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In Six Sigma, hypothesis testing helps identify differences between
machines, formulas, raw materials, etc. and are the differences
statistically significant or not. Without such testing, teams can
run around changing machine settings, formulas and so on causing
more variation. These knee-jerk responses can amplify variation
and cause more problems than doing nothing at all.
In manufacturing, you might want to compare two or more types of
raw materials and determine if they produce the same quality. In
other words, do the products have the same or different means and
variances? If they are the same, which one is less expensive to
produce? If they are different, which one best meets the customer's
requirements?
Hypothesis testing helps identify ways to reduce costs and improve
quality.
There are Three Types of Hypothesis Tests
- Classical Method - comparing a test statistic to a critical
value
- p value Method - the probability of a test statistic being contrary to the null hypothesis
- Confidence Interval Method - is the test statistic between or
outside of the confidence interval
Setting Up a Hypothesis Test
First, you will need to define a null (H0) and
an alternate (Ha) hypothesis.
By default, the null hypothesis assumes that the means, averages
or variation are statistically the same. The goal is to prove that
they are not statistically the same at some level of confidence
(usually 95%, 99%).
Tests can be either two sided or one sided depending on how the
null hypothesis is stated.
| Null Hypothesis- two sided test |
Alternate Hypothesis - two sided
test |
|
Average(Sample 1) = Average(Sample 2)
Mean(Sample 1) = Mean(Sample 2)
Mean1 - Mean2 = 0 (no difference)
|
Average(Sample 1) not = Average(Sample 2)
Mean(Sample 1) not = Mean(Sample 2)
Mean1 - Mean2 not = 0 |
| Variance(Sample 1) = Variance(Sample
2) |
Variance(Sample 1) not = Variance(Sample
2) |
| Null Hypothesis - one sided test |
Alternate Hypothesis - one sided
test |
|
Average(Sample 1) <= Average(Sample 2)
Average(Sample 1) >= Average(Sample 2)
Mean(Sample 1) <= Mean(Sample 2)
Mean(Sample 1) >= Mean(Sample 2)
Mean1 - Mean2 <= 0
Mean1 - Mean2 >= 0
|
Average(Sample 1) > Average(Sample 2)
Average(Sample 1) < Average(Sample 2)
Mean(Sample 1) > Mean(Sample 2)
Mean(Sample 1) < Mean(Sample 2)
Mean1 - Mean2 > 0
Mean1 - Mean2 < 0
|
Variance(Sample 1) <= Variance(Sample
2)
Variance(Sample 1) > = Variance(Sample 2) |
Variance(Sample 1) > Variance(Sample
2)
Variance(Sample 1) < Variance(Sample
2) |
Then, using data from the test:
- Calculate the test statistic (t test, f test, z test, ANOVA,
etc.).
The test statistic is often converted to a p value (probability),
but not always.
- Compare the test statistic to:
- a significance level (a)
or confidence level (1-a)
- a critical value (e.g., Fcrit)
to determine if you can accept or reject the null hypothesis.
|
Hypothesis Test
|
Compare
|
Result
|
| Classical Method |
test statistic > critical value
(i.e. F > F crit)
|
Reject the null hypothesis |
| Classical Method |
test statistic < critical value
(i.e. F < F crit)
|
Accept the null hypothesis |
| p value Method |
p value < a |
Reject the null hypothesis |
| p value Method |
p value > a |
Accept the null hypothesis |
Determining the Correct Test Statistic
Consider your data.
Is it variable (i.e., measured - 3.4 lbs) or attribute (i.e., counted
- 3 defects)?
Are there one, two or more samples?
Are you comparing the means or variance?
Type I and II Errors
Hypothesis testing seeks to determine if the means or variances
are the same or different at some level of confidence. Since we
can never be totally confident, it is possible to encounter
two types of errors:
- Type I error - Reject a null hypothesis that is true
(Producer's Risk)
- Type II error - Not reject a null hypothesis that is
false (Consumer's Risk)
Choose a confidence (or significance) level that will minimize
the risk associated with these errors.
All of these hypothesis tests are included in the QI Macros
Statistical
Process Control software.
 Download
the FREE 30-day Evaluation copy of the QI Macros Excel SPC Software for Six Sigma
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