C.I. Calculator: Two Sample Proportions


Data Input: (Help) (Example)

Input

Result

1-α

d

p1

Lower

p2

Upper

n1

n2


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.




Help Aids Top

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:

  1. Enter

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

  1. Click the button “Calculate” to obtain

a)    The difference between proportions of sample 2 and 1

b)    The 100(1-α)% confidence interval

  1. Click the button “Reset” for another new calculation


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




Example

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).

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