This page will calculate the z-ratio for the significance of the difference between two independent proportions, p_a and p_b. For the notation used here, n_a and n_b represent the total numbers of observations in two independent samples, A and B; k_a and k_b represent the numbers of observations within each sample that are of particular interest; and p_a and p_b represent the proportions k_a/n_a and k_b/n_b, respectively. Thus, if sample A shows 23 recoveries among 60 patients, n_a=60, k_a=23, and the proportion is p_a=23/60=0.3833. If sample B shows 18 recoveries among 72 patients, n_b=72, k_b=18, and the proportion is p_b=18/72=0.2500. The difference between the two proportions is diff=p_a—p_b=0.3833—0.2500=0.1333.

To perform the calculation, enter the values of n and k for samples A and B in the designated places, then click the «Calculate» button. Please note that this procedure can be validly employed only if both samples satisfy the standard binomial requirement: that n(p) and n(1—p) must both be equal to or greater than 5.

The one-tailed and two-tailed probabilities associated with the resulting value of z will be calculated and displayed in the designated text cells.

Sample A	Sample B
ka =	kb =
na =	nb =
pa =	pb =
pa— pb =
Reset         Calculate		z =

Probability
One-Tail	Two-Tail

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©Richard Lowry 2001-
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