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Supplementary material ANALYTICAL METHOD TRANSFER USING EQUIVALENCE TESTS WITH REASONABLE ACCEPTANCE CRITERIA AND APPROPRIATE EFFORT : EXTENSION OF THE ISPE CONCEPT L. Kaminski §, U. Schepers §, H. Wätzig* §both authors equally contributed to this article

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Introduction This file shall provide additional information and hence lead to a better understanding of some circumstances presented in the original paper “ANALYTICAL METHOD TRANSFER USING EQUIVALENCE TESTS WITH REASONABLE ACCEPTANCE CRITERIA AND APPROPRIATE EFFORT: EXTENSION OF THE ISPE CONCEPT” by Kaminski, L., Schepers, U. and Wätzig, H. [1] It does not claim to be an exhaustive explanation of equivalence tests. Please refer to the above mentioned work for detailed information about these tests and their use in analytical method transfer. [1] L. Kaminski, U. Schepers and H. Wätzig, J. Pharm. Biomed. Anal (2010), doi:10.1016/j.jpba.2010.04.034doi:10.1016/j.jpba.2010.04.034

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Test principle Same test principle for classic t-test and for the equivalence test! θ 0 = 0 CUCU CLCL Confidence interval standardized normal distribution of the θ value Reference value

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classic two sided t-test θ 0 = 0 CUCU CLCL CUCU CLCL High precision and/or high number of samples Low precision and/or low number of samples Statistically significant but practically irrelevant difference! transfer wrongly rejected Statistically insignificant but practically relevant difference! transfer wrongly accepted The t-test paradoxically rewards imprecise working and low data numbers

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equivalence test CUCU CLCL High precision and/or high number of samples Low precision and/or low number of samples θ 0 = 0 CUCU CLCL -2%+2% -2% Same starting position, but an interval of relevance (acceptance interval) with e.g. ±2% is introduced in addition here!

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equivalence test CUCU CLCL High precision and/or high number of samples Low precision and/or low number of samples θ 0 = 0 CUCU CLCL -2%+2% -2% The whole confidence interval lies within the interval of relevance equivalence! The confidence interval lies partially outside the interval of relevance no equivalence! The equivalence test rewards precise working and high numbers of samples

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classic two sided t-test (Figure 3) acceptance probability of 95% error probability of 5% (ISPE concept) Acceptance tolerance of approx. 2,3% error probability of 12% When measurement spread gets higher (e.g. ±2%) the error probability increases to almost 40% at the acceptance limit (approx. 60% acceptance probability)!

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equivalence test (Figure 2) Acceptance limit error probability of 5% (ISPE concept) error probability of 12% ~1,65

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Errors In it possible that we may reject the null hypothesis while in reality H 0 is true. This is known as a Type I error and we write that α=P(Type I.

Errors In it possible that we may reject the null hypothesis while in reality H 0 is true. This is known as a Type I error and we write that α=P(Type I.

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