假设检验的总结 Hypothesis Testing Summary

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计量经济学第5章假设检验

5-15
假设检验中的小概率原理
假设检验中的小概率原理
什么小概率？ 1. 在一次试验中，一个几乎不可能发生的事
件发生的概率 2. 在一次试验中小概率事件一旦发生，我们
就有理由拒绝原假设 3. 小概率由研究者事先确定
5-17
假设检验中的小概率原理
由以往的资料可知，某地新生儿的平均体重为3190克，从今年的新生儿中随机抽取100个，测得其平均体重为3210克，问今年新生儿的平均体重是否为 3190克（即与以往的体重是否有显著差异）？
决策:
在 = 0.05的水平上拒绝H0
结论:
有证据表明新机床加工的零件的椭圆度与以前有显著差异
5-56
2 已知均值的检验
(P 值的计算与应用)
第1步：进入Excel表格界面，选择“插入”下拉菜单第2步：选择“函数”点击第3步：在函数分类中点击“统计”，在函数名的菜单下选
与原假设对立的假设表示为 H1
5-12
确定适当的检验统计量
什么检验统计量？
1.用于假设检验决策的统计量 2.选择统计量的方法与参数估计相同，需考虑
是大样本还是小样本总体方差已知还是未知
检验统计量的基本形式为 Z X 0 n
5-13
规定显著性水平(significant level)
(P-value)
1. 是一个概率值
2. 如果原假设为真，P-值是抽样分布中大
于或小于样本统计量的概率
左侧检验时，P-值为曲线上方小于等于检
验统计量部分的面积
右侧检验时，P-值为曲线上方大于等于检
验统计量部分的面积
3. 被称为观察到的(或实测的)显著性水平
5-44
双侧检验的P 值

假设检验

x − μ0
= 山区总体 μ？抽样误差总体均数之差 +抽样误差
10
≠
医学统计二·研2010
9
医学统计二·研2010
基本步骤1
建立检验假设
H0无效假设null hypothesis, H1备择假设alternative hypothesis
基本步骤1
注意
假设只针对总体 H0、H1互相对立，缺一不可 H0通常是：总体均数相等 μ1 = μ2 ，总体率相等，总体分布是某一特定分布等 μ H1是H0的对立： 1 ≠ μ2 μ1 < μ2 μ1 > μ2 H1反映了检验的单双侧，它是由研究目的决定的，而不是由样本决定的
需要从总体上对问题做出判断无法观察到全部个体
假设检验的基本思想
先建立一个关于样本所属总体的假设，考察在假设条件下随机样本的特征信息是否属小概率事件
若为小概率事件，则怀疑假设成立有悖于该样本所提供特征信息，因此拒绝假设反之，不拒绝假设
小概率事件(p=0.05)在随机抽样中还是可能发生的，只是发生的概率很小
0 = 1 − C4 × 0.010 × 0.99 4
假设检验是用来判断样本与样本，样本与总体的差异是由抽样误差引起还是本质差别造成的统计推断方法。
医学统计二·研2010 3
= 0.039
医学统计二·研2010
4
假设检验（hypothesis testing）
依据：小概率事件在一次随机抽样中不大可能发生为何要做假设检验:
不拒绝实际上是不成立的H0, “存伪” II型错误的概率用β表示
医学统计二·研2010 27
图4.1 I、II型错误示意（以单侧t检验为例）

假设检验 Hypothesis Test

Rev. B Printed 2021/4/2 © 2001 by Sigma Breakthrough Technologies, Inc.
“假设” 与决策风险
我们依据已知的风险程度和置信度进行判断，接受或拒绝一项 “假设” 因此，我们必须在分析前预先确定决策风险的大小及可接受的检验灵敏度（ test sensitivity ）一旦上述值设定完成后，我们就有足够的数据来决定理想的抽样大小我们也必须考虑实际的成本、时间及可获得资源的限制，以制定合理的抽样计划
★ 适当地处理不确定性 ★ 降低主观因素 ★ 质疑假设 ★ 避免重要信息的遗漏 ★ 决策错误的风险管理
假设检验-10
Rev. B Printed 2021/4/2 © 2001 by Sigma Breakthrough Technologies, Inc.
实际上
我们可能在流程不佳的情况下，却得到良好的流程样本我们可能在流程良好的状况下，抽取到不良的流程样本不论何种状况，我们都可能做出错误的推断
流程改善方法论
福源集团成本抑减
假设检验（Hypothesis Testing）简介
Rev. B Printed 2021/4/2 © 2001 by Sigma Breakthrough Technologies, Inc.
步骤 I: 定义(Define)
项目启动
. 项目启动 (项目定义表) . 项目背景, 选择理由 . 客户需求分析(VOC/VOB)
潜在关键影响因素的初步挖掘
. 全部影响因素分析(流程图 / 鱼刺图) . 定性确定关键因素(因果矩阵) . 关键因素失效模式分析, 评价控制计划,
并提出初步改善措施(快赢)
假设检验-1

