2 Variance Test

There are times when the variance or 'spread' of a
process is of greater interest than its mean. For
instance, economists and investors use variance as
a measure of risk.

An operations application would be when quality
managers or engineers want to ensure their
company’s product is able to consistently meet
specifications.

The focus on variance is especially important
when you are working to tight specifications
which don't allow for much scope for the
process/product characteristic

Just as you would sometimes wish to compare
the means of two populations, you may also wish
to compare the variances of two populations.

If you had two processes that were already
perfectly centered, a comparison of the
variances could tell you if either process is
better.

A manager is happy with the mean lead time
of two processes (Process A and Process B). But he
is eager to know whether the variance in lead
time of process B is less than the variance in lead
time of process A. He has collected 18 samples
from each processes. At 95% confidence level is
there enough evidence to support the claim.

Let us conduct two variance test to validate the
manager’s claim

Step 1.a: Conduct Normality test
Note 1: Tests of the variance are very sensitive to the
assumption of normality.
Note 2: You can also evaluate the normality test by selecting
 Minitab > Stats > Basic Statistics > Normality Tests (or)
 Minitab > Graph > Probability Plot

Step 1.b:Normality Check and Interpret
Interpret:
 As Pvalue is
greater than 0.05,
we can conclude
that the data are
normal and
doesn’t have any
outliers.
Interpret:
 As Pvalue is
greater than 0.05,
we can conclude
that the data are
normal and
doesn’t have any
outliers.

Step 2: Hypothesis
 Null Hypothesis Ho: There is no significant difference
between the variance in lead time of process A and
processB
 Can be rewrittenas:(σ2
Process A
) / (σ2
Process B
) = 1
 Alternate Hypothesis Ha: The variance in lead time of
process B is less than the variance in lead time
of processA
 Can be rewrittenas:(σ2
process A
) /(σ2
process B
) > 1
Where
σ2
 Process A
: Variance in Lead Time of ProcessA (in days)
σ
2
 Process B
: Variance in Lead Time of ProcessB (in days)
 Ratio = σ
2
Process A /σ2
Process B
 F method was used. As this method is accurate for
normal data.

Step 3: Conduct 2 Variance Test

Step 4: Interpretation
 Estimated ratio is 4.64. At 95% confidence level, the lower bound
for ratio using F test is 2.043
 The lower bound for ratio using F test (2.043) is more than the
target ratio (1) which is inline with the stated Alternate
Hypothesis & hence reject Null Hypothesis
 Pvalue (0.001) is less than alpha (0.05), also indicating to reject
the null hypothesis
 With above two justifications the manager can conclude that the
variance in lead time of process B is less than the variance in lead
time of process A