Dr. Wayne Taylor - Taylor Enterprises, Inc.
for Engineers and Quality
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CAPAs and Trending of Quality Data
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Spec Setting, Tolerance Analysis and Robust Design
Statistical Process Control
Design of Experiments
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Statistical Procedures for the Medical Device Industry
STAT-16: Statistical Techniques for Equivalence Testing
This procedure provides statistical techniques for demonstrating
equivalence of a new product or process to an existing product or
process. This is an alternate approach to demonstrating the product or
process meets established requirements per the following procedures:.
- Confidence Limits for the Difference between Two Averages
- Equivalence Test for Two Averages
- Confidence Limits for the Difference between Two Averages—Paired
- Equivalence Test for Two Averages—Paired Data
- Confidence Limits for the Ratio of Two Standard Deviations
- Equivalence Test for Two Standard Deviations
- Equivalence does not mean identical. It means the
difference is less than some predetermined difference Δ.
- Demonstrating equivalence requires defining a difference Δ
that is considered significant and then demonstrating with high
confidence the different is less than Δ.. Equivalence tests
are based on confidence intervals. The validated spreadsheet
STAT-12 to 16 - Confidence
Intervals and Equivalence Tests.xlsx
accompanying the book can be used for performing equivalence tests.
For example, suppose a difference of 2 or more is considered a
significance difference. As shown below, the 95 confidence
interval for the difference is between -2 and 2 so one can claim
- Procedures for calculating sample size are provided.
However, a passing equivalence test is valid regardless of the
sample size used. For smaller sample sizes the confidence
intervals will be wider, making it harder to pass. The risk of
too small a sample size is falsely failing the equivalence test.
The procedure for calculating sample size is too ensure a reasonable
chance of passing equivalent groups.
- Equivalence tests cannot be chained together. B is
equivalent to A and C is equivalent to B does not mean C is
equivalent to A. The difference could be 2 times Δ. One
must prove directly that C is equivalent to A. An alternate
approach is to use A to establish specification limits and then show
B and C meet the specification limits. Setting specification
limits is described in
STAT-11, Statistical Techniques for Setting Specifications.
- A t-test by itself is not a valid approach for demonstrating
equivalence. If it is believed that equivalence testing
requires fewer samples than demonstrating the specification limits
are meet, equivalence testing is being done wrong. Equivalence
testing is generally used when there are not specification limits.
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September 08, 2017