A z-score tells us how many standard deviations away a certain value is from the mean of a dataset.
A percentile tells us what percentage of observations fall below a certain value in a dataset.
Often you may want to convert between z-scores and percentiles.
You can use the following methods to do so in R:
Method 1: Convert Z-Scores to Percentiles
percentile <- pnorm(z)
Method 2: Convert Percentiles to Z-Scores
z <- qnorm(percentile)
The following examples show how to use each method in practice.
Example 1: Convert Z-Scores to Percentiles in R
We can use the built-in pnorm function in R to convert a z-score to a percentile.
For example, here is how to convert a z-score of 1.78 to a percentile:
#convert z-score of 1.78 to percentile percentile <- pnorm(1.78) #display percentile percentile  0.962462
It turns out that a z-score of 1.78 corresponds to a percentile of 96.2.
We interpret this to mean that a z-score of 1.78 is larger than about 96.2% of all other values in the dataset.
Example 2: Convert Percentiles to Z-Scores in R
We can use the built-in qnorm function in R to convert a percentile to a z-score.
For example, here is how to convert a percentile of 0.85 to a z-score:
#convert percentile of 0.85 to z-score z <- qnorm(0.85) #display z-score z  1.036433
It turns out that a percentile of 0.85 corresponds to a z-score of 1.036.
We interpret this to mean that a data value located at the 85th percentile in a dataset has a z-score of 1.036.
Also note that we can use the qnorm function to convert an entire vector of percentiles to z-scores:
#define vector of percentiles p_vector <- c(0.1, 0.35, 0.5, 0.55, 0.7, 0.9, 0.92) #convert all percentiles in vector to z-scores qnorm(p_vector)  -1.2815516 -0.3853205 0.0000000 0.1256613 0.5244005 1.2815516 1.4050716
Here’s how to interpret the output:
- A percentile of 0.1 corresponds to a z-score of -1.28.
- A percentile of 0.35 correspond to a z-score of -0.38.
- A percentile of 0.5 corresponds to a z-score of 0.
And so on.
The following tutorials explain how to perform other common tasks: