Q.A school teacher wants to analyse results. Identify the appropriate statistical technique to be used along with its justification for the following cases:

This is a plain theory question — it asks you to identify a statistical technique and justify it for two distinct scenarios.

(a) Comparing performance (division secured) between two classes of equal strength

The teacher is comparing two independent groups (Class XII A and Class XII B) on a categorical outcome — division secured (e.g., First, Second, Third, Fail). The data is in the form of frequencies (counts of students in each division), not means or medians.

The appropriate technique is the Chi-square test of independence (or, more precisely, a Chi-square test for a contingency table). This test checks whether the distribution of divisions is independent of the class — i.e., whether the two classes differ significantly in the proportion of students in each division.

Justification: Both variables (class and division) are categorical. The test compares observed frequencies against expected frequencies under the null hypothesis of no association. Since the class strengths are equal, the expected frequencies are straightforward to compute, but the test works for unequal sizes too — equal strength is not a requirement for the test, just a given detail.

(b) Comparing class performance across five unit tests (July to November)

Here the teacher has five repeated measurements on the same group of students — the class's performance in each month. The outcome is likely a continuous score (average marks or total marks per test), and the same students are tested each time.

The appropriate technique is Repeated Measures ANOVA (one-way within-subjects ANOVA). This test compares the means of the same group across three or more time points. …

The core idea here is comparing groups — but the structure of the data determines which statistical tool is appropriate. The key distinction is whether the groups being compared are independent (different sets of students) or related (the same students measured multiple times).

(a) Comparing Class XII A and Class XII B

These are two independent groups — the students in A are different from those in B. The teacher wants to see if the distribution of divisions (First, Second, Third, etc.) differs between the two classes.

The appropriate technique: Chi-square test of independence (for categorical data like division) or, if the teacher has actual marks and wants to compare means, an independent two-sample t-test.

Why this is the right tool:

• The data is categorical (division secured: First, Second, Third, etc.) — not continuous marks.
• We have two independent samples (Class A and Class B).
• The chi-square test checks whether the observed frequencies of divisions in the two classes differ significantly from what we'd expect if the classes were the same.

Justification: The chi-square test compares observed counts in each division category against expected counts under the null hypothesis that class and division are independent. If the p-value is small, we conclude the two classes have different performance distributions.

(b) Comparing Class Performance Across Five Months

Here, the same class (same set of students) is tested five times — July through November. This is repeated measures on the same group.

The appropriate technique: One-way repeated measures ANOVA (if marks are normally distributed) or Friedman test (non-parametric alternative).

Why this is the right tool:

• The same subjects are measured multiple times — so observations are not independent. …