假设检验

假设检验假设检验(Hypothesis Testing)是数理统计学中根据一定假设条件由样本推断总体的一种方法。

具体作法是：根据问题的需要对所研究的总体作某种假设，记作H0；选取合适的统计量，这个统计量的选取要使得在假设H0成立时，其分布为已知；由实测的样本，计算出统计量的值，并根据预先给定的显著性水平进行检验，作出拒绝或接受假设H0的判断。

常用的假设检验方法有u—检验法、t检验法、χ2检验法(卡方检验)、F—检验法，秩和检验等。

中文名假设检验外文名 hypothesis test提出者 K.Pearson 提出时间 20世纪初1、简介假设检验又称统计假设检验（注：显著性检验只是假设检验中最常用的一种方法），是一种基本的统计推断形式，也是数理统计学的一个重要的分支，用来判断样本与样本，样本与总体的差异是由抽样误差引起还是本质差别造成的统计推断方法。

其基本原理是先对总体的特征作出某种假设，然后通过抽样研究的统计推理，对此假设应该被拒绝还是接受作出推断。

[1]2、基本思想假设检验的基本思想是小概率反证法思想。

小概率思想是指小概率事件（P<0.01或P<0.05）在一次试验中基本上不会发生。

反证法思想是先提出假设(检验假设H0)，再用适当的统计方法确定假设成立的可能性大小，如可能性小，则认为假设不成立，若可能性大，则还不能认为假设成立。

[2] 假设是否正确，要用从总体中抽出的样本进行检验，与此有关的理论和方法，构成假设检验的内容。

设A是关于总体分布的一项命题，所有使命题A成立的总体分布构成一个集合h0，称为原假设(常简称假设)。

使命题A不成立的所有总体分布构成另一个集合h1，称为备择假设。

如果h0可以通过有限个实参数来描述，则称为参数假设，否则称为非参数假设(见非参数统计)。

如果h0(或h1)只包含一个分布，则称原假设(或备择假设)为简单假设，否则为复合假设。

对一个假设h0进行检验，就是要制定一个规则，使得有了样本以后，根据这规则可以决定是接受它（承认命题A正确），还是拒绝它（否认命题A正确）。

假设检验的基本思想

假设检验的基本思想假设检验的基本思想⼀、总结⼀句话总结：> 假设检验的基本思想是【“⼩概率事件”原理】，其统计推断⽅法是带有某种概率性质的【反证法】。

> 【⼩概率思想】是指⼩概率事件在⼀次试验中基本上不会发⽣。

> 【反证法思想】是先提出检验假设，再⽤适当的统计⽅法，利⽤⼩概率原理，确定假设是否成⽴。

即为了检验⼀个假设H0是否正确，⾸先假定该假设H0正确，然后根据样本对假设H0做出接受或拒绝的决策。

【如果样本观察值导致了“⼩概率事件”发⽣，就应拒绝假设H0，否则应接受假设H0】。

> 对于不同的问题，检验的显著性⽔平α不⼀定相同，⼀般认为，事件发⽣的概率【⼩于0.1、0.05或0.01等】，即“⼩概率事件”。

1、假设检验(hypothesis testing)？> 假设检验(hypothesis testing)，⼜称统计假设检验，是⽤来判断【样本与样本、样本与总体的差异是由抽样误差引起还是本质差别造成的统计推断⽅法】。

> 【显著性检验】是假设检验中最常⽤的⼀种⽅法，也是⼀种最基本的统计推断形式，其【基本原理】是【先对总体的特征做出某种假设】，然后通过抽样研究的统计推理，对此假设应该被拒绝还是接受做出推断。

