Chapter 14 Sources

14.1 t-test

The data set shows energy expend in two groups of women: stature

library(ISwR)
data(energy)
attach(energy)

## The following objects are masked from energy (pos = 22):
## 
##     expend, stature

head(energy)

##   expend stature
## 1   9.21   obese
## 2   7.53    lean
## 3   7.48    lean
## 4   8.08    lean
## 5   8.09    lean
## 6  10.15    lean

tapply(expend, stature, mean)

##      lean     obese 
##  8.066154 10.297778

H₀: there is no difference in averages between lean and obese.

t.test(expend ~ stature)

## 
##  Welch Two Sample t-test
## 
## data:  expend by stature
## t = -3.8555, df = 15.919, p-value = 0.001411
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -3.459167 -1.004081
## sample estimates:
##  mean in group lean mean in group obese 
##            8.066154           10.297778

Alternative hypothesis is true - means are different.
Mean difference is in between -3.5 and 1.0 with a probability 95%.
The risk of error is 0.15%

14.1.1 Two-tailed test

Compair two sets of variables.

data(intake) # from package ISwR
attach(intake)

## The following objects are masked from intake (pos = 22):
## 
##     post, pre

head(intake)

##    pre post
## 1 5260 3910
## 2 5470 4220
## 3 5640 3885
## 4 6180 5160
## 5 6390 5645
## 6 6515 4680

mean(post - pre)

## [1] -1320.455

Is difference of means significant?

t.test(pre, post, paired=TRUE)

## 
##  Paired t-test
## 
## data:  pre and post
## t = 11.941, df = 10, p-value = 3.059e-07
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  1074.072 1566.838
## sample estimates:
## mean of the differences 
##                1320.455

The difference is significant with a probability 95%.
The difference is in between 1074.1 and 1566.8 kJ/day