Question

In a research article, the authors said that they used a chi-square test for independence for testing whether there is statistically significant correlation between two categorical variables. Each of categorical variables has two categories of outcomes. So, the contingency table for crossclassifying these two variables is a 2x2 table. They reported the chi-square statstic value for this test of independence and it is 5.21. Please mark all statements that are correct.

A		The correlation between the two categorical variables is statistically significant at 5% level of significance.
B		The correlation between the two categorical variables is not statistically significant at 5% level of significance.
C		The correlation between the two categorical variables is statistically significant at 1% level of significance.
D		The correlation between the two categorical variables is not statistically significant at 1% level of significance.

Answer 1

It is a two tailed test.

The chi-square test statistic is 5.21

Degrees of freedom = (number of rows-1)*(number of columns-1)

given 2x2 table therefore number of rows=number of columns =2

Degrees of freedom = (2-1)*(2-1) = 1

Critical value method

If Level of significance is 0.05 then the critical value of chi-square for df=1, alpha=0.05/2 =0.025 is 0.001 and for 1-(0.05/2) is 5.024

Reject null hypothesis if test statistic is greater than 5.024 or less than 0.001.

Here 5.24> 5.024 . Therefore reject null hypothesis that there is no correlation between two categorical values. There is sufficient evidence to conclude that the correlation between the two categorical variable is statistically significant at 5% level of significance.

Now if level of significance is 0.01 then the critical value of chi-square for df=1 and alpha= 0.01/2 is 0 and 1-(0.01/2) is 6.635

Reject null hypothesis if test statistic is greater than 6.635 or less than 0.001.

5.24 <6.6635 Therefore fail to reject null hypothesis hat there is no correlation between two categorical values. There is not sufficient evidence to conclude that the correlation between the two categorical variable is statistically significant at 5% level of significance.

(or)

We can also p-value method

p-value calculator for chi square is used to calculate the p-value .

P-value=0.0225.

Reject null hypothesis if P-value <alpha .

We can reject null hypothesis only at 5% level of significance (0.01<0.0225<0.05) and we fail to reject null hypothesis at 1% level of significance.

Therefore the correct options are option A and option D

The correlation between the two categorical variables is statistically significant at 5% level of significance.

The correlation between the two categorical variables is not statistically significant at 1% level of significance.