Stata How to Calculate Cube Root

Calculating cube roots in Stata is essential for statistical analysis and data transformation. This guide explains the formula, provides a built-in calculator, and includes practical examples to help you work with cube roots in your Stata projects.

What is a Cube Root?

The cube root of a number x is a value that, when multiplied by itself three times, gives the original number. Mathematically, it's represented as:

∛x = y, where y × y × y = x

For example, the cube root of 27 is 3 because 3 × 3 × 3 = 27. Cube roots are particularly useful in statistical analysis for transforming data, calculating volumes, and solving cubic equations.

Stata Cube Root Formula

In Stata, you can calculate cube roots using the cube() function or the real() function with the cube root operation. The basic formula is:

gen cuberoot = real(x)^(1/3)

This formula raises the number to the power of 1/3, which is mathematically equivalent to taking the cube root. The real() function ensures the result is treated as a real number rather than an integer.

How to Calculate Cube Root in Stata

Follow these steps to calculate cube roots in Stata:

Open your dataset in Stata.
Use the generate command with the cube root formula:

generate cuberoot = real(x)^(1/3)
For multiple variables, use a loop or apply the formula to each variable.
Check the results with the list command.

Tip: Use the format command to control decimal places in your output.

Worked Example

Let's calculate the cube roots for the following dataset:

ID	Value
1	8
2	27
3	64

Using the formula:

generate cuberoot = real(value)^(1/3)

The results will be:

ID	Value	Cube Root
1	8	2
2	27	3
3	64	4

Interpreting Results

When interpreting cube root results in Stata:

Positive numbers will yield positive cube roots.
Negative numbers will yield negative cube roots (e.g., ∛(-8) = -2).
Zero will always yield zero as its cube root.
Non-integer results should be formatted to appropriate decimal places for readability.

Cube roots are particularly useful in statistical analysis for transforming skewed data distributions and calculating geometric means.

FAQ

How do I calculate cube roots for multiple variables in Stata?: Use a loop or apply the formula to each variable individually. For example:

foreach var of varlist var1 var2 var3 {
generate cuberoot_`var' = real(`var')^(1/3)
}
What if I get missing values in my cube root calculations?: Check for negative numbers in your dataset, as cube roots of negative numbers are not real numbers. Use the if qualifier to exclude negative values:

generate cuberoot = real(x)^(1/3) if x >= 0
How can I format the cube root results to 2 decimal places?: Use the format command after generating the cube roots:

format cuberoot %9.2f
Is there a difference between cube() and real(x)^(1/3) in Stata?: The cube() function in Stata calculates x³, not the cube root. For cube roots, you must use the power of 1/3 as shown in the formula.