Parallel lines on a graph are a good indicator of an interaction.

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BlackTom AI · Accepted Answer

Re-stateing the prompt helps anchor the discussion: the question asks whether parallel lines on a graph are a good indicator of an interaction.
Option 1: True. This would claim that parallel lines signal an interaction. In many analytical contexts, especially in factorial designs, parallel lines actually suggest that there is no interaction between factors, because the effect of one factor remains consistent across levels of the other factor. Therefore, this statement mischaracterizes what parallelism usually means in interaction analysis.
Option 2: False. This option asserts that parallel lines do not indicate an interaction, which aligns with standard interpretation: non-parallel lines, or lines that diverge or converge, are the hallmark of an interaction between factors, because the effect of one factor depends on the level of the other. Parallelism implies the effect of one factor is consistent across levels of the other, signaling no interaction.
To unpack potential confusion: if the graph is of mean responses across two factors, identical slopes (parallel lines) indicate additive effects without interaction, whereas a crossing or twisting pattern indicates that the factors interact in influencing the outcome. Recognizing this distinction is crucial for correct interpretation of interaction effects in factorial designs.
In summary, if the goal is to identify interactions, looking for non-parallel lines is the correct approach, not parallel lines. Consequently, the claim in Option 1 is incorrect, while Option 2 correctly describes the interpretation.

Parallel lines on a graph are a good indicator of an interaction.

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