Equation for statistical details for the two independent sample equivalence explorer

[#1]

Hi.  In this help document page: https://www.jmp.com/support/help/en/16.1/?os=win&source=application#page/jmp/power-for-two-independe..., for the the equation at the bottom (for power when sigma is known):

1.  This formula appears to be able to generate negative numbers (which it is not supposed to!) for small equivalence range values (say -1 to +1).  Using this formula, can other people recreate this result?

2.  If negative power numbers can be generated in bullet number 1, is this equation correct?  Is there a typo or qualification somewhere that's missing?

Thanks in advance. 

[#2 · Accepted solution]

Hey @jcl!

Thanks for reaching out! I looked into some of the literature surrounding this particular calculation and it looks like what might be missing in the documentation is a qualification that this is based on a very popular approximation formula. You may want to check out Supplement 1 of this article for more information, but essentially the exact power formula is a bit intractable, involving two levels of integration. As multiple researchers have found, the expression used here provides a suitable approximation for the majority of cases. The instance you found happens to be where the approximation breaks down, though it should be in the null hypothesis where power is already expected to be low. You won't be able to see the breakdown in the explorer as it self corrects to zero for that instance. 

Hope that helps!

[#3]

Thank you @calking.

When you mention that the explorer self corrects to zero for those instances, the value returned would be:

if (approximation value) >=0, then power = (approximation value), else power = 0 ?

I don't mean to be pedantic, but I need to provide the exact means of calculation as the power results to be presented are going to be part of a larger report open to public comment and need to be reproducible outside of JMP.

-JCL

[#4]

No worries! Your expression is correct.