'Scaled' average equivalence [General Sta­tis­tics]

posted by d_labes  – Berlin, Germany, 2012-02-22 18:05 (5227 d 10:29 ago) – Posting: # 8156
Views: 4,426

Dear Martin, dear Helmut!

Strange!? :ponder: Writing down the sentence "the calculated sample mean should not differ more than 1.3 standard deviations (SDs) to the known value" as formula, with µ0 the known value

-1.3*SD < µ - µ0 < 1.3*SD
rearranged
-1.3 < (µ - µ0)/SD < 1.3


it strongly reminds me of a thing that is called "scaled ABE" in the context of BE studies, but here as a one group test. Isn't it?

But in the simple application of the above equation, as the sentence suggests, the method is not described properly I think. There is evidence that one should use 95% confidence intervals for the criterion (µ - µ0)/SD or a linearized version of it.

Additionally: Where the constant 1.3 comes from remains questionable.
Wellek[1] proposes 0.36 (strict) or 0.74 (liberal) in the context of a two group test.

BTW: (µ - µ0)/sd is the effect size in the sense of Cohen.

[1] S. Wellek
"Testing Statistical Hypotheses of Equivalence"
Chapman & Hall / CRC
Boca Raton 2000

Regards,

Detlew

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