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One Sample Test of Proportions

The one sample test of proportions compares an unknown proportion, \(p\), to a fixed value, \(p_0\). This calculator uses large sample theory, which relies on the convergance in distribution of a binomial random variable with parameter \(p\) ro 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.
The sample size used to test the hypothesis.
The \(\alpha\) (Type I error rate) level of the hypothesis test.
The power (1 - Type II error rate) of the hypothesis test.
Unknown Proportion
The estimated proportion from the sample (\(p\)). If you are comparing a difference in proportions to zero, set this value to the difference.
Null Proportion
The proportion against which the unknown proportion is compared to (\(p_0\)). If you are comparing a difference in proportions to zero, set this value to zero.
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
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

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Hypothesis: {{ hypothesis }}

N Alpha Power Unk. Proportion Null Proportion Margin
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Power Graph

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