Abstract
Two alternate formulas for chi square are presented in this article. Formula 1 is for two observed frequencies. Formula 2 is for three observed frequencies. The formulas do not require prior calculations of expected frequencies and thus eliminate errors frequently incurred in calculating expected frequencies. Both formulas represent a faster and more economical method for obtaining chi square than the conventional formula and methodology. For example, Formula 1, for two observed frequencies, can yield a chi square value in 10 sec. on a hand calculator equipped with chain functions. Appropriate tables and examples of use are given for both formulas. Degrees of freedom and significance levels required by each formula for chi square are given. The logic of the chi square test and the appropriate null hypothesis are also considered. The two formulas are abridged from a larger series of alternate formulas for chi square developed by the authors.
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