An **arcsine transformation** can be used to “stretch out” data points that range between the values 0 and 1.

This type of transformation is typically used when dealing with proportions and percentages.

We can use the following syntax to perform an arcsine transformation in R:

asin(sqrt(x))

The following examples show how to use this syntax in practice.

**Example 1: Arcsine Transformation of Values in Range 0 to 1**

The following code shows how to perform an arcsine transformation on values in a vector that range between 0 and 1:

#define vector x <- c(0.1, 0.33, 0.43, 0.5, 0.7) #perform arcsine transformation on values in vector asin(sqrt(x)) [1] 0.3217506 0.6119397 0.7151675 0.7853982 0.9911566

**Example 2: Arcsine Transformation of Values Outside Range 0 to 1**

Note that the arcsine transformation only works on values between the range of 0 to 1. Thus, if we have a vector with values outside of this range, we need to first convert each value to be in the range of 0 to 1.

#define vector with values outside of range 0 to 1 x <- c(2, 14, 16, 30, 48, 78) #create new vector where each value is divided by max value y <- x / max(x) #view new vector y [1] 0.02564103 0.17948718 0.20512821 0.38461538 0.61538462 1.00000000 #perform arcsine transformation on new vector asin(sqrt(y)) [1] 0.1608205 0.4374812 0.4700275 0.6689641 0.9018323 1.5707963

**Example 3: Arcsine Transformation of Values in Data Frame**

The following code shows how to perform an arcsine transformation of values in a specific column of a data frame:

#define data frame df <- data.frame(var1=c(.2, .3, .4, .4, .7), var2=c(.1, .2, .2, .2, .3), var3=c(.04, .09, .1, .12, .2)) #perform arcsine transformation on values in 'var1' column asin(sqrt(df$var1)) [1] 0.4636476 0.5796397 0.6847192 0.6847192 0.9911566

And the following code shows how to perform an arcsine transformation of values in multiple columns of a data frame:

#define data frame df <- data.frame(var1=c(.2, .3, .4, .4, .7), var2=c(.1, .2, .2, .2, .3), var3=c(.04, .09, .1, .12, .2)) #perform arcsine transformation on values in 'var1' and 'var3' columns sapply(df[ c('var1', 'var3')], function(x) asin(sqrt(x))) var1 var3 [1,] 0.4636476 0.2013579 [2,] 0.5796397 0.3046927 [3,] 0.6847192 0.3217506 [4,] 0.6847192 0.3537416 [5,] 0.9911566 0.4636476

**Additional Resources**

How to Transform Data in R (Log, Square Root, Cube Root)

How to Perform a Box-Cox Transformation in R

How to Use the Log Function in R

How to Use the Square Root Function in R