1.
Exploratory Data Analysis
1.3. EDA Techniques 1.3.5. Quantitative Techniques


Purpose: Test for Homogeneity of Variances 
Bartlett's test (Snedecor and Cochran, 1983)
is used to test if k
samples have equal variances. Equal variances across samples is
called homogeneity of variances. Some statistical tests, for
example the analysis of variance, assume that variances
are equal across groups or samples. The Bartlett test can
be used to verify that assumption.
Bartlett's test is sensitive to departures from normality. That is, if your samples come from nonnormal distributions, then Bartlett's test may simply be testing for nonnormality. The Levene test is an alternative to the Bartlett test that is less sensitive to departures from normality. 

Definition 
The Bartlett test is defined as:
An alternate definition (Dixon and Massey, 1969) is based on an approximation to the F distribution. This definition is given in the Product and Process Comparisons chapter (chapter 7). 
Example 
Bartlett's test was performed for the
GEAR.DAT data set.
The data set contains 10 measurements of gear
diameter for ten different batches for a
total of 100 measurements.
H_{0}: σ_{1}^{2} = σ_{2}^{2} = ... = σ_{10}^{2} H_{a}: At least one σ_{i}^{2} is not equal to the others.We are testing the null hypothesis that the batch variances are all equal. Because the test statistic is larger than the critical value, we reject the null hypotheses at the 0.05 significance level and conclude that at least one batch variance is different from the others. 
Question 
Bartlett's test can be used to answer the following
question:

Importance  Bartlett's test is useful whenever the assumption of equal variances is made. In particular, this assumption is made for the frequently used oneway analysis of variance. In this case, Bartlett's or Levene's test should be applied to verify the assumption. 
Related Techniques 
Standard Deviation Plot Box Plot Levene Test ChiSquare Test Analysis of Variance 
Case Study  Heat flow meter data 
Software  The Bartlett test is available in many general purpose statistical software programs. Both Dataplot code and R code can be used to generate the analyses in this section. 