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

SECTION 17.2 | An Example of the Chi-Square Test for Goodness of Fit 571
df 5 3
a 5 .05
FIGURE 17.4
For Example 17.2, the
critical region begins at
a chi-square value of 7.81.
0
7.81
STEP 1
Expected frequencies are
computed and may be
decimal values. Observed
frequencies are always
whole numbers.
STEP 2
State the hypotheses and select an alpha level The hypotheses can be stated as
follows:
H 0
: In the general population, there is no preference for any specific orientation.
Thus, the four possible orientations are selected equally often, and the
population distribution has the following proportions:
H 1
:
Top Up
(Correct)
Bottom
Up
Left Side
Up
Right Side
Up
25% 25% 25% 25%
In the general population, one or more of the orientations is preferred over
the others.
We will use α = .05.
Locate the critical region For this example the value for degrees of freedom is
df = C – 1 = 4 – 1 = 3
For df = 3 and α = .05, the table of critical values for chi-square indicates that the critical
χ 2 has a value of 7.81. The critical region is sketched in Figure 17.4.
STEP 3
Calculate the chi-square statistic The calculation of chi-square is actually a twostage
process. First, you must compute the expected frequencies from H 0
and then calculate
the value of the chi-square statistic. For this example, the null hypothesis specifies that
one-quarter of the population (p = 25%) will be in each of the four categories. According
to this hypothesis, we should expect one-quarter of the sample to be in each category. With
a sample of n = 50 individuals, the expected frequency for each category is
f e
= pn = 1 (50) = 12.5
4
The observed frequencies and the expected frequencies are presented in Table 17.3.
TABLE 17.3
The observed frequencies
and the expected
frequencies for the
chi-square test in
Example 17.2.
Observed Frequencies
Top Up
(Correct)
Bottom
Up
Left
Side Up
Right
Side Up
18 17 7 8
Expected Frequencies 12.5 12.5 12.5 12.5