Chi-Square: Correction for Continuity when df=1

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We mentioned at the beginning of this chapter that chi-square procedures involve an extension of the logic of binomial probabilities. This connection between chi-square and binomial probabilities is especially close in the case where the number of degrees of freedom in the chi-square situation is equal to one. In fact, any binomial probability situation could easily be converted into a one-dimensional chi-square analysis. Toward the end of Chapter 6, for example, we calculated a binomial z-ratio (corrected for continuity) of +1.9 for the experimental-medication scenario where 430 recoveries are observed among 1,000 subjects. Recalling that the null hypothesis in this scenario would have led us (absent any effectiveness on the part of the experimental medication) to expect only 400 recoveries, the chi-square set-up would be

		Recover	Not Recover	Total
	O	430	570	1,000
	E	400	600	1,000

and the calculation, using the continuity-correction formula for chi-square, would be

	Recover	Not Recover
	(|430—400|-.5)2 400 = 2.18	(|570—600|-.5)2 600 = 1.45	sum: = 3.63

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