In statistics, **Levene’s test** is an inferential statistic used to evaluate the equality of variances for a variable determined for two or more groups. Some standard statistical procedures find that variances of the populations from which various samples are formed are equal. Levene’s test assesses this assumption. It examines the null hypothesis that the population variances are equal called homogeneity of variance or homoscedasticity. It compares the variances of **k** samples, where k can be more than two samples. It’s an alternative to **Bartlett’s test** that is less sensitive to departures from normality. There are several solutions to test for the equality (**homogeneity**) of variance across groups, including:

- F-test
- Bartlett’s test
**Levene’s test**- Fligner-Killeen test

It is very much easy to perform these tests in R programming. In this article let’s perform **Levene’s test **in R.

#### Statistical Hypotheses for Levene’s test

A hypothesis** **is a statement about the given problem. Hypothesis testing is a statistical method that is used in making a statistical decision using experimental data. Hypothesis testing is basically an assumption that we make about a population parameter. It evaluates two mutually exclusive statements about a population to determine which statement is best supported by the sample data. To know more about the statistical hypothesis please refer to Understanding Hypothesis Testing. For Levene’s test the statistical hypotheses are:

**Null Hypothesis:**All populations variances are equal**Alternative Hypothesis:**At least two of them differ

#### Implementation in R

R provides a function **leveneTest****()** which is available in **car** package that can be used to compute Levene’s test. The syntax for this function is given below:

Syntax:leveneTest(formula, dataset)

Parameters:

formula:a formula of the formvalues ~ groups

dataset:a matrix or data frame

#### Example of Lavene’s test

**Levene’s test with one independent variable:**

Consider the R’s inbuilt **PlantGrowth** dataset that gives the dried weight of three groups of ten batches of plants, wherever every group of ten batches got a different treatment. The **weight** variable gives the weight of the batch and the **group** variable gives the treatment received either **ctrl, trt1 or trt2**. To view the data set please type below command:

## R

`print` `(PlantGrowth)` |

**Output:**

weight group 1 4.17 ctrl 2 5.58 ctrl 3 5.18 ctrl 4 6.11 ctrl 5 4.50 ctrl 6 4.61 ctrl 7 5.17 ctrl 8 4.53 ctrl 9 5.33 ctrl 10 5.14 ctrl 11 4.81 trt1 12 4.17 trt1 13 4.41 trt1 14 3.59 trt1 15 5.87 trt1 16 3.83 trt1 17 6.03 trt1 18 4.89 trt1 19 4.32 trt1 20 4.69 trt1 21 6.31 trt2 22 5.12 trt2 23 5.54 trt2 24 5.50 trt2 25 5.37 trt2 26 5.29 trt2 27 4.92 trt2 28 6.15 trt2 29 5.80 trt2 30 5.26 trt2

As mentioned above, Levene’s test is an alternative to Bartlett’s test when the data is not normally distributed. Here let’s consider only one independent variable. To perform the test, use the below command:

## R

`# R program to illustrate` `# Levene’s test` ` ` `# Import required package` `library` `(car)` ` ` `# Using leveneTest()` `result = ` `leveneTest` `(weight ~ group, PlantGrowth)` ` ` `# print the result` `print` `(result)` |

**Output:**

Levene's Test for Homogeneity of Variance (center = median) Df F value Pr(>F) group 2 1.1192 0.3412 27

**Levene’s test with multiple independent variables:**

If one wants to do the test with multiple independent variables then the **interaction****()** function must be used to collapse multiple factors into a single variable containing all combinations of the factors. Here let’s take the R’s inbuilt **ToothGrowth** data set.

## R

`# R program to illustrate` `# Levene’s test` ` ` `# Import required package` `library` `(car)` ` ` `# Using leveneTest()` `result = ` `leveneTest` `(len ~ ` `interaction` `(supp, dose), ` ` ` `data = ToothGrowth)` ` ` `# print the result` `print` `(result)` |

**Output:**

Levene's Test for Homogeneity of Variance (center = median) Df F value Pr(>F) group 5 1.7086 0.1484 54