<?xml version="1.0" encoding="utf-8"?><!DOCTYPE article  PUBLIC '-//OASIS//DTD DocBook XML V4.4//EN'  'http://www.docbook.org/xml/4.4/docbookx.dtd'><article><articleinfo><title>FAQ/power/nrpt</title><revhistory><revision><revnumber>4</revnumber><date>2013-03-08 10:18:09</date><authorinitials>localhost</authorinitials><revremark>converted to 1.6 markup</revremark></revision><revision><revnumber>3</revnumber><date>2008-01-21 17:06:12</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>2</revnumber><date>2008-01-21 16:55:27</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>1</revnumber><date>2008-01-21 16:53:52</date><authorinitials>PeterWatson</authorinitials></revision></revhistory></articleinfo><section><title>Sample sizes for paired t in R</title><para>mdiff is the difference between the two variables with correlation, rho, type I error, alpha, and (common) sd.  </para><para>[COPY AND PASTE INTO R AND ADJUST INPUTS AS DESIRED] </para><screen><![CDATA[pow <- 0.8
beta <- 0.05
mdiff <- 2
sd <- 4
rho <- 0.5]]></screen><para>[THEN COPY AND PASTE THE BELOW INTO R] [OUTPUTS NUMBER OF PAIRS] </para><screen><![CDATA[fn <- function(n) {
(pow - (1 - pt(abs(qt(beta/2,(2*n)-2)),2*n-2, 
mdiff/sqrt((2*sd*sd)/n*(1-rho)))) )^2
 }
]]><![CDATA[
nout<- nlm(fn,2)
nout<- trunc(nout$estimate+1)
print(nout)
pow <- 0.8
alpha <- 0.05
mdiff <- 2
sd <- 4
rho <- 0.5]]></screen></section></article>