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Design of Experiments Guide > Prospective Sample Size and Power > Two Sample Proportions Calculator > Statistical Details for the Two Proportions Calculator
Publication date: 11/10/2021

Statistical Details for the Two Proportions Calculator

Two proportions calculations are based on exact methods similar to those used for the one proportion calculator. For the two-sided hypothesis

Equation shown here

JMP calculates power under the null hypothesis as follows:

Equation shown here

where the adjusted Wald statistic is defined as follows:

Equation shown here

and:

Equation shown here and 0 otherwise

and χ1-α is the (1 - α)th quantile of the χ2 distribution.

Because there are no closed-form expressions for the ni or δ0, numerical techniques are used to solve for the ni and δ0.

For more information about the adjusted Wald test statistic, see Agresti and Coull (1998). For more information about calculations in JMP, see Barker (2011, Section 3.3).

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