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<!doctype html> < html lang = en > < head > < meta charset = utf-8 > < meta name = description content = "概要 結論に複数の 仮説検定の結果が影響している時，その結論は検定の多重性問題を孕んでいる可能性がある 問題を回避するためには， ， ． ， （ > < meta property = "og:title" content = "仮説検定の多重性問題" > < meta property = "og:description" content = "概要 結論に複数の 仮説検定の結果が影響している時，その結論は検定の多重性問題を孕んでいる可能性がある 問題を回避するためには， ， ． ， （ > < meta property = "og:type" content = "website" > < meta property = "og:image" content = "https://ar.falsy.cat/icon.png" > < meta property = "og:url" content = "https://ar.falsy.cat/note/study/statistics/hypothesis-test-multiplicity/" > < meta property = "og:width" content = "200" > < meta property = "og:height" content = "200" > < meta name = twitter:card content = "summary" > < meta name = twitter:title content = "仮説検定の多重性問題" > < meta name = twitter:description content = "概要 結論に複数の 仮説検定の結果が影響している時 ， その結論は検定の多重性問題を孕んでいる可能性がある 問題を回避するためには ， Holm法などで有意水準を下げる必要があるが ， 完璧ではない 不確実な情報による結論の不確 <EFBFBD>
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Jun 21, 2023< / p > < ul class = tags > < li > < a href = https://ar.falsy.cat/tags/note/ > Note< / a > < / li > < li > < a href = https://ar.falsy.cat/tags/study/ > Study< / a > < / li > < li > < a href = https://ar.falsy.cat/tags/statistics/ > Statistics< / a > < / li > < / ul > < aside class = mainTOC > < details > < summary > Table of Contents< / summary > < nav id = TableOfContents > < ol > < li > < a href = #概要 > 概要< / a > < / li > < li > < a href = #不確実な情報による結論の不確実性 > 不確実な情報による結論の不確実性< / a > < / li > < li > < a href = #holm法による有意水準の調整 > Holm法による有意水準の調整< / a > < ol > < li > < a href = #手法 > 手法< / a > < / li > < / ol > < / li > < li > < a href = #まとめ > まとめ< / a > < / li > < / ol > < / nav > < / details > < / aside > < a href = #概要 > < h2 id = 概要 > < span class = hanchor arialabel = Anchor > # < / span > 概要< / h2 > < / a > < ul > < li > 結論に複数の
< a href = /note/study/statistics/hypothesis-test/ rel = noopener class = internal-link data-src = /note/study/statistics/hypothesis-test/ > 仮説検定< / a > の結果が影響している時，その結論は検定の多重性問題を孕んでいる可能性がある< / li > < li > 問題を回避するためには， ， < / li > < / ul > < a href = #不確実な情報による結論の不確実性 > < h2 id = 不確実な情報による結論の不確実性 > < span class = hanchor arialabel = Anchor > # < / span > 不確実な情報による結論の不確実性< / h2 > < / a > < ul > < li > < strong > 第一種の過誤のみを考慮した場合< / strong > ，有意水準$x$で得られた検定の結果$n$個から導き出された結論は，最大で確率$1-(1-x)^n$で誤りである< ul > < li > $P_1\cup P_2\cup \dots \cup P_n\implies Q$であるとき，$P_i$それぞれについて偽である確率が$e$ならば，$\overline{Q}$である確率は$1-(1-e)^n$である< / li > < li > 故に有意水準を小さくすることで，結論が誤りである可能性を小さくすることができる< / li > < / ul > < / li > < li > ただし，実際には< strong > 第二種の過誤も存在する< / strong > < ul > < li > 有意水準を小さくすれば結論が第二種の過誤である確率は増加する< / li > < / ul > < / li > < li > 以上より，多重検定は非常によろしくない< ul > < li > 有意水準を何らかの方法で小さくした上で，全ての検定の帰無仮説が棄却であった場合のみ，統計的に有意な結論を導ける< ul > < li > 帰無仮説が棄却された場合，それが第二種の過誤であることはありえないから< / li > < / ul > < / li > < / ul > < / li > < / ul > < a href = #holm法による有意水準の調整 > < h2 id = holm法による有意水準の調整 > < span class = hanchor arialabel = Anchor > # < / span > Holm法による有意水準の調整< / h2 > < / a > < p > 多重検定を構成する一つ一つの検定の有意水準を小さくする方法の一つがHolm法である． ， （ < / p > < a href = #手法 > < h3 id = 手法 > < span class = hanchor arialabel = Anchor > # < / span > 手法< / h3 > < / a > < p > $N$個の検定による多重検定の有意水準を$\alpha$としたとき， ． < / p > < ol > < li > 各検定の有意確率をソート< / li > < li > $i=0$とする< / li > < li > 結論が未確定の検定のうち，最も有意確率が小さいものについて，その有意確率を$x$としたとき，< ul > < li > $x < \frac{\alpha}{N-i}$ ならば，その検定を棄却< / li > < li > $x > p$ ならば，結論が未確定の検定すべて（その検定を含む）を受容し，終了< / li > < / ul > < / li > < li > $i$に1を足して， < ul > < li > $i< N$ ならば， < / li > < li > それ以外ならば，終了< / li > < / ul > < / li > < / ol > < a href = #まとめ > < h2 id = まとめ > < span class = hanchor arialabel = Anchor > # < / span > まとめ< / h2 > < / a > < ul > < li > 多重検定は避けるべき< / li > < li > どうしても必要なら有意水準の補正が必要< / li > < li > 有意水準の補正にはHolm法が有効< / li > < / ul > < div class = content-list > < h2 > Related Notes< / h2 > < ul class = section-ul > < li class = section-li > < div class = section > < p class = meta > Jun 21, 2023< / p > < div class = desc > < h3 > < a href = https://ar.falsy.cat/note/study/statistics/hypothesis-test-parametric/ class = internal-link data-src = /note/study/statistics/hypothesis-test-parametric/ > パラメトリック検定とノンパラメトリック検定< / a > < / h3 > < / div > < div class = spacer > < / div > < ul class = tags > < li > < a href = https://ar.falsy.cat/tags/note/ > Note< / a > < / li > < li > < a href = https://ar.falsy.cat/tags/study/ > Study< / a > < / li > < li > < a href = https://ar.falsy.cat/tags/statistics/ > Statistics< / a > < / li > < / ul > < / div > < / li > < li class = section-li > < div class = section > < p class = meta > Jun 18, 2023< / p > < div class = desc > < h3 > < a href = https://ar.falsy.cat/note/study/statistics/hypothesis-test/ class = internal-link data-src = /note/study/statistics/hypothesis-test/ > 仮説検定< / a > < / h3 > < / div > < div class = spacer > < / div > < ul
