When raw data are available, ECDF tests usually surpass the chi-square test in their ability to detect departures from the distribution specified in the null hypothesis.

Question

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ECDF tests have been shown to be more powerful than the chi-square test when using raw data. The ECDF method uses the empirical distribution function to plot the observed data against the expected distribution, while the chi-square test only uses the expected distribution to compare to the observed data. This makes ECDF tests more sensitive to departures from the null hypothesis distribution.

When Raw Data Are Available, ECDF Tests Usually Surpass the Chi-Square