Exploratory Data Analysis
1.3. EDA Techniques
1.3.5. Quantitative Techniques
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 non-normal distributions, then Bartlett's test may simply be testing for non-normality. The Levene test is an alternative to the Bartlett test that is less sensitive to departures from normality.
The Bartlett test is defined as:
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.
H0: σ12 = σ22 = ... = σ102 Ha: At least one σi2 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.
Bartlett's test can be used to answer the following
|Importance||Bartlett's test is useful whenever the assumption of equal variances is made. In particular, this assumption is made for the frequently used one-way analysis of variance. In this case, Bartlett's or Levene's test should be applied to verify the assumption.|
Standard Deviation Plot
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.|