Scaling

library(tidyverse);library(ggplot2);library(grid);library(gridExtra)

1. Data setup

set.seed(123); x=rnorm(30,100,20);ID=1:10
z=(x-mean(x))/sd(x)     #z transformation
x_scaled=x %>% scale()  # scaling transformation
dat=cbind(ID,x,z,x_scaled)
dat=data.frame(dat)
names(dat)=c("ID","x","z_score","x_scaled")
dat

##    ID         x    z_score   x_scaled
## 1   1  88.79049 -0.5232985 -0.5232985
## 2   2  95.39645 -0.1866137 -0.1866137
## 3   3 131.17417  1.6368622  1.6368622
## 4   4 101.41017  0.1198863  0.1198863
## 5   5 102.58575  0.1798022  0.1798022
## 6   6 134.30130  1.7962422  1.7962422
## 7   7 109.21832  0.5178431  0.5178431
## 8   8  74.69878 -1.2415080 -1.2415080
## 9   9  86.26294 -0.6521193 -0.6521193
## 10 10  91.08676 -0.4062648 -0.4062648
## 11  1 124.48164  1.2957653  1.2957653
## 12  2 107.19628  0.4147858  0.4147858
## 13  3 108.01543  0.4565354  0.4565354
## 14  4 102.21365  0.1608374  0.1608374
## 15  5  88.88318 -0.5185744 -0.5185744
## 16  6 135.73826  1.8694796  1.8694796
## 17  7 109.95701  0.5554915  0.5554915
## 18  8  60.66766 -1.9566293 -1.9566293
## 19  9 114.02712  0.7629319  0.7629319
## 20 10  90.54417 -0.4339188 -0.4339188
## 21  1  78.64353 -1.0404567 -1.0404567
## 22  2  95.64050 -0.1741751 -0.1741751
## 23  3  79.47991 -0.9978288 -0.9978288
## 24  4  85.42218 -0.6949706 -0.6949706
## 25  5  87.49921 -0.5891105 -0.5891105
## 26  6  66.26613 -1.6712928 -1.6712928
## 27  7 116.75574  0.9020011  0.9020011
## 28  8 103.06746  0.2043533  0.2043533
## 29  9  77.23726 -1.1121295 -1.1121295
## 30 10 125.07630  1.3260734  1.3260734

mean(x);mean(z);mean(x_scaled)

## [1] 99.05792

## [1] -1.709425e-17

## [1] -1.709425e-17

sd(x);sd(z);sd(x_scaled)

## [1] 19.62061

## [1] 1

## [1] 1

2. Density plot

p1=ggplot(dat,aes(x=x,alpha=0.5))+geom_density()
p2=ggplot(dat,aes(x=z_score,alpha=0.5))+geom_density()
p3=ggplot(dat,aes(x=x_scaled,alpha=0.5))+geom_density()
grid.arrange(p1,p2,p3)

End