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

590 CHAPTER 17 | The Chi-Square Statistic: Tests for Goodness of Fit and Independence
instructions for finding the median). Next, a matrix is constructed with a column for each
of the separate samples and two rows: one for individuals above the median and one for
individuals below the median. Finally, for each sample, you count how many individuals
scored above the combined median and how many scored below. These values are the
observed frequencies that are entered in the matrix.
The frequency distribution matrix is evaluated using a chi-square test for independence.
The expected frequencies and a value for chi-square are computed exactly as described in
Section 17.3. A significant value for chi-square indicates that the discrepancy between the
individual sample distributions is greater than would be expected by chance.
The median test is demonstrated in the following example.
EXAMPLE 17.7
The following data represent self-esteem scores obtained from a sample of n = 40 children.
The children are then separated into three groups based on their level of academic performance
(high, medium, low). The median test will evaluate whether there is a significant
relationship between self-esteem and level of academic performance.
Self-Esteem Scores for Children
at Three Levels of Academic Performance
High Medium Low
22 14 22 13 24 20 11 19
19 18 18 22 10 16 13 15
12 21 19 15 14 19 20 16
20 18 11 18 11 10 10 18
23 20 12 19 15 12 15 11
The median for the combined group of n = 40 scores is X = 17 (exactly 20 scores are
above this value and 20 are below). For the high performers, 8 out of 10 scores are above
the median. For the medium performers, 9 out of 20 are above the median, and for the low
performers, only 3 out of 10 are above the median. These observed frequencies are shown
in the following matrix:
Academic Performance
High Medium Low
Above Median 8 9 3
Below Median 2 11 7
The expected frequencies for this test are as follows:
Academic Performance
High Medium Low
Above Median 5 10 5
Below Median 5 10 5
The chi-square statistic is
x 2 5 9 5 1 9 5 1 1 10 1 1 10 1 4 5 1 4 5 5 5.40