> 常⽤的【假设检验⽅法】有【Z检验、t检验、卡⽅检验、F检验等】⼆、假设检验的基本思想来看看百度百科的说法：假设检验(hypothesis testing)假设检验(hypothesis testing)，⼜称统计假设检验，是⽤来判断样本与样本、样本与总体的差异是由抽样误差引起还是本质差别造成的统计推断⽅法。

显著性检验是假设检验中最常⽤的⼀种⽅法，也是⼀种最基本的统计推断形式，其基本原理是先对总体的特征做出某种假设，然后通过抽样研究的统计推理，对此假设应该被拒绝还是接受做出推断。

常⽤的假设检验⽅法有Z检验、t检验、卡⽅检验、F检验等基本思想假设检验的基本思想是“⼩概率事件”原理，其统计推断⽅法是带有某种概率性质的反证法。

六西格玛工具HypothesisTest假设检验完整版

六西格玛工具HypothesisTest假设检验完整版
六西格玛管理中，由于总体的参数是未知的，只能通过对总体随机变量的抽样，使用样本来估计总体的分布。

我们常说的统计分析，基本是参数估计和假设检验两方面的内容，大约80%以上是关于假设检验的，MSA、归回分析、DOE等都是以假设检验为基础。

下面是常用的假设检验类型：
数据类型假设检验目的
分
类
离散型
Chi-squaretest
卡方检验比较两组或多组数据的方
差
比
例
连续型t-test
T检验
比较两组数据的平均值
均
值Paired t-test
成对T检验
当两组数据成对，比较两组数据
的
平均值
ANOVA
比较两组或多组数据的平
均值
Test for equal variances
等方差检验
(F-test, Bartlett’s test,
Levene’s test)
比较两组或多组数据的方
差
方
差
这篇文章对这些假设检验逐步讲解，包括假设检验的概念，包括区间估计、t和F分布以及P-Value、各种假设检验的概念和方法。

假设检验(Hypothesis Testing)

假设检验（HypothesisTesting）假设检验是用来判断样本与样本，样本与总体的差异是由抽样误差引起还是本质差别造成的统计推断方法。

其基本原理是先对总体的特征作出某种假设，然后通过抽样研究的统计推理，对此假设应该被拒绝还是接受作出推断。

生物现象的个体差异是客观存在，以致抽样误差不可避免，所以我们不能仅凭个别样本的值来下结论。

当遇到两个或几个样本均数（或率）、样本均数（率）与已知总体均数（率）有大有小时，应当考虑到造成这种差别的原因有两种可能：一是这两个或几个样本均数（或率）来自同一总体，其差别仅仅由于抽样误差即偶然性所造成；二是这两个或几个样本均数（或率）来自不同的总体，即其差别不仅由抽样误差造成，而主要是由实验因素不同所引起的。

假设检验的目的就在于排除抽样误差的影响，区分差别在统计上是否成立，并了解事件发生的概率。

在质量管理工作中经常遇到两者进行比较的情况，如采购原材料的验证，我们抽样所得到的数据在目标值两边波动，有时波动很大，这时你如何进行判定这些原料是否达到了我们规定的要求呢？再例如，你先后做了两批实验，得到两组数据，你想知道在这两试实验中合格率有无显著变化，那怎么做呢？这时你可以使用假设检验这种统计方法，来比较你的数据，它可以告诉你两者是否相等，同时也可以告诉你，在你做出这样的结论时，你所承担的风险。

假设检验的思想是，先假设两者相等，即：μ＝μ0，然后用统计的方法来计算验证你的假设是否正确。

假设检验的基本思想1.小概率原理如果对总体的某种假设是真实的，那么不利于或不能支持这一假设的事件A（小概率事件）在一次试验中几乎不可能发生的；要是在一次试验中A竟然发生了，就有理由怀疑该假设的真实性，拒绝这一假设。

2.假设的形式H0——原假设，H1——备择假设双尾检验：H0:μ = μ0，单尾检验：，H1:μ < μ0，H1:μ > μ0假设检验就是根据样本观察结果对原假设（H0）进行检验，接受H0，就否定H1；拒绝H0，就接受H1。

Hypothesis_Testing(统计学假设检验)

we might hypothesize that the mean IQ for UIC students is = 110. we might select a random sample of n = 100 UIC students.
2. Next, we obtain a random sample from the population. For example,
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Statistics for Business (ENV)
Chapter 9
INTRODUCTION TO HYPOTHESIS TESTING
1
Hypothesis Testing
9.1
9.2 9.3
Null and Alternative Hypotheses and Errors in Testing z Tests about a Population with known s t Tests about a Population with unknown s
2
Hypothesis testing-1
Researchers usually collect data from a sample and then use the sample data to help answer questions about the population. Hypothesis testing is an inferential statistical process that uses limited information from the sample data as to reach a general conclusion about the population.

