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#
# PROJECT:      ERC ANALYSIS
# AUTHOR:       NICOLA FOSTER
# LAST UPDATED: 31 JANUARY 2021
# 
# FIGURE-CONCENTRATION INDEX
#
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# finding the right colours
library(colortools)

# using the weighted concentration index estimated using the conindex command in stata
# converts the "robust standard errors" into standard deviations, where sd is estimated from 
# the standard error of a mean by multiplying square root of sample size


# sets initial parameters
n_ci1 <- 90975
sd_ci1 <- 0.03518817
ind_ci1 <- (-0.1036192)

set.seed(ind_ci1)
ci1 <- rnorm(n=n_ci1, mean=ind_ci1, sd=sd_ci1)
# checks whether the summary simulates the original findings
round(c(n=length(ci1), mean=mean(ci1), sd=sd(ci1)), 2)



# sets initial parameters
n_ci2 <- 56260
sd_ci2 <- 0.04633685
# sd_ci2 <- (0.04633685 * sqrt(n_ci2))/2
ind_ci2 <- 0.06548882

set.seed(ind_ci2)
ci2 <- rnorm(n=n_ci2, mean=ind_ci2, sd=sd_ci2)
# checks whether the summary simulates the original findings
round(c(n=length(ci2), mean=mean(ci2), sd=sd(ci2)), 2)

boxplot(ci1, ci2,
        names = c("2007", "2017"),
        ylab = "Concentration index (Standard Error)",
        col = c("#4169E1", "#E1B941"),
        border = c("royalblue4", "goldenrod4"),
        notch = TRUE)
text(x=1, y=0.15, labels="n = 90 975 
     \n ConcentrationIndex = -0.104
     \n p-Value = 0.003")
text(x=2, y=0.15, labels="n = 56 260 
     \n ConcentrationIndex = 0.066
     \n p-Value = 0.158")
abline(h=0.0, col="Black", lty=2)