1. Ch. 15: The Analysis of Frequency Tables

2. Chi-Square
Assesses the discrepancy between the expected frequency and the observed frequency.
A focused test when df = 1.

3. Computing Chi-Square where fo is the observed frequency in each cell.
and fe is the expected frequency in each cell.

4. Calculating the Expected Frequency

5. Alternative Chi-Square Formula for 2 X 2 TablesD
(C + D)
(A + C)
(B + D)
(N = A + B + C + D)

6. Finding the p Value df = (rows – 1)(columns – 1) df p = .10 p = .05
2.71
3.84
6.64 2
4.60
5.99
9.21 3
6.25
7.82
11.34 4
7.78
9.49
13.28 5
9.24
11.07
15.09

7. Options for Calculating the Effects Size for a 2 X 2 Table

8. Procedures for Interpreting Large Table of Counts
Examine individual cells, looking for “unexpected” frequencies.
Partition the tables and compute additional chi-squares.
Standardize the margins.
Set the row totals equal to each other and
Set the column totals equal to each other.

9. Standardizing the Margins: Corrected for Unequal Column Margins
Food choice PC MC
JFJ GE
Row sums
Big Jack
.600
.727
.667
.302
2.296
Soyburger
.400
.273
.333
.698
1.704
Column sums
1.000
4.000

10. Standardizing the Margins: Corrected for Unequal Row Margins
Food choice PC MC
JFJ GE
Row sums
Big Jack
.261
.317
.291
.132
1.001
Soyburger
.235
.160
.195
.410
1.000
Column sums
.496
.477
.486
.542
2.001

11. Standardizing the Margins: Final Corrected Results
Food choice PC MC
JFJ GE
Row sums
Big Jack
.517
.657
.589
.238
2.001
Soyburger
.483
.343
.411
.762
1.999
Column sums
1.000
4.000

12. Final Results Shown as Deviations from Expected Value of .500
Food choice PC MC
JFJ GE
Row sums
Big Jack
+.017
+.157
+.089
-.262
+.001
Soyburger
-.017
-.157
-.089
+.262
-.001
Column sums
.000