什么是假设检验

什么是假设检验
假设检验（hypothesis testing）是指从对总体参数所做的一个假设开始，然后搜集样本数据，计算出样本统计量，进而运用这些数据测定假设的总体参数在多大程度上是可靠的，并做出承认还是拒绝该假设的判断。

如果进行假设检验时总体的分布形式已知，需要对总体的未知参数进行假设检验，称其为参数假设检验；若对总体分布形式所知甚少，需要对未知分布函数的形式及其他特征进行假设检验，通常称之为非参数假设检验。

此外，根据研究者感兴趣的备择假设的内容不同，假设检验还可分为单侧检验（单尾检验）和双侧检验（双尾检验），而单侧检验又分为左侧检验和右侧检验。

假设检验的基本思想是反证法思想和小概率事件原理。

反证法的思想是首先提出假设（由于未经检验是否成立，所以称为零假设、原假设或无效假设），然后用适当的统计方法确定假设成立的可能性大小，如果可能性小，则认为假设不成立，拒绝它；如果可能性大，还不能认为它不成立。

小概率事件原理，是指小概率事件在一次随机试验中几乎不可能发生，小概率事件发生的概率一般称之为“显著性水平”或“检验水平”，用表示，而概率小于多少算小概率是相对的，在进行统计分析时要事先规定，通常取=0.01、0.05、0.10等。

假设检验hypothesistesting

假定查验 (hypothesis testing)方法演变： t 查验、 z 查验、 F 查验、卡方查验，方差剖析( ANOVA)概括假定查验是剖析数据的一种方法。

回答此类问题：“随机发生的事件的概率是多少 ?”另一方面的问题是：“我们从数据中发现的结果是真的吗？” 当问题是相关大的整体而只好获取整体的一个样本时用假定查验。

这种方法被用往返答在质量改良中一系列重要的问题，如“我们在过程中所做的改变对产出创建了存心义的差异吗？”或”顾客对场所 A 的满意度能否是比其余场所高？”最常用的查验是： z 查验、 t 查验、 F 查验、卡方（χ2）查验和方差剖析。

这些查验和其余的查验都是鉴于均值、方差、比率及其余统计量所形成的拥有常有模式的频次散布。

最出名的散布就是正态散布，它是：查验的基础。

t 查验、 F 查验和卡方 (χ2)查验是鉴于 t 散布、 F 散布和卡方散布。

合用处合·想知道一组或更多组数据的均匀值、比率、方差或其余特点时；·当结论是鉴于更大整体中所获得的样本时。

比如：·想确立一个过程的均值或方差有否改变；·想确立好多半据集的均值或方差能否不一样：·想确立两组不一样的数据集的比率能否不一样；·想确立真切的比率、均值或方差能否和一个定值相等（或大于或小于）。

实行步骤假定查验的步骤由三部分构成：理解要解决的问题并安排查验（以下步骤 1～ 3）；数字计算往常由计算机达成（步骤 4 和步骤 5）；应用数值结果到实质问题中（步骤 6）。

