A comparison of the exact and approximate power of the chi-square goodness-of-fit test.
Wright, Brian Theodore.
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This thesis presents a numerical comparison of the exact and approximate powers of the chi-square goodness-of-f it test for small numbers of classes and small sample sizes for the equiprobable null hypothesis . The comparison was performed using an IBM 360 computer and the computational details are presented within the thesis. In addition a comparison of critical points was conducted for the chisquare distribution and the associated exact, (multinomial), distribution. The results of the power comparisons show that the approximate power is surprisingly good and is recommended as an efficient method for determining type two error associated with the test. Further, use of the chisquare distribution for determining a critical point is reinforced through the numerical comparison of significance levels.
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