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

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

Creating a Crosstab Table 3

Creating Crosstab Table and Adding Cell Percents 4

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

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

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

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

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

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

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

Requesting Measures of Association when using Crosstabs 13

Crosstabs Output for WORKSTAT by SEX for 1980 GSS Young Adults

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

Crosstabs Output for HAPPY by DEGREE for 1980 GSS Young Adults

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

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

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