# Levene Test

Many statistical testing procedures require that there is
**equal variance** in the samples. How can it now be checked whether the variances
are homogeneous, i.e. whether there is equality of variance? This is where the
**Levene test** helps. The Levene test checks whether several groups have the same
variance in the population.

Levene's test is therefore used to test the null hypothesis that the samples to be compared come from a population with the same variance. In this case, possible variance differences occur only by chance, since there are small differences in each sampling.

If the p-value for the Levene test is greater than .05, then the variances are not significantly different from each other (i.e., the homogeneity assumption of the variance is met). If the p-value for the Levene's test is less than .05, then there is a significant difference between the variances.

**H**Groups have equal variances_{0}:**H**Groups have different variances_{1}:

It is important to note that the mean values of the individual groups have no influence on the result, they may differ. A big advantage of Levene's test is that it is very stable against violations of the normal distribution. Therefore, Levene's test is used in many statistics programs.

Furthermore, the variance equality can also be checked graphically, this is usually done with a grouped box-plot or with a Scatterplot.

## Assumptions for the Levene test

Der Levene-Test hat grundsätzlich zwei Voraussetzungen:

- independent observations
- the test variable has metric scale level

## Levene Test Example

In this fictitious example, you conducted a survey among students to find out how many cups of coffee they drink per week. Now you want to know whether the variances of the individual subjects are the same and calculate a levene test for this.

Math | History | Psychology |
---|---|---|

21 | 18 | 17 |

23 | 22 | 16 |

17 | 19 | 23 |

11 | 26 | 7 |

9 | 13 | 26 |

27 | 24 | 9 |

22 | 23 | 25 |

12 | 17 | 21 |

20 | 21 | 14 |

4 | 15 | 20 |

To calculate the Levene test, simply copy the upper table into the table in the Statistics Calculator and then click on Hypothesis tests. Now you just need to select the three variables Math, History and Psychology and an ANOVA will be calculated. Here you will now also find a calculated Levene test.

As a result you get two tables and a box plot. The first table describes the variables descriptive and you can read the standard deviation of each variable.

With the help of the boxplot you can visualize the result of the Levene test. The boxplot shows clearly how much the examined variables scatter.

After the boxplot you will now get the table with the Levene test statistics. In this table the significance is the most important value, if the significance is above 0.05 there is no difference between the variances of the samples.

Therefore you can easily calculate a levene's test for equality of variances. If the p-value or significance is less than 0.05, you can assume inhomogeneous variance based on the available data.

## Interpreting the Levene Test

The degree of freedom df1 is obtained by calculating the number of groups minus 1, the degree of freedom df2 is obtained by calculating the number of cases minus the number of groups. In this level-test example the significance of 0.153 is greater than the defined significance level of 5%.

Thus the null hypothesis is maintained and there is no difference between the variances of the three groups. Thus, the three samples come from populations with the same variance.

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