The Levene test is used to test for equality of variance in a dataset. It is used in statistical analysis to determine if two or more samples have similar variances. If the results of the test indicate that the samples do not have similar variances, then it means that one sample has a higher variance than the other and should be treated as an outlier. In this blog post, we’ll take a look at what exactly the Levene test is, how it works, and provide some examples of how it can be applied. As data scientists, it will be important for us to understand the Levene test in order to properly interpret and analyze our data.

## What is the Levene Test?

The Levene test was developed by statistician Harold Levene in 1960 and is used to assess if there are significant differences among variances in different data samples. Essentially, the Levene tests are used to assess whether there are approximately equal variances / homogenous variances or unequal variances between groups. In other words, Levene statistics is used to test the homegeneity of variance between two or more groups. The null hypothesis of the Levene test is that all samples have approximately equal variances. There exists a homegeneity of variance between different groups. The alternative hypothesis is that there are unequal variances between some of the samples. The following represents the null and alternate hypothesis:

The homegeneity of variance between different groups is one of the key assumption of tests such as independent samples t-test, one-way ANOVA test, etc. Although one-way ANOVA test is robust to this assumption, large departures from homogeneity of variance assumption could impact the result of the 1-WAY ANOVA test.

Unlike statistical tests such as t-test where null hypothesis states that the mean of experimental group is different than the control group, in Levene test, the null hypothesis states that variance of two or more groups are same.

## What are the steps to calculate Levene Statistics?

Levene statistics is nothing but F-statistics calculated on absolute value of differences between individual value and median of each group. In other words, perform one-way ANOVA test on groups having value calculated as absolute (individual value – median). Here are the steps:

- Collect the data from each sample. The data should be arranged into two or more columns, with one column corresponding to each of the groups being compared.
- Calculate median for each group.
- Create new groups such that each entry of new group is absolute of difference between individual member of the corresponding previous group and median of the group.
- Calculate F-statistics with transformed data of each group.
- If F statistics is less than the F-value at criticality, we don’t have enough evidence to reject the null hypothesis. Thus, the asssumption around homogeneity of variance between the two groups is met. However, if the F statistics is more than F_critical value, than one can reject the null hypothesis which would mean that the variance are not equal.

## Conclusion

Levene’s Test is an important statistical test to compare the variances of two or more samples and test the homogeneity of variance between two sammplles. It helps you determine if there are significant differences between sample variances and can be used as a precursor for other tests such as ANOVA, t-tests, etc. In this blog post we have discussed what Levene’s Test is, and steps required to calculate it. We hope that by understanding how to use this powerful tool in your data analysis arsenal, you will be able to make informed decisions about your research results with confidence. If you need help using Levene’s Test or any other type of statistical test please don’t hesitate to contact us – our team of experts would love to assist!

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