Testing the mean difference

Simulate some data wfor pre- and post- treatment

set.seed(1234)
n <- 9
pre <- round(rnorm(n,50,2))
pre

## [1] 48 51 52 45 51 51 49 49 49

post <- pre+1+round(rnorm(n))
post

## [1] 48 52 52 45 52 53 50 49 49

Show the data

d <- post-pre
(X <- cbind(pre,post,d))

##       pre post d
##  [1,]  48   48 0
##  [2,]  51   52 1
##  [3,]  52   52 0
##  [4,]  45   45 0
##  [5,]  51   52 1
##  [6,]  51   53 2
##  [7,]  49   50 1
##  [8,]  49   49 0
##  [9,]  49   49 0

Descriptive statistics

(xbar <- round(apply(X,2,mean),2))

##   pre  post     d 
## 49.44 50.00  0.56

(sd <- round(apply(X,2,sd),2))

##  pre post    d 
## 2.13 2.55 0.73

(se <- round(sd/sqrt(n),2))

##  pre post    d 
## 0.71 0.85 0.24

sqrt(sum(se[1:2]^2))  # se of difference

## [1] 1.10752

Test the mean difference

t.test(d)

## 
##  One Sample t-test
## 
## data:  d
## t = 2.2942, df = 8, p-value = 0.05093
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
##  -0.002868833  1.113979944
## sample estimates:
## mean of x 
## 0.5555556

Test the difference of means

t.test(pre,post)

## 
##  Welch Two Sample t-test
## 
## data:  pre and post
## t = -0.5019, df = 15.504, p-value = 0.6228
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -2.908271  1.797160
## sample estimates:
## mean of x mean of y 
##  49.44444  50.00000