Question

Explain the Chi – Square test and when it is appropriate. Give example of such test.

Answer 1

The Chi-square test or goodness of fit statistics' used to test how likely it is that an observed distribution is due to chance. it measures how well the observed distribution of data fits with the distribution that is expected if the variables are independent. in other words the Chi-square test is that it tests the null hypothesis that the variables are independent. or testing relationships between categorical variables.

it is designed to analyze categorical data. data has been counted and divided into categories. other conditions are :-sampling method is simple random sampling. The variable under study is categorical. The expected value of the number of sample observations in each level of the variable is at least 5.

it test the probability of independence of a distribution of data. NOT tell any details about the relationship between them. other condition to use chi square test is The variables in consideration must be mutually exclusive

example :-

suppose we want to test Which holiday do you prefer?"

we have data as follows

Beach	Cruise
Men	209	280
Women	225	248

If Gender does affect Preferred Holiday we say they are dependent.

By calculation p value is 0.132

Now, p < 0.05 is the usual test for dependence. In this case p is greater than 0.05, so we believe the variables are independent (ie not linked together).

In other words Men and Women probably do not have a different preference for Beach Holidays or Cruises.

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