The chief aim of ANOVA is to make a decision about whether there is sufficient evidence to draw inferences about

Question

BlackTom AI · Accepted Answer

Here is a careful evaluation of each option in the context of the chief aim of ANOVA.
Option 1: 'whether the means of two samples are unequal.' This describes a comparison between two samples, which is typically tested with a t-test rather than ANOVA. ANOVA generalizes the idea to more than two groups, so focusing only on two samples does not capture the full scope of ANOVA's aim.
Option 2: 'whether the means of two or more samples are unequal.' This aligns with the fundamental purpose of ANOVA: to assess whether there are any statistically significant differences among the means across multiple groups. It encompasses both two-group and multi-group scenarios, matching the method’s broader goal.
Option 3: 'whether the means of two groups are unequal at population level.' While this statement refers to population means and acknowledges two groups, it limits the scope to two groups and thus does not reflect ANOVA's primary purpose, which is to test across more than two groups when appropriate.
Option 4: 'whether the means or two or more groups are unequal at population level.' This option echoes the population-level focus and includes two or more groups, but the wording is awkward ("means or two or more groups") and introduces potential ambiguity. The intended and clearer description is the broader two-or-more-group comparison across populations, which is captured more directly in Option 2.
Overall, Option 2 provides the most accurate and comprehensive statement of ANOVA’s chief aim by explicitly allowing for two or more samples and emphasizing the comparison of their means across groups.

PSYC20007_2025_SM2 ANOVA, I

The chief aim of ANOVA is to make a decision about whether there is sufficient evidence to draw inferences about

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