# Manuals/calci/LEVENESTESTOLD

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LEVENESTESTOLD(xRange,ConfidenceLevel,NewTableFlag)

• is the set of values for the test.
• is the value from 0 to 1.
• is either TRUE or FALSE. TRUE for getting results in a new cube. FALSE will display results in the same cube.

## Description

• This function used to test the Homogeneity of variances.
• Levene's test is used to test the Samples have equal variances.
• Equal variances across samples is called homogeneity of variance or homoscedasticity.
• To do the Levenes test we need the following assumptions:
  1.The Samples from the populations are independent of one another.
2. The population under consideration are Normally Distributed.

• For three or more variables the following statistical tests for homogeneity of variances are commonly used:
   1.Levene's Test.
2.Bartlett Test.

• Levene's test is an alternative to the Bartlett test.
• If the data surely is of normally distributed or nearly to normally distributed then we can use the Bartlett test.
• The Levene's test is defined as
.
=Not all of the variances are equal.

• Normally there are three versions of the Levenes test.
• There are
• 1.Use of Mean.
• 2.Use of Median.
• 3.Use of 10% of Trimmed Mean.
• The Levene test statistic is:

.

• where is the result of the test.
• is the number of different groups to which the sampled cases belong.
• is the total number of cases in all groups.
• is the number of cases in the group.
• case from the group.
• Zij is satisfying the one of the following conditions:
• 1.,Where is the Mean of the subgroup.
• 2.,Where is the Median of the subgroup
• 3.,Where is the 10%Trimmed Mean of the subgroup.
• Levene's Testing Procedure:
• 1. checking the assumptions.
• 2.State the Null(H0) and alternative(H1) hypothesis.
• 3.Decide on the Significance level (α).
• 4.Finding the Critical value and Rejection Region.Here ,.
• 5.Compute the Levenes statistic using the formula.
• 6.Then decision of the value of the test statistic,W is falls in the rejection region or if p-value ≤ α, then reject .Otherwise, fail to reject . For the computation p-value we have to use the value of and .
• 7. Finally we have to conclude that the rejection of or fail to rejection according to the test statistic at the significance level.

## Examples

1. LEVENESTESTOLD([[3067,2730,2840,2913,2789],[3200,2777,2623,3044,2834]],0.05,0)

Levene's Test