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AlternativeHypothesis

是假设检验函数如 LocationTest 的一个选项，指定备择假设.

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AlternativeHypothesis

AlternativeHypothesis

是假设检验函数如 LocationTest 的一个选项，指定备择假设.

更多信息

  • 对于具有检验统计量 的假设检验，AlternativeHypothesis 可以用来检验零假设 、特定的备择假设 .
  • 典型设置包括：
  • "Unequal" ⟷
    "Less" ⟷
    "Greater" ⟷
  • 对于使用 AlternativeHypothesis 的函数，默认情况下，执行一个双侧检验.

范例

打开所有单元 关闭所有单元

基本范例  (2)

对位置执行双侧检验：

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

默认情况下，选择设置 "Unequal"：

Wolfram Language code: LocationTest[data]

执行其中一个单侧备择假设检验：

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

属性和关系  (3)

来自双侧检验的 值是较小单侧检验 值的两倍：

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

一个双侧检验的解释：

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]

值可以解释为检验统计量的分布下的面积：

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

两个单侧备择检验的解释：

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"]}

面积等于由检验返回的 值：

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 语言函数，https://reference.wolfram.com/language/ref/AlternativeHypothesis.html.

文本

Wolfram Research (2010)，AlternativeHypothesis，Wolfram 语言函数，https://reference.wolfram.com/language/ref/AlternativeHypothesis.html.

CMS

Wolfram 语言. 2010. "AlternativeHypothesis." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/AlternativeHypothesis.html.

APA

Wolfram 语言. (2010). AlternativeHypothesis. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/AlternativeHypothesis.html 年

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: 18-August-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: 18-August-2026]}