固然计算机能办理数字，但理解假没查验隐含的观点对第 1 部分和第 3 部分至关重要。

假如第一次接触假定查验，那么从看“注意事项”中的术语和定义开始。

这些定义解说了假定查验的慨念，而后再回来看这个步骤。

本书不行能详尽地波及假定查验。

这个步骤是个综述和迅速参照。

要获取更多的信息，查阅统计学参照书或讨教统计学家。

1 确立要从数据中获取的结论。

Hypothesis Testing

测定归无假设的确信性程度的值。 Ho 真实时，发生这样可能性 ( 概率 ). ※ 有利水准 (α) : 代表推翻归无假设的最大水准 ( 概率 ) 的一个基准。更难得用语是归无假设的真实度采用对立假设的失误的概率最大限度的降低。 p-value < α 时推翻归无假设 p-value ≥ α 时采用归无假设
假设检定
Null Hypothesis(Ho)
统计性解释 : 工程 A 和 B 的母集团的平均是一样 . 实际性解释 : 两个工程间的收率差异是没有 . 既 , 改善工程的收率比原有工程比提高了 . 母集团的平均是不一样 . 实际性解释 : 工程 B 的平均收率工程 A 的平均收率不一样 .
84.5
Analyze – 假设检定 - 16
假设检定例
实际性的提问 : 改善工程 B 的收率比原有工程 A 的收率有变化吗 ?
• • • • •
想知道什么 ? 怎样知道呢 ? 怎样使用道具 ? 需要什么数据 ? 怎样收集数据 ?
统计性的提问 :
工程 B 的平均 (85.54) 和工程 A 的平均 (84.24) 差异按统计性是否有有意的差异 ? 平均的差异是否只是时间变动的差异 ?
假设检定
假设检定的两个错误
事实 ( 实值 ) H0 H0 不可以弃却正确的决定 H1
第 2 种错误
判断
H0 弃却第 1 种错误正确的决定
第 1 种错误 (TypeⅠError) : 不顾 Null Hypothesis“H0”, 真实 . 弃却 Null Hypothesis 的错误把良品判断为不良的时候 α ( − Risk ) 既 , 可以说生产者危险第 2 种错误 (TypeⅡError) : 不顾 Null Hypothesis“H0” 假的 . 不弃却 Null Hypothesis 的错误不良品当成良品的时候即 , 可以说消费者危险 β ( − Risk )

假设检验（HypothesisTesting）

假设检验（HypothesisTesting）假设检验的定义假设检验：先对总体参数提出某种假设，然后利⽤样本数据判断假设是否成⽴。

在逻辑上，假设检验采⽤了反证法，即先提出假设，再通过适当的统计学⽅法证明这个假设基本不可能是真的。

（说“基本”是因为统计得出的结果来⾃于随机样本，结论不可能是绝对的，所以我们只能根据概率上的⼀些依据进⾏相关的判断。

）假设检验依据的是⼩概率思想，即⼩概率事件在⼀次试验中基本上不会发⽣。

如果样本数据拒绝该假设，那么我们说该假设检验结果具有统计显著性。

⼀项检验结果在统计上是“显著的”，意思是指样本和总体之间的差别不是由于抽样误差或偶然⽽造成的。

假设检验的术语零假设（null hypothesis）：是试验者想收集证据予以反对的假设，也称为原假设，通常记为 H0。

例如：零假设是测试版本的指标均值⼩于等于原始版本的指标均值。

备择假设（alternative hypothesis）：是试验者想收集证据予以⽀持的假设，通常记为H1或 Ha。

例如：备择假设是测试版本的指标均值⼤于原始版本的指标均值。

双尾检验（two-tailed test）：如果备择假设没有特定的⽅向性，并含有符号“=”，这样的检验称为双尾检验。

例如：零假设是测试版本的指标均值等于原始版本的指标均值，备择假设是测试版本的指标均值不等于原始版本的指标均值。

单尾检验（one-tailed test）：如果备择假设具有特定的⽅向性，并含有符号 “>” 或 “<” ，这样的检验称为单尾检验。

单尾检验分为左尾（lower tail）和右尾（upper tail）。

例如：零假设是测试版本的指标均值⼩于等于原始版本的指标均值，备择假设是测试版本的指标均值⼤于原始版本的指标均值。

检验统计量（test statistic）：⽤于假设检验计算的统计量。

例如：Z值、t值、F值、卡⽅值。

显著性⽔平（level of significance）：当零假设为真时，错误拒绝零假设的临界概率，即犯第⼀类错误的最⼤概率，⽤α表⽰。

HypothesisTesting假设检验讲义

Should the sample be random?
We make decisions about the population based on the sample
总体和样本
样品: 总体中具有共同特征的子集。可以计算其形成的统计表（X）.
为何要选取样本？
总体: 统计总体用以定义所有可知或不可知参数(m, 的数据或信息
A Statistical Hypothesis
An assertion or conjecture about one or more parameters of the population To determine whether it is true or false, we must examine the entire population. This is impossible!! Instead use a random sample to provide evidence that either supports or does not support the hypothesis. The conclusion is then based upon statistical significance. It is important to remember that this conclusion is an inference about the population determined from the sample data.
2. Once we have identified these factors and made adjustments for improvement, we need to validate actual improvements in our processes.

