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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
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Creating a Crosstab Table
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Creating Crosstab Table and Adding
Cell Percents
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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?
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Crosstabs Output with Column Percents for HAPPY by HEALTH for 1980 GSS Young Adults
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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.
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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
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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
About Measures of Association (cont.)
• Strength of an association– closer to zero, weaker; further from zero, stronger– guidelines used by text:
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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
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
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Requesting Measures of Association when using Crosstabs
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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
• symmetric15
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.
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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
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