How to repeat the Grubbs test and flag the outliers

Question

I am wanting to apply the Grubbs test to a set of data repeatedly until it ceases to find outliers. I want the outliers flagged rather than removed so that I can plot the d

Answer 1

Looks like you would need a short function to do what you want:

library(outliers)
library(ggplot2)

X <- c(152.36,130.38,101.54,96.26,88.03,85.66,83.62,76.53,
       74.36,73.87,73.36,73.35,68.26,65.25,63.68,63.05,57.53)

grubbs.flag <- function(x) {
  outliers <- NULL
  test <- x
  grubbs.result <- grubbs.test(test)
  pv <- grubbs.result$p.value
  while(pv < 0.05) {
    outliers <- c(outliers,as.numeric(strsplit(grubbs.result$alternative," ")[[1]][3]))
    test <- x[!x %in% outliers]
    grubbs.result <- grubbs.test(test)
    pv <- grubbs.result$p.value
  }
  return(data.frame(X=x,Outlier=(x %in% outliers)))
}

Here's the output:

grubbs.flag(X)
         X Outlier
1   152.36    TRUE
2   130.38    TRUE
3   101.54   FALSE
4    96.26   FALSE
5    88.03   FALSE
6    85.66   FALSE
7    83.62   FALSE
8    76.53   FALSE
9    74.36   FALSE
10   73.87   FALSE
11   73.36   FALSE
12   73.35   FALSE
13   68.26   FALSE
14   65.25   FALSE
15   63.68   FALSE
16   63.05   FALSE
17   57.53   FALSE

And if you want a histogram with different colors, you can use the following:

ggplot(grubbs.flag(X),aes(x=X,color=Outlier,fill=Outlier))+
  geom_histogram(binwidth=diff(range(X))/30)+
  theme_bw()

Answer 2

Sam Dickson's answer is great, but will throw an error if you reach a point where all but two values are flagged as outliers or if you only started with three values in the first place (grubbs.test() won't return a p-value if there are only two values in the input vector).

I added a breakpoint to the while loop for this contingency and it will also throw a warning if this happens. In addition it will throw an informative error when you start with less than two input values.

grubbs.flag <- function(x) {
  outliers <- NULL
  test <- x
  grubbs.result <- grubbs.test(test)
  pv <- grubbs.result$p.value
  # throw an error if there are too few values for the Grubb's test
  if (length(test) < 3 ) stop("Grubb's test requires > 2 input values")
  while(pv < 0.05) {
    outliers <- c(outliers,as.numeric(strsplit(grubbs.result$alternative," ")[[1]][3]))
    test <- x[!x %in% outliers]
    # stop if all but two values are flagged as outliers
    if (length(test) < 3 ) {
      warning("All but two values flagged as outliers")
      break
    }
    grubbs.result <- grubbs.test(test)
    pv <- grubbs.result$p.value
  }
  return(data.frame(X=x,Outlier=(x %in% outliers)))
}

It goes without saying of course that it probably doesn't make much sense to do outlier tests if you only have three data points to begin with, but I don't know your business.