CI on the Proportion

The Confidence Interval on the Proportion uses X, the number of successes found in a sample, and n, the size of the sample, to estimate the population parameters. This implementation uses the Agresti-Coull Interval method, which is appropriate for any sample size n. mctad.confidenceIntervalOnTheProportion() returns an Array of lower, upper values for the (1 - α/2)interval or a Number for the lower or upper (1 - α) boundary.

Assumptions

X is the number of successes found in a sample, n is the size of the sample, and 0.0 < α < 1.0. By default, the confidence interval is two-tailed; this may be changed by specifying type as either 'l' for lower, or 'u' for upper. Any other value for type generates a two-tailed confidence interval.

Use

mctad.confidenceIntervalOnTheProportion(X, n, α, 'u')

Inline Comments

mctad.confidenceIntervalOnTheProportion = function (X, n, α, type) { if (typeof X !== 'number' || !mctad.isInteger(n) || α <= 0.0 || α >= 1.0) { return undefined; }

Apply the Agresti-Coull Interval transformation.

var n_tilde = n + 4, p_tilde = (X + 2) / n_tilde, σ_p_tilde = Math.sqrt(p_tilde * (1.0 - p_tilde) / n_tilde);

Return the upper confidence bound of a one-tailed confidence interval.

if (typeof type !== 'undefined' && type.toLowerCase() === 'u') { return p_tilde + mctad.z(1 - α) * σ_p_tilde; } else {

Return the lower confidence bound of a one-tailed confidence interval; enforce 0 as lowest possible bound.

if (typeof type !== 'undefined' && type.toLowerCase() === 'l') { return Math.max(0, p_tilde - mctad.z(1 - α) * σ_p_tilde); } else {

Return both bounds of a two-tailed confidence interval; enforce 0 as lowest possible bound.

return [ Math.max(0, p_tilde - mctad.z(1 - α / 2) * σ_p_tilde), p_tilde + mctad.z(1 - α / 2) * σ_p_tilde ]; } } };