiointerval/ratio measure of association

11. About Measures of Association (cont.) Strength of an association – closer to zero, weaker; further from zero, stronger – guidelines used by text: 11 If the absolute value of a measure of association is: The association will be described as:.000No relationship.001 to.199Weak.200 to.399Moderate.400 to.599Strong.600 to.999Very strong 1.000Perfect relationship

12. Nominal Measures of Association Usual range: 0.00 to 1.00 Common nominal measures of association Can be symmetric or assymetric – Contingency coefficient symmetric – Cramer’s V symmetric – Lambda symmetric and asymmetric versions – Phi symmetric 12

13. Requesting Measures of Association when using Crosstabs 13

14. Crosstabs Output for WORKSTAT by SEX for 1980 GSS Young Adults

15. Ordinal Measures of Association Usual range: −1.00 to 1.00 Ordinal measures of association – Gamma symmetric – Somer’s d symmetric and asymmetric versions – Kendall’s tau-b symmetric – Kendall’s tau-c symmetric – Spearman’s correlation symmetric 15

16. Crosstabs Output for HAPPY by DEGREE for 1980 GSS Young Adults

17. Using Chi-Square to Test for Significance question: Was there a significant relationship between the marital status of 1980 GSS young adults and the type of place in which they grew up? State the research and the null hypotheses. – research hypothesis: Marital status and type of place in which raised are related. – null hypothesis: Marital status and type of place in which raised are independent. 17

18. Chi-Square Example (cont.) What is the probability of getting the sample results if the null hypothesis is true? In this example, p =.001 (very small probability) At alpha =.05, this association is significant. 18

19. Limitations of Chi-Square unstable if cases spread too thinly across table – if even one cell has an expected frequency less than 1 – if more than 1/5 of cells have expected frequencies less than 5 Note: chi-square is not a measure of association, it tests if two variables are significantly related 19