Equivalence test

[#1]

Hello

I want to compare two analytical methods that measure the purity of my samples and prove they are equivalent. I know they don't provide the exact same results which means the mean of their difference is not 0. However, I only need to prove that the difference between their results is less than 2%. My data are based on 28 different samples and each sample was analyzed once by each method. We tested the equivalence with a two-sided t-test on the purity difference but we are not sure this test is the most appropriate to prove the concept. Please not that the data is not normally distributed. Can someone please advise on this?

[#2]

I’m comparing two analytical methods that assess the purity of my samples and would like to determine whether they are equivalent. I’m aware that they don’t yield identical results—so the mean difference between the two methods isn’t zero—but what matters is whether the difference remains within a 2% tolerance.

Here’s the setup:

• I tested 28 different samples, with each sample analyzed once by each method.

• I’m interested in verifying if the methods are equivalent within a ±2% margin.

• I originally applied a two-sided t-test on the differences in purity, but I’m not confident that this approach is the best suited for establishing equivalence.

• The kicker: the data are not normally distributed.

I’d greatly appreciate any guidance on:

1. Which statistical tests are most appropriate for assessing equivalence when data aren’t normally distributed.

2. Valid ways to implement such tests under these conditions.

3. Pitfalls I should be aware of when assessing equivalence with non-normal data.

Any recommendations or advice would be really helpful—thank you!

[#3]

Hi @AcceptanceFox47 :  If the data are approximately log-normal (the natural log of the data is approximately normal) then this can be carried out as a confidence interval for paired data would be carried out (could do it via Matched Pair platform, for example). But the analysis would be carried out on the natural log of the data.  The endpoints of the 90% confidence interval on the difference (in log-scale) would then be anti-logged (EXP(.) ) to get a confidence interval on the geometric mean ratio. This final interval would need to be within 0.98 to 1.02 to claim equivalence.

And, if the sample size is large enough (n=28 qualifies) then the Central Limit Theorem ( https://en.wikipedia.org/wiki/Central_limit_theorem#:~:text=In%20probability%20theory%2C%20the%20cen....) says not to worry about normality. Edit: so, carry on as I explained above.