Question

Choose either the Chi Square Goodness of Fit test OR the Chi Square Test for Independence. Give an example of a research scenario that would use this test, including your hypothesis AND what makes the test suitable for your variables chosen

Answer 1

Chi square test for independence is applied when you have two categorical variables from a single population and needs to determine whether they have significant association or not.

For example, gender and their preference in subject.

Following are the assumptions of the test:

1. The sampling method is Simple Random Sampling (SRS).

2. Variable understudy are categorical

3. No cell frequency should be less than 5.

Hypothesis

Suppose we have two attributes Gender and color where gender has 2 (r) levels and subject has say 7 (c) levels.

Null hypothesis : Gender and choice of subject are independent.

Alternate hypothesis : Gender and choice of subject are not independent.

Significance Level: Researcher defines a pre decided significance level say ( 0.01, 0.05, 0.1 )

Test Statistic: E is defined as expected frequency of rth gender and cth subject.

E_r,c = (n_r * n_c) / n

where, nr = total observations in rth gender, nc = total observations in cth subject, n = total number of observations.

O defined as the observed frequency of rth gender and cth subject.

Chi² = Σ [ (O_r,c - E_r,c)² / E_r,c ]

Degrees of freedom: DF = (r - 1) * (c - 1)

Using the value of Chi square and DF, computes p value from the table.

Test criteria: Reject null hypothesis if p < alpha, or accept null hypothesis if p > alpha.