In the Lab:Working With Crosstab Tables

Lab: Association and the Chi-square Test Chapters 7, 8 and 9

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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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