Confidence Interval for the Difference Between Two Proportions Using the Normal Approximation

 

Requirements:

(1) events occur with a normal distributions

(2) populations and events are sufficiently large

(3) the proportions for the 2 populations are not too close to 0 or 1

 

	Population 1	Population 2
total number	N1	N2
number showing response	R1	R2

 

proportion responding in population 1 = P1 =

= (R1) / (N1)

 

proportion responding in population 2 = P2 =

= (R2) / (N2)

 

confidence interval =

= P1 - P2 +/- ((one tailed value of the standard normal distribution) * (SQRT (((P1 * (1 - P1)) / N1) + ((P2 * (1 - P2)) / N2)))

 

where:

• The one tailed values for standard normal distributions with two-tailed confidence intervals, assuming an infinite degree of freedom:

Confidence Intervals	one-tailed value
80%	1.282
90%	1.645
95%	1.960
98%	2.326
99%	2.576
99.8%	3.090

 

Interpretation:

• If the confidence interval includes 0, then the data shows no statistically significant difference between the 2 proportions.