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# Two Sample Test of Proportions (Parallel)

The two sample test of proportions compares the proportions of two arms of a study, $$p_1$$ and $$p_2$$. This calculator uses large sample theory, which relies on the convergance in distribution of a binomial random variable with parameter $$p$$ to a normal random variable with mean $$p$$ and variance $$p (1 - p$$).

## Power Calculation Parameters

To input multiple values, seperate them by a comma.

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## Power Calculation Explanation

Solve For
The unknown you are interested in solving for.
N
The sample size used to test the hypothesis.
Alpha
The $$\alpha$$ (Type I error rate) level of the hypothesis test.
Power
The power (1 - Type II error rate) of the hypothesis test.
P (Arm 1)
The estimated proportion from arm 1 ($$p_1$$). If you are comparing a difference in proportions to zero, set this value to the difference.
P (Arm 2)
The estimated proportion from arm 2 ($$p_2$$). If you are comparing a difference in proportions to zero, set this value to zero.
Margin
The margin is a value the effect size needs to exceed to be meaningful. For hypotheses of equivalence, the margin must be greater than 0, or the calculation will not be solvable. For one sided tests, a margin is less than 0 implies a non-inferiority hypothesis. Otherwise, a superiority hypothesis is implied. Read More
Hypothesis
There are three types of hypotheses that can be tested: two-sided, one-sided and equivalence. Tests of equivalence must include a margin if the unknown and null means are equal. Read More

## Calculation Results

No calculation has been generated yet.

Hypothesis: {{ hypothesis }}

N (Arm 1) N (Arm 2) Alpha Power Proportion (Arm 1) Proportion (Arm 2) Margin
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## Power Graph

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## References

• Chow, S., Shao, J., & Wang, H. (2003), Sample size calculations in clinical research, New York: Marcel Dekker.