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Re: TOST Acceptance criteria and Sample Size

Pops

New Contributor

Joined:

Mar 31, 2017

Hello,

I'm analyzing historical data and need to find meaningful equivalence acceptance criteria between groups and calculate sample size for a new experiments. How can I set Practically equivalence acceptance criteria and I'm using the DOE Sample Size and Power calculator K means. Which prospective means should I enter.

Thank You

1 ACCEPTED SOLUTION

Accepted Solutions
markbailey

Staff

Joined:

Jun 23, 2011

Solution

Of course you can set more stringent criteria for this test. This aspect of the TOST is not a statistical matter, though, unless you mean by "more stringent" that you require greater significance (lower alpha level) in the test.

The distribution of the historical data refers to individual outcomes. The TOST is a test of the mean of the population. The historical data could be used to estimate the mean and the standard deviation. 

Use DOE > Design Diagnostics > Sample Size and Power > One Sample Mean. It turns out that sample size is the same as for TOST. The difference to detect is the difference between the mean and the criteria limit.

You have specifications so you could use them for your new criteria. You could determine a reasonable margin of safety. For example, in my example above, if I want a 50% margin, then I would set my criteria as y > 9.95 and y < 10.05. You don't need the distribution of historical data to set the criteria.

5 REPLIES
markbailey

Staff

Joined:

Jun 23, 2011

The practically equivalent acceptance criteria are not statistical confidence bounds or limits. Like specifications, they are based on unacceptable performance or failure criteria. You might, for example, determine that a particular attribute of  the material, part, or device must be within 0.1 of 10 or else it does not perform as claimed. The practically equivalent acceptance criteria are y > 9.9 and y < 10.1 in this case. So the answer to your question is that they come from specifications.

The equivalence test that you mention (TOST) is a pair of hypothesis tests where the acceptance criteria define the null. hypothesis:

H0: mean < 9.9 or mean > 10.1

Pops

New Contributor

Joined:

Mar 31, 2017

Thank You,

I have historical values and all are within specification, but I would like to set equivalency acceptance criteria more stringent than specifications, to demonstrate for examples that two lots are practically equivalent. Can I set stringent equivalency acceptance criteria setting a rule from the distribution of historical data?

Also I need to set Sample size for the test from the Sample size calculator (Could I use Sample size calculator for a t-test and which prospective means do I enter in the calculator)

markbailey

Staff

Joined:

Jun 23, 2011

Solution

Of course you can set more stringent criteria for this test. This aspect of the TOST is not a statistical matter, though, unless you mean by "more stringent" that you require greater significance (lower alpha level) in the test.

The distribution of the historical data refers to individual outcomes. The TOST is a test of the mean of the population. The historical data could be used to estimate the mean and the standard deviation. 

Use DOE > Design Diagnostics > Sample Size and Power > One Sample Mean. It turns out that sample size is the same as for TOST. The difference to detect is the difference between the mean and the criteria limit.

You have specifications so you could use them for your new criteria. You could determine a reasonable margin of safety. For example, in my example above, if I want a 50% margin, then I would set my criteria as y > 9.95 and y < 10.05. You don't need the distribution of historical data to set the criteria.

Pops

New Contributor

Joined:

Mar 31, 2017

Ok many thanks,

DOE > Design Diagnostics > Sample Size and Power > One Sample Mean it also aks me for Std dev, is this from historical data?

Highlighted
markbailey

Staff

Joined:

Jun 23, 2011

Exactly!