Z.prop.test Function

Ok, here’s my own take on what this function should look like! To test it out, I used the data on mist-netting birds and bats from the “Comparing Sample Proportions: Two Sample Z-Tests” section of Module 10.

Z.prop.test<-function(p1,n1,p2=NULL,n2=NULL,p0,alternative="two.sided",conf.level=0.95)
{
  if(is.na(p1))
    stop("You must enter a value for 'p1'!")
  if(is.na(n1))
    stop("You must enter a value for 'n1'!")
  if(is.na(p0))
    stop("You must enter a value for 'p0'!")
  if(!missing(conf.level) &&
       (length(conf.level) != 1 || !is.finite(conf.level) ||
        conf.level < 0 || conf.level > 1))
    stop("'conf.level' must be a single number between 0 and 1")
  if(is.null(p2) || is.null(n2)) {
    phat1<-p1
    pi<-p0
    n<-n1
    z<-(phat1-pi)/sqrt(pi*((1-pi)/n1))
      names(z)<-"Z score"
    if(alternative=="two.sided") {
    stop("You must choose alternative = 'upper' or 'lower'")}
      }
  else {
    phat1<-p1
    phat2<-p2
    pi<-p0
    n1<-n1
    n2<-n2
    z<-(phat2-phat1)/sqrt((p0*(1-p0))*(1/n1+1/n2))
        names(z)<-"Z score"}
  
  if(alternative=="two.sided"){
    p<-1-pnorm(z,lower.tail=TRUE)+pnorm(z,lower.tail=FALSE)
    names(p)<-"P-value"
    lower<-sqrt(((phat1*(1-phat1))/n1)+((phat2*(1-phat2))/n2))
    upper<-pi+qnorm(1-conf.level/2)*sqrt(pi*(1-pi)/n1)
    ci<-c(lower,upper)
    names(ci)<-"CI"
    #crit<-qnorm(conf.level/2)
    #test<-p<-crit || p>crit
    }
  
  if(alternative=="lower") {
    p<-pnorm(z,lower.tail=TRUE)
    names(p)<-"P-value"
    lower<-phat1-qnorm(1-conf.level/2) * sqrt(phat1 * (1-phat1)/n1)
    upper<-phat1+qnorm(1-conf.level/2) * sqrt (phat1 * (1-phat1)/n1)
    ci<-c(lower,upper)
    names(ci)<-"CI"
    #crit<-qnorm(conf.level/2)
    #test<-p<-crit || p>crit
    }
  
  if(alternative=="upper") {
    p<-pnorm(z,lower.tail=FALSE)
    names(p)<-"P-value"
    lower<-phat1-qnorm(1-conf.level/2)*sqrt(phat1*(1-phat1)/n1)
    upper<-phat1+qnorm(1-conf.level/2)*sqrt(phat1*(1-phat1)/n1)
    ci<-c(lower,upper)
    names(ci)<-"CI"
    #crit<-qnorm(conf.level/2)
    #test<-p<-crit || p>crit
    }

  names(p0)<-"p0"
  names(p1)<-"p1"
  names(n1)<-"n1"
  attr(ci,"conf.level") <- conf.level
  if(is.null(p2) || is.null(n2)) {
RVAL <- list(method = "One-Sample Z Test of Proportions",
             data.name = paste0((p1), " success rate in mist nets"),
             null.value = p0,
             estimate = p1,
             statistic = z, 
             p.value = as.numeric(p), 
             conf.int = ci,
             alternative = alternative)
    class(RVAL) <- "htest"
    return(RVAL)}
  
  else {
  names(p2)<-"p2"
  names(n2)<-"n2"
RVAL <- list(method = "Two-Sample Z Test of Proportions",
             data.name = paste0((p1), " lactation rate vs. ", (p2), " lactation rate in bats"),
             null.value = p0,
             estimate = c(p1,p2),
             statistic = z, 
             p.value = as.numeric(p), 
             conf.int = ci,
             alternative = alternative)
    class(RVAL) <- "htest"
    return(RVAL)
  }
}

Here’s a test of it on the one-sample test example using the mist-netted birds data example:

v1 <- c(0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0,
    1, 1, 0, 1, 0, 1, 1)
p1<-mean(v1)
n1<-length(v1)
p0<-0.8

Z.prop.test(p1=p1,n1=n1,p0=p0,alternative='lower')

## 
##  One-Sample Z Test of Proportions
## 
## data:  0.6 success rate in mist nets
## Z score = -2.7386, p-value = 0.003085
## alternative hypothesis: true p0 is  0.8
## 95 percent confidence interval:
##  0.5943913 0.6056087
## sample estimates:
##  p1 
## 0.6

And here’s a two-sample test example using the mist-netted bats:

v1 <- c(1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0,
    1, 0)
v2 <- c(1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0,
    0, 1, 1, 0, 1, 1, 1)
p1<-mean(v1)
n1<-length(v1)
p2<-mean(v2)
n2<-length(v2)
p0<-(sum(v1) + sum(v2))/(length(v1) + length(v2))

Z.prop.test(p1=p1,n1=n1,p2=p2,n2=n2,p0=p0)

## 
##  Two-Sample Z Test of Proportions
## 
## data:  0.56 lactation rate vs. 0.7 lactation rate in bats
## Z score = 1.0747, p-value = 0.2825
## alternative hypothesis: true p0 is not equal to 0.6363636
## 95 percent confidence interval:
##  0.1298307 0.6423966
## sample estimates:
##   p1   p2 
## 0.56 0.70