Recreate minitab normal probability plot

Question

I am trying to recreate the following plot with R. Minitab describes this as a normal probability plot.

The probplot gets you most of the way there. Unfortunately, I cannot figure out how to add the confidence interval bands around this plot.

Similarly, ggplot's stat_qq() seems to present similar information with a transformed x axis. It seems that geom_smooth() would be the likely candidate to add the bands, but I haven't figure that out.

Finally, the Getting Genetics Done guys describe something similar here.

Sample data to recreate the plot above:

x <- c(40.2, 43.1, 45.5, 44.5, 39.5, 38.5, 40.2, 41.0, 41.6, 43.1, 44.9, 42.8)

If anyone has a solution with base graphics or ggplot, I'd appreciate it!

EDIT

After looking at the details of probplot, I've determined this is how it generates the fit line on the graph:

> xl <- quantile(x, c(0.25, 0.75))
> yl <- qnorm(c(0.25, 0.75))
> slope <- diff(yl)/diff(xl)
> int <- yl[1] - slope * xl[1]
> slope
   75% 
0.4151 
> int
   75% 
-17.36 

Indeed, comparing these results to what you get out of the probplot object seem to compare very well:

> check <- probplot(x)
> str(check)
List of 3
 $ qdist:function (p)  
 $ int  : Named num -17.4
  ..- attr(*, "names")= chr "75%"
 $ slope: Named num 0.415
  ..- attr(*, "names")= chr "75%"
 - attr(*, "class")= chr "probplot"
> 

However, incorporating this information into ggplot2 or base graphics does not yield the same results.

probplot(x)

Versus:

ggplot(data = df, aes(x = x, y = y)) + geom_point() + geom_abline(intercept = int, slope = slope)

I get similar results using R's base graphics

plot(df$x, df$y)
abline(int, slope, col = "red")

Lastly, I've learned that the last two rows of the legend refer to the Anderson-Darling test for normality and can be reproduced with the nortest package.

> ad.test(x)

    Anderson-Darling normality test

data:  x 
A = 0.2303, p-value = 0.7502

Answer 1

Perhaps this will be something you can build on. By default, stat_smooth() uses level=0.95.

df <- data.frame(sort(x), ppoints(x))
colnames(df) <- c("x","y")

ggplot(df, aes(x,y)) + 
geom_point() + 
stat_smooth() + 
scale_y_continuous(limits=c(0,1),breaks=seq(from=0.05,to=1,by=0.05), formatter="percent")

Answer 2

Try the qqPlot function in the QTLRel package.

require("QTLRel")
qqPlot(rnorm(100))

Answer 3

I know it's an old question, but for others who also still look for a solution, have a look at ggqqplot from the ggpubr package.

library(ggpubr)
ggqqplot(data$sample)

Answer 4

you are using the incorrect "y", they should be quantiles (labeled with probabilities). The following shows the line in the right spot:

df<-data.frame(x=sort(x),y=qnorm(ppoints(length(x)))) 
probs <- c(0.01, 0.05, seq(0.1, 0.9, by = 0.1), 0.95, 0.99)
qprobs<-qnorm(probs)

xl <- quantile(x, c(0.25, 0.75))
yl <-  qnorm(c(0.25, 0.75))
slope <- diff(yl)/diff(xl)
int <- yl[1] - slope * xl[1]
ggplot(data = df, aes(x = x, y = y)) + geom_point() + geom_abline(intercept = int,slope = slope)+scale_y_continuous(limits=range(qprobs), breaks=qprobs, labels = 100*probs)+labs(y ="Percent" , x="Data")

to add the confidence bounds as in Minitab, you can do the following

fd<-fitdistr(x, "normal") #Maximum-likelihood Fitting of Univariate Dist from MASS 
xp_hat<-fd$estimate[1]+qprobs*fd$estimate[2]  #estimated perc. for the fitted normal
v_xp_hat<- fd$sd[1]^2+qprobs^2*fd$sd[2]^2+2*qprobs*fd$vcov[1,2] #var. of estimated perc
xpl<-xp_hat + qnorm(0.025)*sqrt(v_xp_hat)  #lower bound
xpu<-xp_hat + qnorm(0.975)*sqrt(v_xp_hat)  #upper bound

df.bound<-data.frame(xp=xp_hat,xpl=xpl, xpu = xpu,nquant=qprobs)

and add the following two lines to your ggplot from above (in addition, replace the slope and intercept line approach with the estimated percentiles)

geom_line(data=df.bound,aes(x = xp, y = qprobs))+
geom_line(data=df.bound,aes(x = xpl, y = qprobs))+
geom_line(data=df.bound,aes(x = xpu, y = qprobs))