# Techniques for testing basic assumptions in R:
# normality and homogeneity of variance


# more standard plots
library(car)

#install psych if you haven't already
install.packages("psych", dependencies = TRUE)

# use psych for the describe function
library(psych)


# load the countries dataset, including 
# corruption and internet growth variables
load("Countries.Rdata")
summary(Countries)

### Normality

# use a histogram to see if the distribution of gdp looks normal
hist(Countries$gdp2012)
hist(Countries$gdp2012, breaks = 20)

# Check some numerical measures using describe
describe(Countries$gdp2012)


# check normality using a qqplot
qqnorm(Countries$gdp2012)

# Finally, use a Shapiro-Wilk test to see if normality is a plausible hypothesis
shapiro.test(Countries$gdp2012)



# Next, let's do the same thing with the log of gdp
# This is a very common transformation in econometrics
Countries$loggdp = log10(Countries$gdp2012)

# Begin with the Shapiro-Wilk test
shapiro.test(Countries$loggdp)

# And look at the shape of the qqplot
qqnorm(Countries$loggdp)

# use a histogram to see if the distribution of loggdp looks normal
hist(Countries$loggdp)

### Homogeneity of Variance

# Let's use compare loggdp between two groups of countries: 
# those with higher fertility and those with lower fertility

Countries$high_fertility = factor(Countries$fertility_rate > mean(Countries$fertility_rate, na.rm = TRUE))

# First, check the means
by(Countries$loggdp, Countries$high_fertility, mean, na.rm = TRUE)

# check if the variances are the same for both groups
by(Countries$loggdp, Countries$high_fertility, var, na.rm = TRUE)

# use a Levene test to see if equal variances is a plausible hypothesis
leveneTest(Countries$loggdp, Countries$high_fertility)