
56 Nonparametric Statistics for Social and Behavioral Sciences
χ
2
equals the sum of observed frequencies minus expected frequencies
squared and divided by the expected frequencies. The following calcu-
lations demonstrate the differences between the observed and expected
frequencies squared divided by the expected frequencies:
()()()
χ= +++
17 – 26.15
26.15
40 – 30.85
30.85
33 – 23.85
23.85
19 – 28.15
28.15
3.20 2.71 3.51 2.97 12.39
2
22
Results of the chi-square test are based on a chi-square distribution that
has a range between zero and one—not to be confused with the value
of the chi-square statistic. Chi-square cannot have a negative value. ...