Chi-Square Tests of Association and Goodness of Fit from Proportions and Percentages

Formulas are derived for computing the chi-square statistic from proportions or percentages, both for tests of goodness of fit and association. The advantages of the new formulas are: (1) computation is conceptually more congruent with the hypothesis being tested; (2) interpretation is facilitated (expected frequencies and discrepancies in frequencies are a function of sample size, whereas expected proportions and corresponding discrepancies are not); and (3) computation is facilitated in contingency tables since expected proportions do not need to be determined separately for each cell.