1. Applied Statistics Using SPSS
Topic: Chi-square tests
By Prof Kelly Fan, Cal. State Univ., East Bay

2. Outline ALL variables must be categorical
Goal one: verify a distribution of Y
One-sample Chi-square test (SPSS lesson 40)
Goal two: test the independence between two categorical variables
Chi-square test for two-way contingency table (SPSS lesson 41)
McNemar’s test for paired data (SPSS lesson 44)
Measure the dependence (Phil and Kappa coefficients) (SPSS lesson 41, 44)
Goal three: test the independence between two categorical variables after controlling the third factor
Mantel-Haenszel Chi-square test (SPSS in class)

3. Example: Postpartum Depression Study
Are women equally likely to show an increase, no change, or a decrease in depression as a function of childbirth?
Are the proportions associated with a decrease, no change, and an increase in depression from before to after childbirth the same?

4. Raw data vs. Grouped data
Grouped data are shown in next slide. ID
Name
Depression level after birth in comparison with before birth 1
***
Same 2
Less depressed 3
More depressed

5. Example: Postpartum Depression Study
Depression after birth in comparison with before birth
Observed frequencies
Hypothesized proportions
Expected frequencies
Less depressed (-1) 14
1/3 20
Neither less nor more depressed (0) 33
More depressed (1) 13
From a random sample of 60 women

6. One-sample Chi-Square Test
Must be a random sample
The sample size must be large enough so that expected frequencies are greater than or equal to 5 for 80% or more of the categories

7. One-sample Chi-Square Test
Test statistic:
Oi = the observed frequency of i-th category
ei = the expected frequency of i-th category

8. SPSS Output Weight your data by count first (data>>weight cases)
Analyze >> Nonparametric Tests >> Legacy Dialogs >> Chi Square, count as test variable

9. Conclusion
Reject Ho
The proportions associated with a decrease, no change, and an increase in depression from before to after childbirth are significantly different to 1/3, 1/3, 1/3.

10. Example: Postpartum Depression Study
Are the proportions associated with a change and no change from before to after childbirth the same?

11. Example: Postpartum Depression Study
Depression after birth in comparison with before birth
Observed frequencies
Hypothesized proportions
Expected frequencies
Same amount of depression (0) 33
1/2 30
More or less depressed (1) 27
From a random sample of 60 women

12. SPSS Output

13. Conclusion
It is equally like to experience change or no change in depression before and after child birth.
Question: For those who do experience change, is it equally like to be less or more depressed?

14. Two-way Contingency Tables
Report frequencies on two variables
Such tables are also called crosstabs.

15. Contingency Tables (Crosstabs)
1991 General Social Survey
Frequency
Party Identification
Democrat
Independent
Republican
Race
White
341
105
405
Black
103 15 11

16. Crosstabs Analysis (Two-way Chi-square test)
Chi-square test for testing the independence between two variables:
For a fixed column, the distribution of frequencies over rows keeps the same regardless of the column
For a fixed row, the distribution of frequencies over columns keeps the same regardless of the row

17. Measure of dependence for 2x2 tables
The phi coefficient measures the association between two categorical variables
-1 < phi < 1
| phi | indicates the strength of the association
If the two variables are both ordinal, then the sign of phi indicate the direction of association

18. SPSS Output
P. 332 : Data>> weight cases>> Weight cases by, select count variable
P. 333: Analyze >> descriptive statistics >> crosstabs, cell

19. Measure of dependence for non-2x2 tables
Cramers V
Range from 0 to 1
V may be viewed as the association between two variables as a percentage of their maximum possible variation.
V= phi for 2x2, 2x3 and 3x2 tables

20. Fisher’s Exact Test for Independence
The Chi-squared tests are ONLY for large samples:
The sample size must be large enough so that expected frequencies are greater than or equal to 5 for 80% or more of the categories

21. SPSS Output
SPSS output: in “crosstabs” window, click “exact”, then tick “exact”:

22. Matched-pair Data
Comparing categorical responses for two “paired” samples
When either
Each sample has the same subjects (or say subjects are measured twice) Or
A natural pairing exists between each subject in one sample and a subject from the other sample (eg. Twins)

23. Example: Rating for Prime Minister
Second Survey
First Survey
Approve
Disapprove
794
150 86
570

24. Marginal Homogeneity
The probabilities of “success” for both samples are identical
Eg. The probability of “approve” at the first and 2nd surveys are identical

25. McNemar Test (for 2x2 Tables only)
SPSS: Lesson 44
Ho: marginal homogeneity
Ha: no marginal homogeneity
Exact p-value
Approximate p-value (When n12+n21>10)

26. Output
In SPSS: Analyze >> Descriptive statistics >> crosstabs,
in “statistics” tick “Kappa” and “McNemar”
McNemar's Test
Statistic (S) DF
Asymptotic Pr > S <.0001
Exact Pr >= S E-05
Simple Kappa Coefficient
Kappa
ASE
95% Lower Conf Limit
95% Upper Conf Limit
Sample Size = 1600
Level of agreement

27. SPSS Output
SPSS(p. 361): Analyze >> Nonparametric tests >> Legacy dialogs >> 2 related samples; in “two-samples tests” tick “McNemar” and click “exact”, then tick “exact” again

28. Stratified 2 by 2 Tables (Meta-Analysis)
Goal: to investigate the risk factor (lack of sleep) to the outcome (failing a test)
Test Results, Boys
Sleep
Fail
Pass
Low 20
100
High 15
150
Test Results, Girls
Sleep
Fail
Pass
Low 30
100
High 25
200

29. Cochran Mantel-Haenszel Test
After Importing your dataset, and providing names to variables, click on:
ANALYZE >> DESCRIPTIVE STATISTICS >> CROSSTABS
For ROWS, Select the Independent Variable
For COLUMNS, Select the Dependent Variable
For LAYERS, Select the Strata Variable
Under STATISTICS, Click on COCHRAN’S AND MANTEL-HAENSZEL STATISTICS
NOTE: You will want to code the data so that the outcome present (Yes) category has the lower value (e.g. 1) and the outcome absent (No) category has the higher value (e.g. 2). Do the same for risk factor: 1 for exposure; 2 for no exposure. Use Value Labels to keep output straight.

30. SPSS Output

31. SAS Output Common Odds Ratio and Relative Risks Statistic Method Value
Cochran-Mantel-Haenszel Statistics (Based on Table Scores)
Statistic
Alternative Hypothesis DF
Value
Prob 1
Nonzero Correlation
0.0004 2
Row Mean Scores Differ 3
General Association
Breslow-Day Test for Homogeneity of the Odds Ratios
Chi-Square
0.1501 DF 1
Pr > ChiSq
0.6985
Common Odds Ratio and Relative Risks
Statistic
Method
Value
95% Confidence Limits
Odds Ratio
Mantel-Haenszel
2.2289
1.4185
3.5024
Logit
2.2318
1.4205
3.5064
Relative Risk (Column 1)
1.9775
1.3474
2.9021
1.9822
1.3508
2.9087
Relative Risk (Column 2)
0.8891
0.8283
0.9544
0.8936
0.8334
0.9582