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The Chi-Square Test Statistic
The chi-square test statistic
is an overall measure of how close the
observed frequencies are to the expected frequencies. It has the form
The null hypothesis of independence is rejected if
is large, because this means
that observed frequencies and expected frequencies are far apart.
The chi-square curve is used to judge whether the calculated test statistic
is large enough. We reject H0 if the test statistic is large enough so that
the area beyond it (under the chi-square curve with (r-1)(c-1) degrees of freedom) is less than .05.
The P-value is the area greater than
under the chi-square curve with (r-1)(c-1)
degrees of freedom.