The correction adjust the statistic toward the zero.
p1 < p2: F = 1.
p1 > p2: F = -1.
p1 = p2: F = 0.
The continuity correction cannot change the direction of the statistic i.e. correct positive statistic to negative, or vice versa.
Cont = Min(Cont,Abs(p1 - p2)).
|Z =||p̂1 - p̂2 + Cont|
|√( p̂(1-p̂)(1/n1 + 1/n2) )|
|Binomial distribution - the probability for event within each group is identical|
|Expected difference d between the populations's average is known|
|p̂1, p̂2 the sample probabilities or x1, x2 the number of successes|
|n1,n2 - Sample size of group1 and group2|
The following R code should produce the same results:
The prop.test uses the Chi-squared statistic with one degree of freedom, which is exactly as using the Z test: z2=χ2(1)