Statistical-hypothesis-testing统计假设检验毕业论文外文文献翻译及原文

毕业设计（论文）外文文献翻译文献、资料中文题目：统计假设检验文献、资料英文题目：Statistical hypothesis testing 文献、资料来源：文献、资料发表（出版）日期：院（部）：专业：班级：姓名：学号：指导教师：翻译日期： 2017.02.14Statistical hypothesis testingAdriana Albu，Loredana UngureanuPolitehnica University Timisoara, adrianaa@aut.utt.roPolitehnica University Timisoara, loredanau@aut.utt.roAbstract In this article, we present a Bayesian statistical hypothesis testing inspection, testing theory and the process Mentioned hypothesis testing in the real world and the importance of, and successful test of the Notes.Key words Bayesian hypothesis testing; Bayesian inference; Test of significance IntroductionA statistical hypothesis test is a method of making decisions using data, whether from a controlled experiment or an observational study (not controlled). In statistics, a result is called statistically significant if it is unlikely to have occurred by chance alone, according to a pre-determined threshold probability, the significance level. The phrase "test of significance" was coined by Ronald Fisher: "Critical tests of this kind may be called tests of significance, and when such tests are available we may discover whether a second sample is or is not significantly different from the first."[1]Hypothesis testing is sometimes called confirmatory data analysis, in contrast to exploratory data analysis. In frequency probability, these decisions are almost always made using null-hypothesis tests. These are tests that answer the question Assuming that the null hypothesis is true, what is the probability of observing a value for the test statistic that is at least as extreme as the value that was actually observed?)2[]More formally, they represent answers to the question, posed before undertaking an experiment, of what outcomes of the experiment would lead to rejection of the null hypothesis for a pre-specified probability of an incorrect rejection. One use of hypothesis testing is deciding whether experimental results contain enough information to cast doubt on conventional wisdom.Statistical hypothesis testing is a key technique of frequentist statistical inference. The Bayesian approach to hypothesis testing is to base rejection of the hypothesis on the posterior probability.[3][4]Other approaches to reaching a decision based on data are available via decision theory and optimal decisions.The critical region of a hypothesis test is the set of all outcomes which cause the null hypothesis to be rejected in favor of the alternative hypothesis. The critical region is usually denoted by the letter C.One-sample tests are appropriate when a sample is being compared to the population from a hypothesis. The population characteristics are known from theory or are calculated from the population.Two-sample tests are appropriate for comparing two samples, typically experimental and control samples from a scientifically controlled experiment.Paired tests are appropriate for comparing two samples where it is impossible to control important variables. Rather than comparing two sets, members are paired between samplesso the difference between the members becomes the sample. Typically the mean of the differences is then compared to zero.Z-tests are appropriate for comparing means under stringent conditions regarding normality and a known standard deviation.T-tests are appropriate for comparing means under relaxed conditions (less is assumed).Tests of proportions are analogous to tests of means (the 50% proportion).Chi-squared tests use the same calculations and the same probability distribution for different applications:∙Chi-squared tests for variance are used to determine whether a normal population has a specified variance. The null hypothesis is that it does.∙Chi-squared tests of independence are used for deciding whether two variables are associated or are independent. The variables are categorical rather than numeric. It can be used to decide whether left-handedness is correlated with libertarian politics (or not). The null hypothesis is that the variables are independent. The numbers used in the calculation are the observed and expected frequencies of occurrence (from contingency tables).∙Chi-squared goodness of fit tests are used to determine the adequacy of curves fit to data. The null hypothesis is that the curve fit is adequate. It is common to determine curve shapes to minimize the mean square error, so it is appropriate that the goodness-of-fit calculation sums the squared errors.F-tests (analysis of variance, ANOVA) are commonly used when deciding whether groupings of data by category are meaningful. If the variance of test scores of the left-handed in a class is much smaller than the variance of the whole class, then it may be useful to study lefties as a group. The null hypothesis is that two variances are the same - so the proposed grouping is not meaningful.The testing processIn the statistical literature, statistical hypothesis testing plays a fundamental role. The usual line of reasoning is as follows:1.There is an initial research hypothesis of which the truth is unknown.2.The first step is to state the relevant null and alternative hypotheses. This isimportant as mis-stating the hypotheses will muddy the rest of the process.Specifically, the null hypothesis allows attaching an attribute: it should be chosen in such a way that it allows us to conclude whether the alternative hypothesis can either be accepted or stays undecided as it was before the test.[9]3.The second step is to consider the statistical assumptions being made about thesample in doing the test; for example, assumptions about the statistical independence or about the form of the distributions of the observations. This is equally important as invalid assumptions will mean that the results of the test are invalid.4.Decide which test is appropriate, and state the relevant test statistic T.5.Derive the distribution of the test statistic under the null hypothesis from theassumptions. In standard cases this will be a well-known result. For example the test statistic may follow a Student's t distribution or a normal distribution.6.Select a significance level (α), a probability threshold below which the nullhypothesis will be rejected. Common values are 5% and 1%.7.The distribution of the test statistic under the null hypothesis partitions the possiblevalues of T into those for which the null-hypothesis is rejected, the so called critical region, and those for which it is not. The probability of the critical region is α.pute from the observations the observed value t obs of the test statistic T.9.Decide to either fail to reject the null hypothesis or reject it in favor of thealternative. The decision rule is to reject the null hypothesis H0if the observed value t obs is in