Computing the Chi Square Test of Independence (4 of 5)
The same procedures are used for analyses with more than two rows and/or more than two columns. For example, consider the following hypothetical experiment: A drug that decreases anxiety is given to one group of subjects before they attempted to play a game of chess against a computer. The control group was given a placebo. The contingency table is shown below.
Condition |
Win |
Lose |
Draw |
Total |
|---|---|---|---|---|
Drug |
12 (14.29) |
18 (14.29) |
10 (11.43) |
40 |
Placebo |
13 (10.71) |
7 (10.71) |
10 (8.57) |
30 |
Total |
25 |
25 |
20 |
70 |
The expected frequencies are shown in parentheses. As in the previous example, each expected frequency is computed by multiplying the row total by the column total and dividing by the total number of subjects. For example, the expected frequency for the "Drug-Lose" condition is the product of the row total (40) and the column total (25) divided by the total number of subjects (70): (40)(25)/70 = 14.29.
The chi square is calculated using the formula:
The df are (R-1)(C-1) = (2-1)(3-1) = 2. A chi square table shows that the probability of a chi square of 3.52 with 2 degrees of freedom is 0.172. Therefore, the effect of the drug is not significant.