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The Wald procedure uses the sample proportion to calculate the standard error. The score test uses the hypothesized proportion to calculate the standard error. With large sample sizes, the two methods will give similar results. For small sample sizes, the two could give vastly different values.
So, which of the two is better for small sample sizes? It depends on which of these two values is closer to the true population proportion: the sample proportion or the hypothesized proportion. And, since we do not know the population proportion, we cannot tell. Most texts use the Wald test out of deference to one of the luminaries of statistics, Abraham Wald (photograph at right).
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