Which of the following describes the logic of a one-way ANOVA?

Question

BlackTom AI · Accepted Answer

To evaluate the statement, let's consider what a one-way ANOVA is designed to do and what its logic entails.
Option 1: 'One-way ANOVA is used to compare the means of three or more independent groups to determine if there are significant differences between them.' This accurately captures the core purpose and logic of a one-way ANOVA: compare multiple independent group means to see if at least one differs, while controlling for within-group variability. It aligns with the fundamental hypotheses and the F-test framework.
Option 2: 'One-way ANOVA assesses the variability within a single group relative to the variability between multiple groups.' This phrasing is more about the comparison of within-group versus between-group variability but the wording is awkward since ANOVA explicitly partitions total variability into within-group and between-group components across groups. The core idea is correct (between vs within), but the description emphasizes the relative variability rather than the comparison of means across groups, making it a less precise articulation of the logic.
Option 3: 'One-way ANOVA is a statistical test used for comparing the means of dependent groups to determine if there are significant differences between them.' Here the key flaw is the use of 'dependent groups.' A one-way ANOVA requires independent samples (groups should be independent). If groups are dependent or related (repeated measures), a one-way repeated-measures ANOVA or a different approach is appropriate. This option misstates the assumption about independence.
Option 4: 'One-way ANOVA assumes that the samples are drawn from populations with unequal variances and tests whether the population means are all equal.' This statement mixes two issues: ANOVA typically assumes homogeneity of variances (equal variances) across groups and uses random error structure consistent with that assumption. When variances are unequal (heteroscedasticity), standard ANOVA can be problematic unless adjustments (like Welch ANOVA) are used. Also, the typical null hypothesis in one-way ANOVA is that all group means are equal, but the assumption about variances being unequal is not a defining assumption of the standard one-way ANOVA. Therefore this option contains incorrect assumptions about both variance homogeneity and the basic testing framework.

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Which of the following describes the logic of a one-way ANOVA?

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