The Chi-Square test is known as the test of goodness of fit and Chi-Square test of Independence. In the Chi-Square test of Independence, goodness of fit frequency of one nominal variable is compared with the theoretical expected frequency. In the Chi-Square test of Independence, the frequency of one nominal variable is compared with different values of the second nominal variable. The Chi-square test of Independence is used when we have two nominal variables. The Chi-square test of Independence data may be in the R*C form. In the Chi-Square test of Independence, R is the row and C is the column. In the Chi-Square test of Independence, the test variable may be more than two.
Procedure in Chi-Square test of Independence:
To perform the Chi-Square test of Independence, first we have to calculate the expected value of the two nominal variables. We can calculate the expected value of the two nominal variables by using this formula:
Where
= expected value for Chi-Square test of Independence
= Sum of the ith column in the Chi-Square test of Independence
= Sum of the kth column in the Chi-Square test of Independence
N = total number in the Chi-Square test of Independence
After calculating the expected value, we will apply the following formula to calculate the value of the Chi-Square test of Independence:
= Chi-Square test of Independence
= Observed value of two nominal variables for the Chi-Square test of Independence
= Expected value of two nominal variables for the Chi-Square test of Independence
Degree of freedom in Chi-Square test of Independence: In the Chi-Square test of Independence, the degree of freedom is calculated by using the following formula:
DF = (r-1)(c-1)
Where
DF = Degree of freedom for the Chi-Square test of Independence
r = number of rows in the Chi-Square test of Independence
c = number of columns in the Chi-Square test of Independence
Hypothesis:
Null hypothesis: In Chi-Square test of Independence, null hypothesis assumes that there is no association between the two variables.
Alternative hypothesis: In Chi-Square test of Independence, alternative hypothesis assumes that there is an association between the two variables.
Hypothesis testing: It is the same for the Chi-Square test of Independence as it is for other tests like ANOVA,t-test, etc. If the calculated value of the Chi-Square test is greater than the table value, we will reject the null hypothesis. If the calculated value is less, then we will accept the null hypothesis.
Chi-square Test of Independence in SPSS: Like the other statistical tests, the Chi-Square test of Independence is also performed. To calculate this test, we have to perform the following steps:
1.Open SPSS from the start menu.
2.Click on the “analysis” menu.
3.Select “descriptive statistics” from the analysis menu.
4.Select “cross tab,” from the descriptive statistics. As we click on the cross tab, the following window will appear in front of us:
From this window, select the row variable and insert it as a marked row. Select the second variable and put them in to mark a column. Click on the “statistics” button and select “chi-square” from them. Click on the “cell button,” select the “expected frequency” from there and click on the “ok” button. The result window for the chi-square test of independence will appear in front of us. The following table will show the chi-square test of independence SPSS output:
The case processing summary for the Chi-Square test of Independence will show the number of observations and the missing value.
The cross tabulation table for the Chi-Square test of Independence will show the expected value for two nominal variables.
The Chi-square tests table will show the value of Pearson Chi-Square value, associated with the significance value. From the two-tailed significance value, we can make a statistical decision and accept or reject the null hypothesis. If the value of significance is less than the predetermined level of significance, we will reject the null hypothesis and conclude that relationship is significant.
