Several Grubbs tests simultaneously in R - r

Question

I'm new using R, I'm just starting with the outliers package. Probably this is very easy, but could anybody tell me how to run several Grubbs tests at the same time? I have 20 columns and I want to test all of them simultaneously.
Thanks in advance
Edit: Sorry for not explaining well. I'll try. I started using R today and I learned how to make Grubbs test using grubbs.test(data$S1, type=10 or 11 or 20) and it goes well. But I have a table with 20 columns, and I want to run Grubbs test for each of them simultaneously. I can do it one by one, but I think there must be a way to do it faster.
I ran the code at How to repeat the Grubbs test and flag the outliers as well, and works perfectly, but again, I would like to do it with my 20 samples.
As an example of my data:
S1 S2 S3 S4 S5 S6 S7
96 40 99 45 12 16 48
52 49 11 49 59 77 64
18 43 11 67 6 97 91
79 19 39 28 45 44 99
9 78 88 6 25 43 78
60 12 29 32 2 68 25
18 61 60 30 26 51 70
96 98 55 74 83 17 69
19 0 17 24 0 75 45
42 70 71 7 61 82 100
39 80 71 58 6 100 94
100 5 41 18 33 98 97
Hope this helps.

Answer 1

You can use lapply:
library(outliers)
df = data.frame(a=runif(20),b=runif(20),c=runif(20))
tests = lapply(df,grubbs.test)
# or with parameters:
tests = lapply(df,grubbs.test,opposite=T)
Results:
> tests
$a
Grubbs test for one outlier
data: X[[i]]
G = 1.80680, U = 0.81914, p-value = 0.6158
alternative hypothesis: highest value 0.963759744539857 is an outlier
$b
Grubbs test for one outlier
data: X[[i]]
G = 1.53140, U = 0.87008, p-value = 1
alternative hypothesis: highest value 0.975481075001881 is an outlier
$c
Grubbs test for one outlier
data: X[[i]]
G = 1.57910, U = 0.86186, p-value = 1
alternative hypothesis: lowest value 0.0136249314527959 is an outlier
You can access the results as follows:
> tests$a$statistic
G U
1.8067906 0.8191417
Hope this helps.

Answer 2

A #Florian answer can be updated a bit. For example fancy and easy-reading result can be achieved with purrr package and tidyverse. It can be useful if you are comparing loads of groups:
Load necessary packages:
library(dplyr)
library(purrr)
library(tidyr)
library(outliers)
Create some data - we're going to use the same from Florian's answer, but transformed to a modern tibble and long format:
df <- tibble(a = runif(20),
b = runif(20),
c = runif(20)) %>%
# transform to along format
tidyr::gather(letter, value)
Then instead of apply functions we can use map and map_dbl from purrr:
df %>%
group_by(letter) %>%
nest() %>%
mutate(n = map_dbl(data, ~ nrow(.x)), # number of entries
G = map(data, ~ grubbs.test(.x$value)$statistic[[1]]), # G statistic
U = map(data, ~ grubbs.test(.x$value)$statistic[[2]]), # U statistic
grubbs = map(data, ~ grubbs.test(.x$value)$alternative), # Alternative hypotesis
p_grubbs = map_dbl(data, ~ grubbs.test(.x$value)$p.value)) %>% # p-value
# Let's make the output more fancy
mutate(G = signif(unlist(G), 3),
U = signif(unlist(U), 3),
grubbs = unlist(grubbs),
p_grubbs = signif(p_grubbs, 3)) %>%
select(-data) %>% # remove temporary column
arrange(p_grubbs)
And the desired output would be this:
# A tibble: 3 x 6
letter n G U grubbs p_grubbs
<chr> <dbl> <dbl> <dbl> <chr> <dbl>
1 c 20 1.68 0.843 lowest value 0.0489965472370386 is an outlier 0.84
2 a 20 1.58 0.862 lowest value 0.0174888013862073 is an outlier 1
3 b 20 1.57 0.863 lowest value 0.0656482006888837 is an outlier 1