The Significance of the Difference Between Two Independent Proportions
This page will calculate the z-ratio for the significance of the difference between two independent proportions, pa and pb. For the notation used here, na and nb represent the total numbers of observations in two independent samples, A and B; ka and kb represent the numbers of observations within each sample that are of particular interest; and pa and pb represent the proportions ka/na and kb/nb, respectively. Thus, if sample A shows 23 recoveries among 60 patients, na=60, ka=23, and the proportion is pa=23/60=0.3833. If sample B shows 18 recoveries among 72 patients, nb=72, kb=18, and the proportion is pb=18/72=0.2500. The difference between the two proportions is diff=papb=0.38330.2500=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(1p) 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 =
 z =
One-Tail Two-Tail

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