Sas 简明教程

SAS - Hypothesis Testing

假设检验是用统计数据确定给定假设为真的概率。假设检验的通常过程由以下四步组成。

Hypothesis testing is the use of statistics to determine the probability that a given hypothesis is true. The usual process of hypothesis testing consists of four steps as shown below.

Step-1

制定原假设 H0（通常为观测结果是纯粹机会的结果）和备择假设 H1（通常为观测结果显示真实的效应与机会变异组成）。

Formulate the null hypothesis H0 (commonly, that the observations are the result of pure chance) and the alternative hypothesis H1 (commonly, that the observations show a real effect combined with a component of chance variation).

Step-2

识别可用于评估原假设真值的检验统计量。

Identify a test statistic that can be used to assess the truth of the null hypothesis.

Step-3

计算 P 值，即假设原假设为真的情况下得到一个至少与观测者一样重要的检验统计量的概率。P 值越小，对原假设的反证就越有力。

Compute the P-value, which is the probability that a test statistic at least as significant as the one observed would be obtained assuming that the null hypothesis were true. The smaller the P-value, the stronger the evidence against the null hypothesis.

Step-4

将 p 值与可接受的显著性值 alpha（有时称为 alpha 值）比较。如果 p ⇐alpha，即观测效应具有统计显着性，则排除原假设，而备择假设有效。

Compare the p-value to an acceptable significance value alpha (sometimes called an alpha value). If p ⇐alpha, that the observed effect is statistically significant, the null hypothesis is ruled out, and the alternative hypothesis is valid.

SAS 编程语言具有执行各种类型假设检验的功能，如下所示。

SAS programming language has features to carry out various types of hypothesis testing as shown below.

Test

Description

SAS PROC

T-Test

A t-tests is used to test whether the mean of one variable is significantly different than a hypothesized value.We also determine whether means for two independent groups are significantly different and whether means for dependent or paired groups are significantly different.

PROC TTEST

ANOVA

It is also used to compare means when there is one independent categorical variable. We want to use one-way ANOVA when testing to see if the means of the interval dependent variable are different according to the independent categorical variable.

PROC ANOVA

Chi-Square

We use chi square goodness of fit to assess if frequencies of a categorical variable were likely to happen due to chance. Use of a chi square test is necessary whether proportions of a categorical variable are a hypothesized value.

PROC FREQ

Linear Regression

Simple linear regression is used when one wants to test how well a variable predicts another variable. Multiple linearregression allows one to test how well multiple variables predict a variable of interest. When using multiple linear regression, we additionally assume the predictor variables are independent.

PROC REG