Sometimes it is necessary to standardize the data due to its distribution or simply because we need to have a fair comparison of a value (e.g, body weight) with a reference population (e.g., school, city, state, country). The calculation of z-score is simple, but less information we can find on the web for its purpose and mean.
In this post, I will explain what the z-score means, how it is calculated with an example, and how to create a new z-score variable in R. As usual, I will use the data from National Health and Nutrition Examination Survey (NHANES).
What is Z-score
In short, the z-score is a measure that shows how much away (below or above) of the mean is a specific value (individual) in a given dataset. In the example below, I am going to measure the z value of body mass index (BMI) in a dataset from NHANES.
Get the data and packages
Loading packages and creating the dataset:
library(tidyverse)
library(RNHANES)
dat = nhanes_load_data("DEMO_E", "2007-2008") %>%
select(SEQN, RIAGENDR) %>%
left_join(nhanes_load_data("BMX_E", "2007-2008"), by="SEQN") %>%
select(SEQN, RIAGENDR, BMXBMI) %>%
filter(RIAGENDR == "1", !is.na(BMXBMI)) %>%
transmute(SEQN, Gender = RIAGENDR, BMI = BMXBMI)
dat
SEQN Gender BMI
1 41475 2 58.04
2 41476 2 15.18
3 41477 1 30.05
4 41479 1 27.56
5 41480 1 17.93
6 41481 1 23.34
7 41482 1 33.64
8 41483 1 44.06
9 41485 2 25.99
10 41486 2 31.21
How to calculate the z-score for BMI
To calculate the z-score of BMI, we need to have the average of BMI, the standard deviation of BMI.
Mean of BMI:
mean(dat$BMI)
## [1] 25.70571
Standard deviation of BMI:
sd(dat$BMI)
## [1] 7.608628
Suppose we want to calculate the z-score of the first participant in the dataset `dat`. The calculation will be: I take the actual BMI (58.04), substract the mean (25.70571), and divide the difference by the standard deviation (7.608628). The result is 4.249687. This indicate that first participant in the dataset has the BMI 4.249687 z-score unit above the average of population.
(58.04 - 25.70571)/7.608628 = 4.249687
How to calculate the z-score in R
dat %>%
mutate(zscore = (BMI - mean(BMI))/sd(BMI))
SEQN Gender BMI zscore
1 41475 2 58.04 4.249687006
2 41476 2 15.18 -1.383391690
3 41477 1 30.05 0.570968558
4 41479 1 27.56 0.243708503
5 41480 1 17.93 -1.021959902
6 41481 1 23.34 -0.310925004
7 41482 1 33.64 1.042801328
8 41483 1 44.06 2.412299228
9 41485 2 25.99 0.037363810
10 41486 2 31.21 0.723427057
Now we see the z-score for each individual, and the values corresponded to what we calculated above.
If you calculate the mean and standard deviation of the zscore above, you will find that mean is 0, and standard deviation is 1.
Feel free to comment!