## ----setup, include=FALSE, cache=FALSE-------------------------------------------------------------------------------------------------------------------------------------------
require(knitr)
is.key <- TRUE
# set global chunk options
opts_chunk$set(echo=TRUE,eval=TRUE,fig.path='figs/', fig.align='center', fig.show='hold')
options(formatR.arrow=TRUE, width=90)


## --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
pnorm(95,mean=100,sd=2.236,lower.tail=TRUE) # prob of getting a score <= 95
pnorm(105,mean=100,sd=2.236,lower.tail=FALSE) # prob of getting a score >= 105
0.01267143+0.01267143 # prob of getting a score <= 95 OR >= 105


## --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
 # the probability of getting a score <= 95.6 is 0.025...
qnorm(.025,mean=100,sd=2.236,lower.tail=TRUE) # qnorm... not pnorm
pnorm(95.61752,mean=100,sd=2.236,lower.tail=TRUE)
# the probability of getting a score >= 104.38 is 0.025...
pnorm(104.3825,mean=100,sd=2.236,lower.tail=FALSE)
0.02499999 + 0.02499946 # the JOINT probability of getting a score <=95.6 OR >=104.38


## --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
my.scores <- c(96, 94, 102,  86, 100,  92, 105,  86, 111,
  82,  96,  79,  79,  85,  99,  97, 105,  98,  94,  73)
t.test(x=my.scores,alternative="two.sided", mu=100)


## --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
t.test(x=my.scores,alternative="less", mu=100)


## --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
t.test(x=my.scores,alternative="greater", mu=100)


## --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
power.t.test(n=20,delta=5,sd=10,sig.level=0.05,type="one.sample",alternative="two.sided")


## --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
power.t.test(n=20,delta=5,sd=10,sig.level=0.05,type="one.sample",alternative="one.sided")


## --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
sample.A <- c(95, 92, 93, 96, 98, 99)
sample.B <- c(101, 99, 106, 100, 98, 111)
t.test(x=sample.A,y=sample.B,alternative="two.sided", var.equal=TRUE)


## --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
t.test(x=sample.A,y=sample.B,alternative="two.sided")


## --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
t.test(x=sample.A,y=sample.B,paired=TRUE)