File:T-test vs equivalence test.png
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![File:T-test vs equivalence test.png](https://upload.wikimedia.org/wikipedia/commons/thumb/0/08/T-test_vs_equivalence_test.png/800px-T-test_vs_equivalence_test.png?20211030130649)
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t-test vs equivalence test
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[edit]DescriptionT-test vs equivalence test.png |
English: Chances to pass the t-test or the equivalence test depending on the actual error 𝜇. Different lines denote different sample sizes obtained from different a priori choices of the standard deviation σ. The golden, solid curve always represents a correctly estimated sample size, the green curve a sample which is too large and the other curves samples which are too small. Neglecting the t-test type II (or the equivalence test type I) error implies a power of 50%. The thick grey lines denote 𝛥=1%. For comparison: in the bottom graph, the incorrect decisions of a reference test are red, the correct decisions are coloured blue. The reason for red areas to exist are economic considerations to limit the test costs: further increasing the sample size towards infinity would make the red areas disappear, at least for the revised t-test or the equivalence test. For the t-test, the areas with systematic error 𝜇>1% and 𝜇<−1% remain blue, but the inner turns red. This behaviour is counterintuitive to the idea that the error of a statistic test goes to zero as the sample size goes to infinity.
Original Source: Figure 2 from https://doi.org/10.1007/s11116-019-09991-9 Reworked version source code see https://gist.github.com/xor2k/2256abe4106cc8ac04a24f42bd36f2c6 |
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Source | Own work |
Author | Xor2k |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 13:06, 30 October 2021 | ![]() | 2,889 × 1,621 (589 KB) | Xor2k (talk | contribs) | stricter adhere to original diagram, using α_{t-test} instead of α_t etc. |
12:41, 30 October 2021 | ![]() | 2,809 × 1,621 (577 KB) | Xor2k (talk | contribs) | minor optimization of the x axis labels | |
11:53, 30 October 2021 | ![]() | 2,809 × 1,575 (573 KB) | Xor2k (talk | contribs) | adjusted colors | |
11:37, 30 October 2021 | ![]() | 2,809 × 1,575 (613 KB) | Xor2k (talk | contribs) | Added a normal distribution based simulation otherwise complete rework | |
20:30, 22 June 2019 | ![]() | 1,754 × 1,240 (182 KB) | Xor2k (talk | contribs) | Renamed ν to σ for better consistence with general notation. | |
11:01, 30 May 2019 | ![]() | 1,373 × 903 (161 KB) | Xor2k (talk | contribs) | User created page with UploadWizard |
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