the critical region, and to accept or "fail to reject" the hypothesis otherwise.Use and ImportanceStatistics are helpful in analyzing most collections of data. This is equally true of hypothesis testing which can justify conclusions even when no scientific theory exists. Real world applications of hypothesis testing include [7]:∙Testing whether more men than women suffer from nightmares∙Establishing authorship of documents∙Evaluating the effect of the full moon on behavior∙Determining the range at which a bat can detect an insect by echo∙Deciding whether hospital carpeting results in more infections∙Selecting the best means to stop smoking∙Checking whether bumper stickers reflect car owner behavior∙Testing the claims of handwriting analystsStatistical hypothesis testing plays an important role in the whole of statistics and in statistical inference. For example, Lehmann (1992) in a review of the fundamental paper by Neyman and Pearson (1933) says: "Nevertheless, despite their shortcomings, the new paradigm formulated in the 1933 paper, and the many developments carried out within its framework continue to play a central role in both the theory and practice of statistics and can be expected to do so in the foreseeable future".Significance testing has been the favored statistical tool in some experimental social sciences (over 90% of articles in the Journal of Applied Psychology during the early 1990s).[8]Other fields have favored the estimation of parameters. Editors often consider significance as a criterion for the publication of scientific conclusions based on experiments with statistical results.CautionsThe successful hypothesis test is associated with a probability and a type-I error rate. The conclusion might be wrong.The conclusion of the test is only as solid as the sample upon which it is based. The design of the experiment is critical. A number of unexpected effects have been observed including:∙The Clever Hans effect. A horse appeared to be capable of doing simple arithmetic.∙The Hawthorne effect. Industrial workers were more productive in better illumination, and most productive in worse.∙The Placebo effect. Pills with no medically active ingredients were remarkably effective.A statistical analysis of misleading data produces misleading conclusions. The issue of data quality can be more subtle. In forecasting for example, there is no agreement on a measure of forecast accuracy. In the absence of a consensus measurement, no decision based on measurements will be without controversy.The book How to Lie with Statistics is the most popular book on statistics ever published.[28] It does not much consider hypothesis testing, but its cautions are applicable, including: Many claims are made on the basis of samples too small to convince. If a report does not mention sample size, be doubtful.Hypothesis testing acts as a filter of statistical conclusions; Only those results meeting a probability threshold are publishable. Economics also acts as a publication filter; Only those results favorable to the author and funding source may be submitted for publication. The impact of filtering on publication is termed publication bias. A related problem is that of multiple testing (sometimes linked to data mining), in which a variety of tests for a variety of possible effects are applied to a single data set and only those yielding a significant result are reported.Those making critical decisions based on the results of a hypothesis test are prudent to look at the details rather than the conclusion alone. In the physical sciences most results are fully accepted only when independently confirmed. The general advice concerning statistics is, "Figures never lie, but liars figure" (anonymous).ControversySince significance tests were first popularized many objections have been voiced by prominent and respected statisticians. The volume of criticism and rebuttal has filled books with language seldom used in the scholarly debate of a dry subject. Much of the criticism was published more than 40 years ago. The fires of controversy have burned hottest in the field of experimental psychology. Nickerson surveyed the issues in the year 2000. He included 300 references and reported 20 criticisms and almost as many recommendations, alternatives and supplements. The following section greatly condenses Nickerson's discussion, omitting many issues.Results of the controversyThe controversy has produced several results. The American Psychological Association has strengthened its statistical reporting requirements after review,[10] medical journal publishers have recognized the obligation to publish some results that are not statistically significant to combat publication bias.and a journal (Journal of Articles in Support of the Null Hypothesis) has been created to publish such results exclusively. Textbooks have added some cautions and increased coverage of the tools necessary to estimate the size of the sample required to produce significant results. Major organizations have not abandoned use of significance tests although they have discussed doing so.References[1] R. A. Fisher (1925). Statistical Methods for Research Workers, Edinburgh: Oliver and Boyd, 1925, p.43.[2] Cramer, Duncan; Dennis Howitt (2004). The Sage Dictionary of Statistics. p. 76. ISBN 0-7619-4138-X.[3] Schervish, M (1996) Theory of Statistics, p. 218. Springer ISBN 0-387-94546-6[4] Kaye, David H.; Freedman, David A. (2011). "Reference Guide on Statistics". Reference manual on scientific evidence (3rd ed.). Eagan, MN Washington, D.C: West National Academies Press. p. 259. ISBN 978-0-309-21421-6.[5] C. S. Peirce (August 1878). "Illustrations of the Logic of Science VI: Deduction, Induction, and Hypothesis". Popular Science Monthly 13.[6] Fisher, Sir Ronald A. (1956) [1935]. "Mathematics of a Lady Tasting Tea". In James Roy Newman. The World of Mathematics, volume 3 [Design of Experiments]. Courier Dover Publications. ISBN 978-0-486-41151-4.[7] Box, Joan Fisher (1978). R.A. Fisher, The Life of a Scientist. New York: Wiley. p. 134. ISBN 0-471-09300-9[8] Lehmann, E.L.; Romano, Joseph P. (2005). Testing Statistical Hypotheses (3E ed.). New York: Springer. ISBN 0-387-98864-5.[9] Adèr,J.H. (2008). Chapter 12: Modelling. In H.J. Adèr & G.J. Mellenbergh (Eds.) (with contributions by D.J. Hand), Advising on Research Methods: A consultant's companion (pp. 183–209). Huizen, The Netherlands: Johannes van Kessel Publishing[10] Triola, Mario (2001). Elementary statistics (8 ed.). Boston: Addison-Wesley. p. 388. ISBN 0-201-61477-4.American Journal of Mathematics, 2007, 126(5): 2387-2425统计假设检验Adriana Albu，Loredana UngureanuPolitehnica University Timisoara, adrianaa@aut.utt.roPolitehnica University Timisoara, loredanau@aut.utt.ro摘要在这篇文章中，我们给出统计假设检验的贝叶斯检验，介绍了检验理论和其过程。

