Question

In: Math

This chapter extends the hypothesis testing to analyze difference between population proportions based on 2 or...

This chapter extends the hypothesis testing to analyze difference between population proportions based on 2 or more samples, and to test the hypothesis of independence in the joint responses to 2 categorical variables. Can we provide a real world example for using the Chi-square test along with expectation of the outcomes?

Solutions

Expert Solution

Chi-Square Test - It is used to test the relationship between two (nominal) categorical variables of a sample likely to reflect association for the given population. The test is also known as Pearson's Chi-Square Test

It has the following hypothesis:

Null hypothesis(H0) - There exists no relationship between categorical variables in the population.

Alternative hypothesis(H1) - There exists a relationship between categorical variables in the population.

Symbol - X2

Formula - ((observed value - expected value)2)/expected value

Example - Consider we have two Zodiac Signs who like two different Colours. We performed a survey on the frequency of the above two traits to find the relationship between person zodiac sign and colour preference. Result Table :

Survey Yellow Blue Total
Leo 60 30 90
Aries 40 70 110
Total 100 100 200

Solution: The expected value for each cell

For the (Leo/yellow) cell - (row total * column total)/total = (90*100)/200 = 45

Calculated - chi-square( X2) = ((observed value - expected value)2)/expected value =( 45 - 60)2/45 = 5

Tabulated - Test Statistic value to be calculated from chi-square Table with df (degree of freedom = (rows -1)(col -1)) and alpha = 0.05(Level of significance)

Interpretation - 1) If tabulated >= calculated, there exists a relationship so we will reject the null hypothesis

2) If tabulated < calculated, there exists no relationship so we will accept the null hypothesis

Chi-square( X2) test can also be calculated on SPSS, R, Excel and Python.


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