UGC NET Questions (Paper – 1)

The chi-square test is designed to assess whether there is a significant association between two categorical variables in a contingency table by comparing observed frequencies with expected frequencies under independence. It does not require assumptions about normal distribution of a quantitative variable and is therefore considered non-parametric. When the calculated chi-square value exceeds the critical value, the null hypothesis of independence is rejected. Hence, the test described in the stem is the chi-square test.

Option A:
The chi-square statistic summarises the squared differences between observed and expected frequencies scaled by the expected frequencies. Because it is suited to nominal data in contingency tables, it is the standard method for testing independence among categorical variables, matching the stem precisely and making this option correct.

Option B:
The t test compares means of one or two groups on a quantitative variable and assumes approximate normality; it is not used for testing independence in contingency tables of categorical data.

Option C:
The F test underlies analysis of variance and regression, focusing on ratios of variances for comparing multiple means rather than associations between categorical variables.

Option D:
The z test is used for large-sample inference about means or proportions under normal approximations and is not the typical choice for contingency table analysis of categorical data.

The chi-square test is a non-parametric statistical procedure used mainly to analyse relationships between categorical variables organised in contingency tables. It compares observed frequencies in each cell with the frequencies expected if there were no association between the variables. A significant chi-square suggests that the distribution of one categorical variable depends on the categories of the other. Because the stem refers to examining the association between two variables in social science, the correct description is categorical variables.

Option A:
Interval variables have equal intervals between values and support arithmetic operations, typically analysed with parametric tests like t-tests or ANOVA when assumptions are met. While chi-square can sometimes be applied to grouped interval data, its primary use is with categorical variables, so interval is not the most accurate answer.

Option B:
Ratio variables possess all the properties of interval variables plus a true zero point, facilitating meaningful ratio statements. They are usually analysed using parametric tests or other methods that exploit their quantitative properties. The chi-square test, however, is best known for work with categories, making ratio an unsuitable choice.

Option C:
Categorical variables classify observations into distinct groups such as gender, type of institution or preference category. The chi-square test is designed to assess whether the distribution across categories differs significantly between groups, or whether two categorical variables are independent. This close alignment with the stem’s description confirms categorical as the correct completion.

Option D:
Continuous variables can take on any value within a range and are more naturally analysed with methods based on means and variances. While they can be converted into categories, chi-square is not primarily defined for continuous variables in their raw form. Hence, continuous is not the right answer here.