QQplots explained

qqplots.R

## My understanding of a qqplot was it was the sorted values for a variable on the
## y against the theoretical values from a normal (or whatever distribution)
## distribution on the x. We can get the y values from our sample and the x values
## from looking up the p value in a given distribution and getting the
## corresponding nromal value. Now to get the p value I thought we divide the 1
## through length of the sample by n + 1. I have never actually tried to do this
## and used qqplot or the same geom_qq from ggplot. But today I tried to make the
## qqplot by hand and I don't get the same scale for the theoretical values and am
## unsure why. The points look the same but the scale is different. Why?

## This is wrong (almost right)
x <- c(3.89, 4.75, 4.75, 5.2, 5.78, 5.8, 6.33, 7.21, 7.9)

par(mfrow = c(2, 1))
plot(qnorm((1:length(x))/(1 + length(x))), sort(x))
qqnorm(x)

## R uses 
x <- c(3.89, 4.75, 4.75, 5.2, 5.78, 5.8, 6.33, 7.21, 7.9)

par(mfrow = c(2, 1))
plot(qnorm((1:length(x))/(1 + length(x))), sort(x))
qqnorm(x)

## See: https://www.youtube.com/watch?v=X9_ISJ0YpGw
##      http://www.talkstats.com/threads/quantile-quantile-plot-qqplot-in-r-by-hand-ish.71391/#post-206769
 

correct