# ci.pd: Compute confidence limits for a difference of two independent... In Epi: A Package for Statistical Analysis in Epidemiology

## Description

The usual formula for the c.i. of at difference of proportions is inaccurate. Newcombe has compared 11 methods and method 10 in his paper looks like a winner. It is implemented here.

## Usage

 ```1 2 3 4 5 6``` ```ci.pd(aa, bb=NULL, cc=NULL, dd=NULL, method = "Nc", alpha = 0.05, conf.level=0.95, digits = 3, print = TRUE, detail.labs = FALSE ) ```

## Arguments

 `aa` Numeric vector of successes in sample 1. Can also be a matrix or array (see details). `bb` Successes in sample 2. `cc` Failures in sample 1. `dd` Failures in sample 2. `method` Method to use for calculation of confidence interval, see "Details". `alpha` Significance level `conf.level` Confidence level `print` Should an account of the two by two table be printed. `digits` How many digits should the result be rounded to if printed. `detail.labs` Should the computing of probability differences be reported in the labels.

## Details

Implements method 10 from Newcombe(1998) (method="Nc") or from Agresti & Caffo(2000) (method="AC").

`aa`, `bb`, `cc` and `dd` can be vectors. If `aa` is a matrix, the elements `[1:2,1:2]` are used, with successes `aa[,1:2]`. If `aa` is a three-way table or array, the elements `aa[1:2,1:2,]` are used.

## Value

A matrix with three columns: probability difference, lower and upper limit. The number of rows equals the length of the vectors `aa`, `bb`, `cc` and `dd` or, if `aa` is a 3-way matrix, `dim(aa)[3]`.

## Author(s)

Bendix Carstensen, Esa Laara. http://BendixCarstensen.com

## References

RG Newcombe: Interval estimation for the difference between independent proportions. Comparison of eleven methods. Statistics in Medicine, 17, pp. 873-890, 1998.

A Agresti & B Caffo: Simple and effective confidence intervals for proportions and differences of proportions result from adding two successes and two failures. The American Statistician, 54(4), pp. 280-288, 2000.

`twoby2`, `binom.test`
 ```1 2 3 4 5 6 7``` ```( a <- matrix( sample( 10:40, 4 ), 2, 2 ) ) ci.pd( a ) twoby2( t(a) ) prop.test( t(a) ) ( A <- array( sample( 10:40, 20 ), dim=c(2,2,5) ) ) ci.pd( A ) ci.pd( A, detail.labs=TRUE, digits=3 ) ```