Statistical Details for the One Proportion Calculator
The one proportion sample size computations use exact methods based on the binomial distribution. Exact calculations guarantee that the stated power level is obtained.
Agresti-Coull Method
The exact Agresti-Coull method uses the adjusted Wald-based test statistic. JMP calculates power under the two-sided null hypothesis as follows:
where:
and 0 otherwise, and
χ1-α is the (1 - α)thquantile of the χ12 distribution.
Because there is not a closed-form expression for n or p0, numerical techniques are used to solve for n or p0.
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).
Clopper-Pearson Method
The exact Clopper-Pearson method is based on the binomial distribution. This method results in an alpha level equal to or greater than the stated level. The Clopper-Pearson method is more conservative (larger sample size) than the Agresti-Coull method.
The exact Clopper-Pearson method uses the binomial distribution directly. Numerical techniques are used to solve for the unknown parameter.
For more information about the Clopper-Pearson exact method, see Clopper and Pearson (1934) or Agresti and Coull (1998, Section 1).