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

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Question restatement: Which statement describes the logic of a one-way ANOVA?

Option 1: 'One-way ANOVA is a statistical test used for comparing the means of dependent groups to determine if there are significant differences between them.' This is inaccurate because a one-way ANOVA is designed to compare means across independent groups, not dependent (paired) groups. When measurements are repeated on the same subjects, a repeated measures ANOVA is typically used instead.

Option 2: 'One-way ANOVA assumes that the samples are drawn from populations with unequal variances and tests whether the population means are all equal.' This misstates two things: (a) ANOVA assumes homogeneity of variances (equal variances) across groups, not unequal variances; (b) it tests whether the means are all equal across groups, not that they are necessarily unequal. In short, this option mischaracterizes both variance assumption and the null hypothesis.

Option 3: '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 captures the core logic: comparing multiple (three or more) independent group means to assess if at least one group mean differs from the others, using the F-statistic to test the null hypothesis of equal means.

Option 4: 'One-way ANOVA assesses the variability within a single group relative to the variability between multiple groups.' This wording is misleading: ANOVA partitions total variability into within-group and between-group components, but the phrase 'within a single group' is incorrect because the analysis concerns variability within each group across observations, not within a single group itself. The comparison is between within-group dispersion and between-group dispersion across all groups, not a comparison of a single group’s internal variability to others in isolation.

Summary note: The statement most accurately describing the logic of a one-way ANOVA is the option that emphasizes comparing means across three or more independent groups to detect potential differences, while the other options either misstate assumptions, the type of groups, or the fundamental partitioning of variance.

PSYC20007_2025_SM2 Supplementary or Special Exam: Cognitive Psychology (PSYC20007_2025_SM2)- Requires Respondus LockDown Browser

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

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