Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

596 CHAPTER 17 | The Chi-Square Statistic: Tests for Goodness of Fit and Independence
For df = 2 with α = .05, the critical chi-square value is 5.99. Thus, our obtained chi-square
must exceed 5.99 to be in the critical region and to reject H 0
.
STEP 3
Compute the test statistic Computing chi-square requires two calculations: finding the
expected frequencies and calculating the chi-square statistic.
Expected frequencies, f e
. For the test for independence, the expected frequencies can be
found using the column totals ( f c
), the row totals ( f r
), and the following formula:
f e
5 f c f r
n
For people younger than 30, we obtain the following expected frequencies:
f e
5 100s140d
200
f e
5 80s140d
200
f e
5 20s140d
200
5 14,000
200
5 11,200
200
5 2800
200
5 70 for digital
5 56 for analog
5 14 for undecided
For individuals 30 or older, the expected frequencies are as follows:
f e
5 100s60d
200
5 6000
200
5 30 for digital
f e
5 80s60d
200 5 4800 5 24 for analog
200
f e
5 20s60d
200 5 1200 5 6 for undecided
200
The following table summarizes the expected frequencies:
Digital Analog Undecided
Younger than 30 70 56 14
30 or Older 30 24 6
The chi-square statistic. The chi-square statistic is computed from the formula
x 2 5S s f o 2 f e d2
f e
The following table summarizes the calculations:
Cell f o
f e
(f o
– f e
) (f o
– f e
) 2 (f o
– f e
) 2 /f e
Younger than 30—digital 90 70 20 400 5.71
Younger than 30—analog 40 56 –16 256 4.57
Younger than 30—undecided 10 14 –4 16 1.14
30 or Older—digital 10 30 –20 400 13.33
30 or Older—analog 40 24 16 256 10.67
30 or Older—undecided 10 6 4 16 2.67