Lecture 08a Activity

Unit C · Chapter 08

An in-class activity. Nothing to turn in and no answer key – this one needs other people, which is why it happens in class rather than at home.

The idea. Most moderation hypotheses are stated in words that sound precise and are compatible with three different plots. You find that out when someone else draws your sentence.

Format. About 12 minutes · pairs · no laptop needed.

1. Write one (3 minutes)

On the top half of a sheet, write a moderation hypothesis from your own area, in this form and nothing more:

The effect of ___ on ___ is stronger when ___ is higher.

On the bottom half, hidden or folded over, draw the plot you expect: outcome on \(y\), predictor on \(x\), three lines for low, average, and high moderator.

2. Draw each other’s (5 minutes)

Swap sheets, sentence side up. Draw the plot their sentence describes to you. Then unfold and compare.

• Do the two drawings match? Most pairs find they do not.
• If they differ, is the sentence wrong or the drawing? Fix whichever is wrong.
• Now the harder one: draw the plot that would refute their hypothesis while still showing a significant interaction. Compare with what they had in mind.

3. Say it backwards (4 minutes)

The model has exactly one interaction coefficient and does not know which variable you nominated as the moderator.

• Restate your partner’s hypothesis with the roles swapped – the effect of the moderator depends on the predictor – and read it aloud.
• Does the swapped version still make theoretical sense? For whose hypothesis does it, and for whose does it not?
• If the swap is nonsense but the model cannot tell, where does the asymmetry live: in the statistics, the design, or the theory?

If you have more time: which of these is moderation? (a) therapy works better for more severe patients; (b) therapy works because it improves sleep; (c) therapy worked in the clinical sample but not the community sample; (d) scores were more variable in the treatment group.

If you were not in class

The mismatch in part 2 is the finding. “Stronger when the moderator is higher” is compatible with lines that fan out from a common origin, lines that start apart and diverge, and lines that cross – and most people have exactly one of those in mind while writing a sentence that licenses all three. A hypothesis you cannot draw uniquely is a hypothesis you cannot test, and you will not notice on your own, because you can see your own picture.

On the swap: the interaction coefficient is symmetric and both readings are always available. The asymmetry lives entirely in the theory and the design – which variable was manipulated, which came first, which one your field treats as the intervention. Nothing in the output encodes it, so “X moderates Y” is a claim you are making. The swapped reading is often the more useful one when the moderator is the thing you can change.

On the extension: only (a) is moderation. (b) is mediation, a chain rather than a condition. (c) is treating “significant here, not there” as a difference in effect, which it is not – the two effects may not differ at all, and the only way to know is to test the interaction. (d) is a difference in variance, which no interaction term will find.