Inaccuracy of the x2 Test of Goodness of Fit When Expected Frequencies Are Small

摘要: Abstract In applied statistics there is an increasing tendency toward leniency regarding minimum expectation prerequisite to Pearson's X 2 test for goodness of fit, based on various empirical studies the distribution X2 in sampling from multinomial populations with given parameters. this study it shown that chi-square probabilities may differ markedly exact cumulative probabilities. Contrary prevailing opinion, approximation did not improve, when samples were small, as increased nor number categories or degrees freedom increased.