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AlternativeHypothesis

LocationTest等の仮説検定関数のオプションで対立仮説を指定する．

詳細
Details and Options Details and Options
例題  
例  
特性と関係  
関連項目
関連するガイド
履歴
引用書式

AlternativeHypothesis

AlternativeHypothesis

LocationTest等の仮説検定関数のオプションで対立仮説を指定する．

詳細

  • 検定統計 の仮説検定では，AlternativeHypothesisを使って帰無仮説 と特定の対立仮説 で検定が行える．
  • よく使われる設定値
  • "Unequal" と
    "Less" と
    "Greater" と
  • AlternativeHypothesisを使う関数ではデフォルトで両側検定が行われる．

例題

すべて開く すべて閉じる

例  (2)

位置についての両側検定を行う：

Wolfram Language code: data = RandomVariate[NormalDistribution[], 100];
Wolfram Language code: LocationTest[data, AlternativeHypothesis -> "Unequal"]

デフォルトで"Unequal"が選ばれる：

Wolfram Language code: LocationTest[data]

代りに，2つの片側検定の一方を行う：

Wolfram Language code: data = RandomVariate[NormalDistribution[], 100];
Wolfram Language code: LocationTest[data, AlternativeHypothesis -> "Less"]
Wolfram Language code: LocationTest[data, AlternativeHypothesis -> "Greater"]

特性と関係  (3)

両側検定からの 値は，片側検定の 値の半分である：

Wolfram Language code: data = RandomVariate[NormalDistribution[], 100];
Wolfram Language code: ptwo = LocationTest[data, AlternativeHypothesis -> "Unequal"]
Wolfram Language code: pone = Min[LocationTest[data, AlternativeHypothesis -> "Less"], LocationTest[data, AlternativeHypothesis -> "Greater"]]
Wolfram Language code: ptwo / pone

両側検定の解釈：

Wolfram Language code: data = RandomVariate[NormalDistribution[1, 1], 15];
Wolfram Language code: ℋ = LocationTest[data, 1.3, "HypothesisTestData", AlternativeHypothesis -> "Unequal"];
Wolfram Language code: 𝒟 = StudentTDistribution[14];
Wolfram Language code: T = ℋ["TestStatistic", "T"]
Wolfram Language code: twosided = Show[Plot[PDF[𝒟, x], {x, -5, -Abs[T]}, Filling -> Axis], Plot[PDF[𝒟, x], {x, Abs[T], 5}, Filling -> Axis], PlotRange -> {{-5, 5}, All}];
Wolfram Language code: Show[Plot[PDF[𝒟, x], {x, -5, 5}], twosided]

値は，検定統計の分布における領域として解釈することができる：

Wolfram Language code: (Integrate[PDF[𝒟, x], {x, -Infinity, -Abs[T]}] + Integrate[PDF[𝒟, x], {x, Abs[T], Infinity}])
Wolfram Language code: ℋ["T"]

代替する2つの片側検定の解釈：

Wolfram Language code: data = RandomVariate[NormalDistribution[1, 1], 15];
Wolfram Language code: Subscript[ℋ, L] = LocationTest[data, 1.3, "HypothesisTestData", AlternativeHypothesis -> "Less"]; Subscript[ℋ, G] = LocationTest[data, 1.3, "HypothesisTestData", AlternativeHypothesis -> "Greater"];
Wolfram Language code: 𝒟 = StudentTDistribution[14];
Wolfram Language code: T = Subscript[ℋ, L]["TestStatistic", "T"]
Wolfram Language code: less = Plot[PDF[𝒟, x], {x, -5, T}, Filling -> Axis, PlotRange -> {{-5, 5}, All}];
Wolfram Language code: greater = Plot[PDF[𝒟, x], {x, T, 5}, Filling -> Axis, PlotRange -> {{-5, 5}, All}];
Wolfram Language code: {Show[Plot[PDF[𝒟, x], {x, -5, 5}], less, PlotLabel -> "Less"], Show[Plot[PDF[𝒟, x], {x, -5, 5}], greater, PlotLabel -> "Greater"]}

領域は，検定で返された 値に等しい：

Wolfram Language code: {Integrate[PDF[𝒟, x], {x, -Infinity, T}], Subscript[ℋ, L]["T"]}
Wolfram Language code: {Integrate[PDF[𝒟, x], {x, T, Infinity}], Subscript[ℋ, G]["T"]}
Wolfram Research (2010), AlternativeHypothesis, Wolfram言語関数， https://reference.wolfram.com/language/ref/AlternativeHypothesis.html.

テキスト

Wolfram Research (2010), AlternativeHypothesis, Wolfram言語関数， https://reference.wolfram.com/language/ref/AlternativeHypothesis.html.

CMS

Wolfram Language. 2010. "AlternativeHypothesis." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/AlternativeHypothesis.html.

APA

Wolfram Language. (2010). AlternativeHypothesis. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AlternativeHypothesis.html

BibTeX

@misc{reference.wolfram_2026_alternativehypothesis, author="Wolfram Research", title="{AlternativeHypothesis}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/AlternativeHypothesis.html}", note=[Accessed: 09-September-2026]}

BibLaTeX

@online{reference.wolfram_2026_alternativehypothesis, organization={Wolfram Research}, title={AlternativeHypothesis}, year={2010}, url={https://reference.wolfram.com/language/ref/AlternativeHypothesis.html}, note=[Accessed: 09-September-2026]}