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.