Obtaining absolute deviation from mean for two sets of scores

Question

To obtain absolute deviation from the mean for two groups of scores, I usually need to write long codes in R such as the ones shown below.

Question

I was won

Answer 1

How about

score <- lapply(split(y, groups), FUN = function (u) abs(u - mean(u)))

or

score <- ave(y, groups, FUN = function (u) abs(u - mean(u)))

The results are organized in a different way. Choose the one that is most comfortable to you.

---

There is something wrong with your wording. mad returns a single statistic / value for data. For example,

sapply(split(y, groups), mad)

You are not vectorizing mad, but simply computing the deviation for each datum as your example code shows.

Answer 2

If you stick everything in a data.frame, it's much cleaner. In base R,

set.seed(0)

df <- data.frame(y = rnorm(20),
                 group = rep(1:2, each = 10))

df$abs_dev <- with(df, ave(y, group, FUN = function(x){abs(mean(x) - x)}))

df
#>               y  group    abs_dev
#> 1   1.262954285      1 0.90403032
#> 2  -0.326233361      1 0.68515732
#> 3   1.329799263      1 0.97087530
#> 4   1.272429321      1 0.91350536
#> 5   0.414641434      1 0.05571747
#> 6  -1.539950042      1 1.89887401
#> 7  -0.928567035      1 1.28749100
#> 8  -0.294720447      1 0.65364441
#> 9  -0.005767173      1 0.36469114
#> 10  2.404653389      1 2.04572943
#> 11  0.763593461      2 1.12607477
#> 12 -0.799009249      2 0.43652794
#> 13 -1.147657009      2 0.78517570
#> 14 -0.289461574      2 0.07301974
#> 15 -0.299215118      2 0.06326619
#> 16 -0.411510833      2 0.04902952
#> 17  0.252223448      2 0.61470476
#> 18 -0.891921127      2 0.52943981
#> 19  0.435683299      2 0.79816461
#> 20 -1.237538422      2 0.87505711

or dplyr,

library(dplyr)
set.seed(0)

df <- data_frame(y = rnorm(20),
                 group = rep(1:2, each = 10))

df <- df %>% group_by(group) %>% mutate(abs_dev = abs(mean(y) - y))

df
#> # A tibble: 20 x 3
#> # Groups:   group [2]
#>               y  group    abs_dev
#>           <dbl>  <int>      <dbl>
#>  1  1.262954285      1 0.90403032
#>  2 -0.326233361      1 0.68515732
#>  3  1.329799263      1 0.97087530
#>  4  1.272429321      1 0.91350536
#>  5  0.414641434      1 0.05571747
#>  6 -1.539950042      1 1.89887401
#>  7 -0.928567035      1 1.28749100
#>  8 -0.294720447      1 0.65364441
#>  9 -0.005767173      1 0.36469114
#> 10  2.404653389      1 2.04572943
#> 11  0.763593461      2 1.12607477
#> 12 -0.799009249      2 0.43652794
#> 13 -1.147657009      2 0.78517570
#> 14 -0.289461574      2 0.07301974
#> 15 -0.299215118      2 0.06326619
#> 16 -0.411510833      2 0.04902952
#> 17  0.252223448      2 0.61470476
#> 18 -0.891921127      2 0.52943981
#> 19  0.435683299      2 0.79816461
#> 20 -1.237538422      2 0.87505711

or data.table:

library(data.table)
set.seed(0)

dt <- data.table(y = rnorm(20),
                 group = rep(1:2, each = 10))

dt[, abs_dev := abs(mean(y) - y), by = group][]
#>                y group    abs_dev
#>  1:  1.262954285     1 0.90403032
#>  2: -0.326233361     1 0.68515732
#>  3:  1.329799263     1 0.97087530
#>  4:  1.272429321     1 0.91350536
#>  5:  0.414641434     1 0.05571747
#>  6: -1.539950042     1 1.89887401
#>  7: -0.928567035     1 1.28749100
#>  8: -0.294720447     1 0.65364441
#>  9: -0.005767173     1 0.36469114
#> 10:  2.404653389     1 2.04572943
#> 11:  0.763593461     2 1.12607477
#> 12: -0.799009249     2 0.43652794
#> 13: -1.147657009     2 0.78517570
#> 14: -0.289461574     2 0.07301974
#> 15: -0.299215118     2 0.06326619
#> 16: -0.411510833     2 0.04902952
#> 17:  0.252223448     2 0.61470476
#> 18: -0.891921127     2 0.52943981
#> 19:  0.435683299     2 0.79816461
#> 20: -1.237538422     2 0.87505711