The first thing I did was enter “?swiss” so that I could get an explanation of what each variable represented, which I have copied below:
[,1] Fertility Ig, ‘common standardized fertility measure’
[,2] Agriculture % of males involved in agriculture as occupation
[,3] Examination % draftees receiving highest mark on army examination
[,4] Education % education beyond primary school for draftees.
[,5] Catholic % ‘catholic’ (as opposed to ‘protestant’).
[,6] Infant.Mortality live births who live less than 1 year.
Then, I looked at some descriptive statistics for the data
str(swiss)
## 'data.frame': 47 obs. of 6 variables:
## $ Fertility : num 80.2 83.1 92.5 85.8 76.9 76.1 83.8 92.4 82.4 82.9 ...
## $ Agriculture : num 17 45.1 39.7 36.5 43.5 35.3 70.2 67.8 53.3 45.2 ...
## $ Examination : int 15 6 5 12 17 9 16 14 12 16 ...
## $ Education : int 12 9 5 7 15 7 7 8 7 13 ...
## $ Catholic : num 9.96 84.84 93.4 33.77 5.16 ...
## $ Infant.Mortality: num 22.2 22.2 20.2 20.3 20.6 26.6 23.6 24.9 21 24.4 ...
library(psych)
describe(swiss)
## vars n mean sd median trimmed mad min max
## Fertility 1 47 70.14 12.49 70.40 70.66 10.23 35.00 92.5
## Agriculture 2 47 50.66 22.71 54.10 51.16 23.87 1.20 89.7
## Examination 3 47 16.49 7.98 16.00 16.08 7.41 3.00 37.0
## Education 4 47 10.98 9.62 8.00 9.38 5.93 1.00 53.0
## Catholic 5 47 41.14 41.70 15.14 39.12 18.65 2.15 100.0
## Infant.Mortality 6 47 19.94 2.91 20.00 19.98 2.82 10.80 26.6
## range skew kurtosis se
## Fertility 57.50 -0.46 0.26 1.82
## Agriculture 88.50 -0.32 -0.89 3.31
## Examination 34.00 0.45 -0.14 1.16
## Education 52.00 2.27 6.14 1.40
## Catholic 97.85 0.48 -1.67 6.08
## Infant.Mortality 15.80 -0.33 0.78 0.42
boxplot(swiss)
hist(swiss$Fertility)
hist(swiss$Agriculture)
hist(swiss$Examination)
hist(swiss$Education)
hist(swiss$Catholic)
hist(swiss$Infant.Mortality)
Based on the histogram and box plots for the Catholic and Education variables, I don’t think these variables are normally distributed, so I have excluded them from the additional analysis.
I calculated a 95% confidence interval for the remaining variables: Fertility, Agriculture, Examination, and Infant.Mortality.
mean(swiss$Fertility)+(qnorm(0.025)*sd(swiss$Fertility)/sqrt(47))
## [1] 66.5713
mean(swiss$Fertility)+(qnorm(0.975)*sd(swiss$Fertility)/sqrt(47))
## [1] 73.71381
mean(swiss$Agriculture)+(qnorm(0.025)*sd(swiss$Agriculture)/sqrt(47))
## [1] 44.16666
mean(swiss$Agriculture)+(qnorm(0.975)*sd(swiss$Agriculture)/sqrt(47))
## [1] 57.15249
mean(swiss$Examination)+(qnorm(0.025)*sd(swiss$Examination)/sqrt(47))
## [1] 14.20856
mean(swiss$Examination)+(qnorm(0.975)*sd(swiss$Examination)/sqrt(47))
## [1] 18.77016
mean(swiss$Infant.Mortality)+(qnorm(0.025)*sd(swiss$Infant.Mortality)/sqrt(47))
## [1] 19.10984
mean(swiss$Infant.Mortality)+(qnorm(0.975)*sd(swiss$Infant.Mortality)/sqrt(47))
## [1] 20.77526
I found an alternative method for calculating confidence intervals online.
library(Rmisc)
## Loading required package: lattice
## Loading required package: plyr
CI(swiss$Fertility,ci=0.95)
## upper mean lower
## 73.81025 70.14255 66.47485
CI(swiss$Agriculture,ci=0.95)
## upper mean lower
## 57.32784 50.65957 43.99131
CI(swiss$Examination,ci=0.95)
## upper mean lower
## 18.83176 16.48936 14.14697
CI(swiss$Infant.Mortality,ci=0.95)
## upper mean lower
## 20.79775 19.94255 19.08735
The results are slightly different, so I’m curious if anyone knows why.