[問題] 不同複合假說對相同多重測試的解釋
To demonstrate that the new algorithm A is superior to the old
algorithms B, C, and D, three comparison tests were performed.
The results showed that A>B (p=0.009), A>C (p=0.002), and A>D (p=0.04).
The overall significance level was 0.03. The multiplicity was corrected
using the Bonferroni method.
How does one interprete the results if the following tests were
performed, respectively:
(1) union-intersection test,
(2) intersection-union test, and
(3) intersection-intersection test?
根據上述多重測試的設定，整體顯著水準是 0.03/3 = 0.01。所以三個個別
測試的顯著與否如下:
A>B (p=0.009), 顯著
A>C (p=0.002), 顯著 and
A>D (p=0.04), 不顯著
單看上述測試結果，其解釋似乎是:
演算法 A 只比 B 和 C 好，但是無法判定其是否比 D 好--能說不比 D 差嗎?
還是只要不顯著就啥也不能宣稱?
問題是，完整的多重假說測試應該要考慮整體假說的不同(內容)類型去詮釋測試
結果(?)
那麼在上述三種不同類型的整體假說下，怎樣個別詮釋上面所得的測試結果?
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