2 Variance Test
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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.
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An operations application would be when quality
managers or engineers want to ensure their
company’s product is able to consistently meet
specifications.
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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
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Just as you would sometimes wish to compare
the means of two populations, you may also wish
to compare the variances of two populations.
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If you had two processes that were already
perfectly centered, a comparison of the
variances could tell you if either process is
better.
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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.
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Let us conduct two variance test to validate the
manager’s claim
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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
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Step 1.b:Normality Check and Interpret
Interpret:
- As P-value is
greater than 0.05,
we can conclude
that the data are
normal and
doesn’t have any
outliers.
Interpret:
- As P-value 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
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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
- P-value (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