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参数估计与假设检验的区别

参数估计与假设检验是统计推断的两个组成部分，都是利用样本信息对总体进行推断，但是角度不同。
参数估计是样本统计量估计总体参数的方法，总体参数在估计前是未知的。
假设检验是先对总体参数提出一个假设，后用样本信息去验证这个假设是否正确。
参数估计不知道总体的信息，也不进行假定，假设不知道总体，需要验证信息。

1.假设检验的基本思想和原理
2.假设检验的步骤
3.一个总体参数的检验
4.两个总体参数的检验
5.P值的计算与应用
6.用EXCEL进行检验

假设检验的基本问题

1.假设问题的提出
2.假设的表达式
3.两类错误
4.假设检验的流程
5.利用P值进行决策

什么是假设？
对总体参数的具体数值所做的陈述
-总体参数包括总体均值、比例、方差等
-分析之前必需陈述

什么是假设检验
1.先对总体的参数(或分布形式)提出某种假设，然后利用样本信息判断假设是否成立的过程
2.有参数检验和非参数检验
3.逻辑上运用反证法，统计上依据小概率原理

原假设
1.研究者想收集证据予以反对的假设
2.又称为"0假设"
3.总是有符号=,≤或≥
4.表示为H0​
H0​:\mu=某一数值
指定为符号=,≤或≥
例如 H0​:μ=10cm
一般情况下，记原假设为H0​所谓为零假设
备择假设
1.研究者想收集证据予以支持的假设
2.也称为研究假设
3.总是有符号 !=,≤或≥
4.表示为H1​
H1​:μ<某一数值，或μ>某一数值
例如：H1​:μ<10cm,或mu>10cm
原假设和备择假设是属于非此即彼的关系，一般来说，原假设是包含等于的
提出假设
1.原假设和备择假设是一个完备事件组，而且相互独立
在一项假设检验中，原假设和备择假设必有一个条件成立，而且只有一个成立
2.先确定备择假设，再确定原假设
3.等号=总是放在原假设上
4.因研究目的不同，对同一问题可能提出不同的假设(也可能得出不同的结论)
双侧检验和单侧检验
1.备择假设没有特定的方向性，并含有符号≠的假设检验，称为双侧检验或双尾检验
2.备择假设具有特定的方向性，并含有符号≤和\req的假设检验，称为单侧检验或单尾检验

• 备择假设的方向为<,称为左侧检验
• 备择假设的方向为>,称为右侧检验

双侧检验和单侧检验的假设形式

假设	双侧检验	单侧检验(左侧)	单侧检验(右侧)
原假设	H0​:μ=μ0​	H0​:μ≥μ0​	H0​:μ≤μ0​
备择假设	H1​:μ≠μ0​	H1​:μ<μ0​	H1​:μ>μ0​

假设检验中的两类错误

• 1.第I类错误(弃真错误)
• 原假设为真，拒绝原假设
  第I类错误的概率记为α,被称为显著性水平
  2.第II类错误(取伪错误)
• 原假设为假设时未拒绝原假设
• 第II类错误的概率记为β
  两类错误时此消彼长的关系，不可能同时达到平衡，需要有所取舍

影响beta错误的因素

• 1.总体参数的真值
• 随着假设的总体参数的减少而增大
  2.显著性水平α
  当α减少时增大
  3.总体标准差
  当α增大时增大
  4.样本容量n
  当n减少时增大

显著性水平α
1.是一个概率值
2.原假设为真时，拒绝原假设的概率被称为抽样分布的拒绝域
表示为α

• 常用的alpha有0.01,0.05,0.1
  由研究者提出

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