商务统计学第六版 第十一章笔记

Chapter 11 chi-square tests

11.1 chi-square test for thedifference between two proportions

Using: Categorical variables    and   categorical variable

Tool: Contingency table 

Test statistic: χ²   (卡方统计量，不是未知数x，是卡方，写出来比x要长，右上方还有一个2.)

χ²  test for the difference between two proportions

step1: hypothesis:

H0: π1=π2  （theseis no difference between the two population proportions）

H1: π1≠π2  （theseis difference between the two population proportions）

Step2: χ² test for the difference between two proportions

Step3: make decision

11.2 chi-square test for differencesamong more than two proportions

step1: hypothesis:

H0: π1=π2=……=πn

H1: not all πj are equal  （wherej=1,2…，c）

Step2: χ² test for the difference between two proportions

f₀= observed frequency in aparticular cell of a 2 ╳contingency table

f_e= expected frequency in aparticular cell if the null hypothesis is true

degrees of freedom =(2-1)(c-1)=c-1

Step3: make decision

11.3 chi-square test of independence

STEP1: H₀:the two categoricalvariables are independent

H₁:the two categorical variables are dependent

STEP2：

STEP3:　

(degrees of freedom=(r-1)(c-1))