1. Contingency Tables (cross tabs)
Generally used when variables are nominal and/or ordinal
Even here, should have a limited number of variable attributes (categories)
Inside the cells of the table are frequencies (number of cases that fit criteria)
To examine relationships within the sample, most use percentages to standardize the cells

2. Example A survey of 2883 U.S. residents
Is one’s political ideology (liberal, moderate, conservative) related to their satisfaction with their financial situation?
Null = ideology is not related to satisfaction with financial status (the are independent)
Convention for bivariate tables
IV (Ideology) is on the top of the table (dictates columns)
The DV ($ status)is on the side (dictates rows).

3. Are these variable related within the sample?
Satisfaction
With
Current $
Situation
Political Ideology
Total
Liberal
Moderate
Conservative
Satisfied
242
300
334
876
More or Less
329
499
439
1267
Unsatisfied
213
294
233
740
784
1093
1006
2883

4. The Test Statistic for Contingency Tables
Chi Square, or χ2
Calculation
Observed frequencies (your sample data)
Expected frequencies (UNDER NULL)
Intuitive: how different are the observed cell frequencies from the expected cell frequencies
Degrees of Freedom:
1-way = K-1
2-way = (# of Rows -1) (# of Columns -1)

5. Calculating χ2 = ∑ [(fo - fe)2 /fe]
Where Fe= Row Marginal X Column Marginal N
So, for each cell, calculate the difference between the actual frequencies (“observed”) and what frequencies would be expected if the null was true (“expected”). Square, and divide by the expected frequency.
Add the results from each cell.

6. Political Ideology Satisfaction With Current $ Situation 876 1267 740
Total
Liberal
Moderate
Conservative
Satisfied
242 (238)
300 (332)
334 (305)
876
More or Less
329
499
439
1267
Unsatisfied
213
294
233
740
784
1093
1006
2883
FIND EXPECTED FREQUENCIES UNDER NULL
Example: 876(784)/2883 = 238

7. Political Ideology Satisfaction With Current $ Situation 876 1267 740
Total
Liberal
Moderate
Conservative
Satisfied
242 (238)
300 (332)
334 (305)
876
More or Less
329 (344)
499 (480)
439 (442)
1267
Unsatisfied
213 (201)
294 (280)
233 (258)
740
784
1093
1006
2883
FIND EXPECTED FREQUENCIES UNDER NULL
Example: 876(784)/2883 = 238

8. Calculating χ2 χ2 = ∑ [(fo - fe)2 /fe] [(242-238) 2 / 238 ] = .067
[( ) 2 / 332 ] = 3.08
Do the same for the other seven cells…
Calculate obtained χ2
Figure out appropriate df and then Critical χ2 (alpha = .05)
Would decision change if alpha was .01?

9. Interpreting Chi-Square
Chi-square has no intuitive meaning, it can range from zero to very large
As with other test statistics, the real interest is the “p value” associated with the calculated chi-square value
Conventional testing = find χ2 (critical) for stated “alpha” (.05, .01, etc.)
Reject if χ2 (observed) is greater than χ2 (critical)
SPSS: find the exact probability of obtaining the χ2 under the null (reject if less than alpha)

10. SPSS Procedure Statistics Analyze Descriptive Statistics  Crosstabs
Rows = DV
Columns = IV
Cells
Column Percentages
Statistics
Chi square

11. Agenda Today Monday Wednesday
Group based assignment (review for exam, review chi-square)
Monday
More “hands on” review for exam + final project time
Wednesday
Go over HW#4, review conceptual stuff, more practice