Suppose we are interested in whether a drug reduces the level of bad cholesterol significantly. We measure cholesterol before and after treatment.
#dataset
before <- c(155, 151, 80, 112, 179, 170, 131, 175, 153, 175)
after <- c(139, 93, 133, 150, 135, 160, 155, 82, 84, 137)
summary(before)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 80.0 136.0 154.0 148.1 173.8 179.0
summary(after)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 82.0 103.0 136.0 126.8 147.2 160.0
sd(before)
## [1] 31.96335
sd(after)
## [1] 29.39312
#converting datasets into data.frame
data <- data.frame(before, after)
data
## before after
## 1 155 139
## 2 151 93
## 3 80 133
## 4 112 150
## 5 179 135
## 6 170 160
## 7 131 155
## 8 175 82
## 9 153 84
## 10 175 137
summary(data)
## before after
## Min. : 80.0 Min. : 82.0
## 1st Qu.:136.0 1st Qu.:103.0
## Median :154.0 Median :136.0
## Mean :148.1 Mean :126.8
## 3rd Qu.:173.8 3rd Qu.:147.2
## Max. :179.0 Max. :160.0
res <- t.test(before, after, paired = TRUE, alternative = "two.sided")
res
##
## Paired t-test
##
## data: before and after
## t = 1.401, df = 9, p-value = 0.1947
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -13.09182 55.69182
## sample estimates:
## mean of the differences
## 21.3
#Two sided Paired Sample T Test shows that there is no significant difference between before and after as p-value > 0.05 fails to reject the null
res2 <- t.test(before, after, paired = TRUE, alternative = "less")
res2
##
## Paired t-test
##
## data: before and after
## t = 1.401, df = 9, p-value = 0.9026
## alternative hypothesis: true difference in means is less than 0
## 95 percent confidence interval:
## -Inf 49.16901
## sample estimates:
## mean of the differences
## 21.3
res3 <- t.test(before, after, paired = TRUE, alternative = "greater")
res3
##
## Paired t-test
##
## data: before and after
## t = 1.401, df = 9, p-value = 0.09737
## alternative hypothesis: true difference in means is greater than 0
## 95 percent confidence interval:
## -6.569011 Inf
## sample estimates:
## mean of the differences
## 21.3