This test involves with nominal data produced by
multinomial experiment It is a generalisation of a binomial experiment These test the null hypothesis that data in the target population has a particular probability distribution. Example 1 We might test whether consumers are indifferent to which of four materials (glass, plastic, steel or aluminium) that could be used to make soft drink containers.
Under the null hypothesis We expect 25 consumers to nominate glass, 25 to nominate plastic, 25 to nominate steel and 25 to nominate aluminium

These are the expected frequencies, Ei.

Hypotheses


The alternative is that at least one material is more preferred (or less preferred) than the others.
Example 1cont..
Procedure:

Select a random sample of, say, 100 consumers and determine their preferences.
确定待检验个案的取值范围(expected range)
get from data:全部样本 use specified range:用户自定义个案范围 指定期望频数(expected values) all categories equal:所有类别有相同的构成比 value:用户自定义构成比

Categorical variable
Variables that describe categories of entities
Dealing with them all the time in statistics Making comparisons among variables For example, whether consumers prefer a particular brand of a product among other competing brands. Checking whether there is a relationship between

The null hypothesis is that they are indifferent (or that equal numbers prefer glass, plastic, steel and aluminium).
Example 1
Data


Let pG be the probability that an individual selected at random will nominate glass as his/her preference if required to make a choice. Similarly for pP (plastic), pS (steel) and pA (aluminium) HO: pG = pP = pS = pA = 0.25. HA: at least one pi 0.25.
方值 – 卡方值较小,则实际频数和期望频数相差较小.如果P大 于a,不能拒绝H0,认为总体分布与已知分布无显著i-square检验
(4)基本操作步骤:
菜单:analyze->nonparametric test->chi square 选定待检验变量入test variable list 框

Ei = n pi.


We compare the expected frequencies with the sample results or the observed frequencies, Oi. If they are approximately the same we would conclude that the null hypothesis is true. Oi Ei HO is probably true.
BEO2255 Applied Statistics for Business
Week Six – Analyzing categorical data: Chi-squared tests
This week lecture will cover...
Analysing categorical data (nominal) Chi-square test of differences between proportions Chi-square test of independence
SPSS单样本非参数检验
总体分布的chi-square检验
(1)目的: 根据样本数据推断总体的分布与某个已知分布是否有显著差异--吻合性检验。
适用于分类资料的统计推断
SPSS单样本非参数检验

总体分布的chi-square检验
(2)基本假设: H0:总体分布与理论分布无显著差异 (3)基本方法 – 根据已知总体的构成比计算出样本中各类别的期望频 数，计算实际观察频数与期望频数的差距,即：计算卡
two categorical variables
Gender and preference for a product, whether the
preference for a product is independent from gender
Chi-square test for differences between proportions