Note:
Variables |
Descriptions |
1-α |
Two-sided confidence level |
p1 |
Success proportion in sample 1 |
p2 |
Success proportion in sample 2 |
n1 |
Sample size of sample 1 |
n2 |
Sample size of sample 2 |
d |
Difference between p2 and p1 |
Lower |
Lower C.I. |
Upper |
Upper C.I. |
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Application:
It is to estimate the difference of 2 proportions and provide a confidence interval for the estimation.
Confidence intervals of difference not containing 0 imply that there is a statistically significant difference between the population proportions.
Procedure:
a) Value of 1-α, the two-sided confidence level
b) Value of p1,p2 the success proportion of each sample
c) Value of n1,n2 the sample size of each sample
a) The difference between proportions of sample 2 and 1
b) The 100(1-α)% confidence interval
Formula:
Define:
Define:
The 100(1-α)% confidence interval with continuity correction is defined as:
Notation:
100(1-α)% confidence interval: We are 100(1-α)% confident that the true value of the parameter is included in the confidence interval
: The z-value for standard normal distribution with left-tail probability
Suppose there are two anti-microbial agents. The response rate of agent 1 is 0.244 (p1=0.244), the response rate of agent 2 is 0.046 (p2=0.046).
The sample size 1 is 197 (n1=197) and the sample size 2 is 65 (n2=65), the corresponding 95% C.I. ((1-α) = 0.95) is (-0.286911, 0.109089).