paired t-test

paired t-test example

data setup

Systolic blood pressure of 5 patients assessed at baseline and at 2 weeks follow-up, after being adminstered a blood-pressure lowering drug.

• group 1 = baseline
• group 2 = follow-up at week 2

SBP_data <- data.frame("SBP" = c(140,138,150,148,135,132,135,151,146,130),"group"=as.factor(c(rep(1,5),rep(2,5))),"ID"=as.factor(c(rep(1:5,2))))

data visualisation

library(ggplot2)

g <- ggplot(SBP_data, aes(x=group, y=SBP, group=factor(ID)))
g + geom_point() + geom_line(size=1, aes(col=ID))

t-test

perform two-sided paired t-test (utilising within-subject variance)

with(SBP_data, t.test(SBP[group == 2], SBP[group ==1], alternative="two.sided", paired= TRUE))

## 
##  Paired t-test
## 
## data:  SBP[group == 2] and SBP[group == 1]
## t = -2.2616, df = 4, p-value = 0.08652
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -7.5739122  0.7739122
## sample estimates:
## mean of the differences 
##                    -3.4

Fail to reject the null hypothesis (p = 0.087) at significance level .05. Mean difference of 3.4 with confidence interval (-7.58, 0.77).

Manually

g1 <- SBP_data$SBP[SBP_data$group == 1]
g2 <- SBP_data$SBP[SBP_data$group == 2]

dif <- g2-g1

sample_mn <- mean(dif)
sample_sd <- sd(dif)
n <- 5

sample_mn + c(-1,1)*qt(.975,df=n-1)*sample_sd/sqrt(n)

## [1] -7.5739122  0.7739122