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Level I

## Equivalence test for different variance

Hi, to viewers

I am checking equivalence test for each batch.

Purpose: To answer this question (Each batch's variance is equivalent?)

Question:

1. What is the meaning of "Margin and Alpha" when selecting the ratio of the standard deviations?
2. It is indicated into "specific practical equivalence interval". Then, how can I set reasonable interval value because equivalence count depends on this margin set?

Thanks!

3 REPLIES 3
Level IV

## Re: Equivalence test for different variance

I checked for you and found some information that might help.

I hope this information is helpful to you. Please note that I'm not an expert with JMP, but I wanted to provide some assistance while one of our experts reviews your message and gets back to you.

Margin and Alpha

Defines the significance levels for the test.

Difference

(Available only for tests for risk difference.) Specifies the equivalence, superiority, or noninferiority margin. This margin, or delta, is the difference that has practical significance. For equivalence tests, the difference must be greater than zero.

Ratio

(Available only for tests for relative risk.) Specifies the equivalence, superiority, or noninferiority margin as a risk ratio. This margin, or delta, defines a risk ratio that has practical significance. The range of values is defined as (Ratio, 1/Ratio). For equivalence tests, the ratio must be different from 1.

Alpha

Specifies the significance level for the test.

https://www.jmp.com/support/help/en/18.0/index.shtml#page/jmp/equivalence-test-reports-2.shtml

Staff

## Re: Equivalence test for different variance

It sounds like you might be looking for the equivalence of means.

Equivalence of means is used for population comparisons. For Example, I have some historical batches and some batches from a new CDMO site. Are the CQA's for the batches equivalent?

The equivalence of variance is often used for determining if the variance between measurement methods is the same. For example, I used a titration method to measure the concentration of an API, and now I'm using an HPLC method. The new system is fit for use, can I determine if the variation is equivalent (or, non-inferior)?

JMP Systems Engineer, Health and Life Sciences (Pharma)
Super User

## Re: Equivalence test for different variance

Hi @Summer7702 : You can think of "margin" as an acceptable (and don't confuse "acceptable" with "desirable") ratio r.  i.e., if the ratio of population SD's is within 1/r to r then the population SD's are considered "equivalent" ("equivalent" in this sense means that they are close enough to be considered "equivalent"). The choice of r (the margin) is chosen before you collect the data. It is a scientifically (rather than statistically) justifiable difference (ratio) that is considered allowable as a worst case.  If the 90% confidence interval for the ratio is contained entirely within 1/r to r then you can claim equivalence at alpha = 0.05. Alpha is the Type 1 error rate.  It is typically set at 0.05. This basically means that the probability of claiming equivalence, when in fact they are not equivalent, is 5%.   The confidence interval used is a 100*(1-2*alpha)% interval.

Equivalence testing is fundamentally different than testing for "statistically significant" differences. "Statistically significant" differences may not be practically significant. Equivalence testing is testing for a practical/meaningful difference.

Questions? Come back.