calculating z scores
July 16, 2020
The scale() function will center and/or scale a numeric object. Use center = TRUE to subtract the mean from the values; use scale = TRUE to divide the centered values by the standard deviation to produce z scores.
center variable A
scale(A, center = TRUE, scale = FALSE)
generate z-scores for variable A
scale(A, center = TRUE, scale = TRUE)
Lets try it with EMG data
read in clean EMG data
Sample data from N=5 participants
library(tidyverse)
emg <- read_csv("sampleEMG.csv")
glimpse(emg)
## Rows: 1,760
## Columns: 8
## $ ...1 <dbl> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 1…
## $ pp_no <chr> "pp1", "pp1", "pp1", "pp1", "pp1", "pp1", "pp1", "pp1", "pp1…
## $ condition <chr> "stimtype1", "stimtype1", "stimtype1", "stimtype1", "stimtyp…
## $ bin <chr> "bin_0", "bin_0", "bin_1", "bin_1", "bin_2", "bin_2", "bin_3…
## $ bin_no <dbl> 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, …
## $ trial <chr> "trial1", "trial1", "trial1", "trial1", "trial1", "trial1", …
## $ muscle <chr> "brow", "cheek", "brow", "cheek", "brow", "cheek", "brow", "…
## $ rms <dbl> 2.1998, 9.1660, 2.1451, 5.7558, 2.7000, 10.9498, 1.1724, 7.4…
Get data set up
This dataset is long with muscle (brow,cheek) in a single variable. We want to z score each muscle separately, so easiest to make the brow and cheek data wide.
Make data wide
emg_wide <- emg %>%
pivot_wider(names_from = "muscle", values_from = "rms")
glimpse(emg_wide)
## Rows: 1,760
## Columns: 8
## $ ...1 <dbl> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 1…
## $ pp_no <chr> "pp1", "pp1", "pp1", "pp1", "pp1", "pp1", "pp1", "pp1", "pp1…
## $ condition <chr> "stimtype1", "stimtype1", "stimtype1", "stimtype1", "stimtyp…
## $ bin <chr> "bin_0", "bin_0", "bin_1", "bin_1", "bin_2", "bin_2", "bin_3…
## $ bin_no <dbl> 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, …
## $ trial <chr> "trial1", "trial1", "trial1", "trial1", "trial1", "trial1", …
## $ brow <dbl> 2.1998, NA, 2.1451, NA, 2.7000, NA, 1.1724, NA, 1.6986, NA, …
## $ cheek <dbl> NA, 9.1660, NA, 5.7558, NA, 10.9498, NA, 7.4457, NA, 6.1996,…
Now use mutate to create new columns that contain z scores.
Option 1: mutate z scores manually
mutate(z_score = (value - mean(value)) / sd(value))
emg_z_manual <- emg_wide %>%
mutate(Zbrow = (brow - mean(brow))/sd(brow)) %>%
mutate(Zcheek = (cheek - mean(cheek))/sd(cheek))
Option 2: mutate z scores using scale()
emg_z_scale <- emg_wide %>%
mutate(Zbrow = scale(brow, center = TRUE, scale = TRUE)) %>%
mutate(Zcheek = scale(cheek, center = TRUE, scale = TRUE))
Check
Use summary to check that the mean is now 0
summary(emg_z_scale)
## ...1 pp_no condition bin
## Min. : 1.0 Length:1760 Length:1760 Length:1760
## 1st Qu.: 440.8 Class :character Class :character Class :character
## Median : 880.5 Mode :character Mode :character Mode :character
## Mean : 880.5
## 3rd Qu.:1320.2
## Max. :1760.0
##
## bin_no trial brow cheek
## Min. : 0 Length:1760 Min. : 0.9923 Min. : 1.513
## 1st Qu.: 2 Class :character 1st Qu.: 4.4201 1st Qu.: 2.968
## Median : 5 Mode :character Median : 7.2572 Median : 3.817
## Mean : 5 Mean : 7.2396 Mean : 6.042
## 3rd Qu.: 8 3rd Qu.: 9.0815 3rd Qu.: 6.122
## Max. :10 Max. :40.6425 Max. :168.999
## NA's :880 NA's :880
## Zbrow.V1 Zcheek.V1
## Min. :-1.5555 Min. :-0.4094
## 1st Qu.:-0.7020 1st Qu.:-0.2779
## Median : 0.0044 Median :-0.2012
## Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.4586 3rd Qu.: 0.0073
## Max. : 8.3169 Max. :14.7318
## NA's :880 NA's :880
EMG z scores by participant
In the context of EMG, we want to standardise scores separately for each participant. You can do that using group_by(pp_no) before the mutate.
emg_z_scale_bypp <- emg_wide %>%
group_by(pp_no) %>%
mutate(Zbrow = scale(brow, center = TRUE, scale = TRUE)) %>%
mutate(Zcheek = scale(cheek, center = TRUE, scale = TRUE))
Use a filter then summary to check that it gives you the same values as before for a single participant.
emg_z_scale_bypp %>%
filter(pp_no == "pp1") %>%
summary()
## ...1 pp_no condition bin
## Min. : 1.00 Length:352 Length:352 Length:352
## 1st Qu.: 88.75 Class :character Class :character Class :character
## Median :176.50 Mode :character Mode :character Mode :character
## Mean :176.50
## 3rd Qu.:264.25
## Max. :352.00
##
## bin_no trial brow cheek
## Min. : 0 Length:352 Min. : 0.9923 Min. : 4.389
## 1st Qu.: 2 Class :character 1st Qu.: 1.6991 1st Qu.: 6.171
## Median : 5 Mode :character Median : 2.2721 Median : 7.627
## Mean : 5 Mean : 2.9080 Mean : 13.934
## 3rd Qu.: 8 3rd Qu.: 3.0276 3rd Qu.: 10.047
## Max. :10 Max. :22.2281 Max. :168.999
## NA's :176 NA's :176
## Zbrow.V1 Zcheek.V1
## Min. :-0.84411 Min. :-0.42046
## 1st Qu.:-0.53267 1st Qu.:-0.34200
## Median :-0.28023 Median :-0.27786
## Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.05266 3rd Qu.:-0.17125
## Max. : 8.51278 Max. : 6.83100
## NA's :176 NA's :176