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

SECTION 17.3 | The Chi-Square Test for Independence 577
TABLE 17.5
An empty frequency
distribution matrix showing
only the row totals
and column totals. (These
numbers describe the
basic characteristics of the
sample from Table 17.4.)
Red Yellow Green Blue
Introvert 50
Extrovert 150
100 20 40 40
consists of 200 people, the proportion selecting red is 100 out of 200, or 50%. The
complete set of color preference proportions is as follows:
100 out of 200 = 50% prefer red
20 out of 200 = 10% prefer yellow
40 out of 200 = 20% prefer green
40 out of 200 = 20% prefer blue
The row totals in the matrix define the two samples of personality types. For example, the
matrix in Table 17.5 shows a total of 50 introverts (the top row) and a sample of 150 extroverts
(the bottom row). According to the null hypothesis, both personality groups should
have the same proportions for color preferences. To find the expected frequencies, we simply
apply the overall distribution of color preferences to each sample. Beginning with the
sample of 50 introverts in the top row, we obtain expected frequencies of
50% prefer red: f e
= 50% of 50 = 0.50(50) = 25
10% prefer yellow: f e
= 10% of 50 = 0.10(50) = 5
20% prefer green: f e
= 20% of 50 = 0.20(50) = 10
20% prefer blue: f e
= 20% of 50 = 0.20(50) = 10
Using exactly the same proportions for the sample of n = 150 extroverts in the bottom row,
we obtain expected frequencies of
50% prefer red: f e
= 50% of 150 = 0.50(50) = 75
10% prefer yellow: f e
= 10% of 150 = 0.10(50) = 15
20% prefer green: f e
= 20% of 150 = 0.20(50) = 30
20% prefer blue: f e
= 20% of 150 = 0.20(50) = 30
The complete set of expected frequencies is shown in Table 17.6. Notice that the row totals
and the column totals for the expected frequencies are the same as those for the original
data (the observed frequencies) in Table 17.4.
TABLE 17.6
Expected frequencies
corresponding to the data
in Table 17.4. (This is the
distribution predicted by
the null hypothesis.)
Red Yellow Green Blue
Introvert 25 5 10 10 50
Extrovert 75 15 30 30 150
100 20 40 40