回归直线的斜率的假设检验

回归直线的斜率的假设检验英文回答：Hypothesis testing for the slope of a regression lineis a common statistical procedure used to determine ifthere is a significant relationship between the independent and dependent variables. The null hypothesis, denoted as H0, typically states that the slope is equal to zero,indicating no relationship between the variables. The alternative hypothesis, denoted as Ha, states that theslope is not equal to zero, suggesting a significant relationship.To conduct the hypothesis test for the slope of a regression line, we can use the t-test for the slope coefficient in a simple linear regression model. The t-test evaluates whether the estimated slope is significantly different from zero. The test statistic for the t-test is calculated by dividing the estimated slope coefficient byits standard error. If the absolute value of the teststatistic is greater than the critical t-value at a specified significance level, we reject the null hypothesis in favor of the alternative hypothesis.In conducting the hypothesis test, we also need to calculate the degrees of freedom for the t-distribution, which is equal to the sample size minus 2. With the degrees of freedom and the critical t-value, we can determine if the slope of the regression line is statistically significant at a given level of significance.Once the hypothesis test is conducted, we can interpret the results and make inferences about the relationship between the variables. If the null hypothesis is rejected, we can conclude that there is a significant relationship between the independent and dependent variables, as indicated by the non-zero slope of the regression line. On the other hand, if the null hypothesis is not rejected, we do not have sufficient evidence to conclude that there is a significant relationship between the variables.In summary, hypothesis testing for the slope of aregression line is a valuable tool for determining the significance of the relationship between variables in a linear regression model. By conducting a t-test for the slope coefficient, we can assess the strength of the relationship and make informed decisions based on theresults of the hypothesis test.中文回答：回归直线斜率的假设检验是一种常用的统计程序，用于确定自变量和因变量之间是否存在显著关系。