How to interpret results from MiniTab's Test for Equal Variance.

1. John C Smith
Master Black Belt
Using charts and information from minitab.com

2.  Understand, Apply, and Interpret results from
MiniTab’s Test for Equal Variances

3.  Confidence Intervals
◦ The range of values that is likely to contain the
population parameter within some percent
 Confidence Intervals for Standard Deviations
◦ The range of values that is likely to contain the
standard deviation within some percent

4.  Bonferroni Confidence Intervals for Standard
Deviations
◦ The upper boundary for a factor level is equal to (((n-1) *
var) / U)**0.5
◦ where:
◦ n = the sample size of the factor level
◦ var = variance of the factor level
◦ U = the inverse cumulative chi-square distribution
function for K with n - 1 degrees of freedom
◦ K = (desired family error rate) / (2 * number of levels)
◦ The lower boundary is calculated the same way, using L
instead of U, where L = inverse cumulative chi-square
distribution function for 1 - K with n - 1 degrees of
freedom.
◦ Calculate “by hand” – NERD ALERT!!

5.  F-Test
◦ Fisher’s Test
◦ Basic assumption is that data is normal.
◦ Any statistical test in which the test statistic has an
F-distribution under the null hypothesis.
 Levene’s Test
◦ An inferential statistic used to assess the equality of
variances in different samples.
◦ Test is robust to non-normal data.
◦ Some common statistical procedures assume that
variances of the populations from which different
samples are drawn are equal.

6.  According to Design and Analysis of Experiments, 6th edition, by
Douglas C. Montgomery: "The modified Levene's test uses the
absolute deviation of the observations in each treatment from
the treatment median. It then evaluates whether or not the mean
of these deviations are equal for all treatments. It turns out that
if the mean deviations are equal, the variances of the
observations in all treatments will be the same. The test statistic
for Levene's test is simply the usual ANOVA F statistic for testing
equality of means applied to the absolute deviations."
 You can do this in Minitab by making a new column where each
value is the absolute value of the response minus the median of
that treatment. Then run One-Way ANOVA using the new column
as the Response. The F statistic and p-value will be the test
statistic and p-value for Levene's test. For an example, see the
link, Calculating Levene's Test Using Oneway ANOVA, below.

7.  Place response (data) in one column
 Place factor (descriptor) in another column
◦ Before or After
◦ Treatment 1 or Treatment 2
◦ Etc or etc
 Select STAT > ANOVA > Test for Equal
Variances

9. If the p is Low, Not lower than .05,
the Null must GO! fail to reject the Null

10.  Boxplot of data from Treatments 1 and 2.
 Follow standard boxplot graphic rules.

11.  This test compares the standard deviations,
or spreads, of two or more sets of data.
 Produces results for normal and non-normal
data.
 Produces graphical and analytical data for
comparison.
◦ Graphical: Bonferroni’s CI for StDev’s chart and
Boxplot of data
◦ Analytical: p-value results