If there is a systematic effect of our manipulation on the observed data then:

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BlackTom AI · Accepted Answer

To evaluate the statements, we start from the premise: there is a systematic effect of the manipulation on the observed data.
Option 1: 'The means of our conditions will be different.' If there is a systematic effect, it would shift the data in a consistent way across conditions, leading to different means between groups. This is a plausible consequence of a true systematic effect.
Option 2: 'The between groups variation will be larger than the within-groups variation.' A systematic effect tends to create more pronounced differences between conditions than would be expected from random noise alone, increasing between-group variance relative to within-group variance.
Option 3: 'The F-ratio will be sufficiently large.' In ANOVA, the F-ratio is the between-group mean square divided by the within-group mean square. If there is a genuine systematic effect causing clear differences between groups, the numerator grows relative to the denominator, producing a larger F-ratio, which aligns with detecting a real effect.
Option 4: 'All of the above.' Since options 1–3 each describe consequences consistent with a true systematic effect, they collectively point to the same overarching claim. If the manipulation systematically shifts scores, you would expect differing means (Option 1), increased between-group vs. within-group variation (Option 2), and a larger F-ratio (Option 3), making the combined statement coherent.
In summary, each of the first three statements describes a facet that would arise from a genuine systematic effect, and the final option asserts that all of these facets occur together. The logic links the presence of a systematic manipulation to changes in group means, variance structure, and the F-statistic, and the collective alignment supports the interpretation that Option 4 is consistent with the premise.}

PSYC20007_2025_SM2 ANOVA, III

If there is a systematic effect of our manipulation on the observed data then:

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