This
page will calculate the zratio 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 onetailed and twotailed probabilities associated with the resulting value of z will be calculated and displayed in the designated text cells.
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©Richard Lowry 2001
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