If the events for two proportions are normally distributed, then the confidence interval for the difference between the two proportions can be calculated 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.