Transcript Slide 1
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 pair of variables type of measure of association nominal & nominal nominal measure of association nominal & ordinal nominal measure of association nominal & interval/ratio nominal measure of association ordinal & ordinal ordinal measure of association ordinal & interval/ratio ordinal measure of association interval/ratio & interval/ratio interval/ratio measure of association 10 About Measures of Association (cont.) • Strength of an association – closer to zero, weaker; further from zero, stronger – guidelines used by text: If the absolute value of a measure of association is: The association will be described as: .000 No relationship .001 to .199 Weak .200 to .399 Moderate .400 to .599 Strong .600 to .999 Very strong 1.000 Perfect relationship 11 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