# Comparing an observed proportion to a population value 
# - The Binomial test

# from website:
mydataframe <- read.delim("http://www.robin-beaumont.co.uk/virtualclassroom/book2data/binary_n1361.dat", header=TRUE)

### local ignore:
# mydataframe <- read.delim("D:\\web_sites_mine\\HIcourseweb new\\book2data\\binary_n1361.dat", 
# header=TRUE)
###
names(mydataframe)

mytable <- xtabs(~ value , data= mydataframe )
mytable
binom.test(rbind(mytable), alternative='two.sided', p=.25, conf.level=.95)

binom.test(c(328, 1033), alternative='two.sided', p=.25, conf.level=.95)

# If we can't even be bothered to work out 
# how many there are in the second category you can use:
binom.test(328, 1361, alternative='two.sided', p=.25, conf.level=.95)

####  drawing distribution
# auto generated from R Commander
.x <- 289:394
plotDistr(.x, dbinom(.x, size=1361, prob=0.25), 
  xlab="Number of Successes", ylab="Probability Mass", 
  main="Binomial Distribution:  Binomial trials=1361, Probability of success=0.25",
   discrete=TRUE)
remove(.x)
#  adding the line manually
abline(v=328, lwd=5, col="red")
abline(v=352, lwd=5, col="blue")

# now consider the critical values for CV= 0.05
qbinom(c(.025,.975), size=1361, prob=0.25, lower.tail=TRUE)
# [1] 309 372
# add then to the plot
abline(v=309, lwd=5, col="red", lty=2)
abline(v=372, lwd=5, col="blue", lty=2)
text(309,.02,"lower CV")
text(372,.02,"upper CV")