# Manuals/calci/LEVENESTEST

LEVENESTEST (DataRange,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.

## Example

 X1 X2 3067 3200 2730 2777 2840 2623 2913 3044 2789 2834
• =LEVENESTEST(B1:C5,.05,0)
LEVENES TEST
DATA-0 DATA-1
Median 2840 2834
Mean 2867.8 2895.6
Variance 16923.7 51713.3
Count 5 5
df 4 4
SUMMARY OUTPUT
LEVENESTEST STATISTICS
W 1.0439235110342522
F-Test 0.38245649772919
a 0.05
F 0.32726010523405
p 1 & 2 Tail 0.1524069466470822 0.3048138932941644

Levene's Test