Lecture 08b 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. An interaction is a difference between differences. You can read that off a plot or off a coefficient table, and being forced to go from one to the other – through another person – is what makes the two representations lock together.

Format. About 10 minutes · pairs · no laptop needed.

1. Draw one (2 minutes)

The model is expenditure ~ duration * sex, with female as the reference.

Draw a plot: expenditure on \(y\), duration on \(x\), one line for each sex. Choose any pattern you like, but commit to something specific. Do not show your partner.

2. Trade blind (5 minutes)

Describe your plot to your partner in words only – no pointing, no drawing in the air. Their job is to write down the sign of all three coefficients: duration, sexmale, and duration:sexmale, each positive, negative, or about zero.

Then show them the plot and check. Swap roles.

Do it twice more, and make the second pattern one where duration is about zero but the plot clearly shows duration mattering.

3. Whole class (3 minutes)

  • Which pattern was hardest to transmit in words? That is usually the one whose published description would also be ambiguous.
  • With three programs instead of two sexes there are two interaction coefficients. What comparison does each represent, and which one is missing from the table?

If you have more time: your interaction has \(p = .21\). Do you drop it? Argue both sides, then say what would have settled it before you saw the number.

If you were not in class

The pattern asked for in part 2 – duration near zero while duration clearly matters – is one flat line for females and a rising line for males. The duration coefficient is the slope for the reference group only, so a zero there means “duration does not matter for females,” not “duration does not matter.” That single misreading is behind a large share of misinterpreted interaction tables, and it is much easier to catch when you have just failed to describe the plot to somebody.

Two parallel lines with a constant gap is the other one worth fixing in memory: that is duration positive, sexmale positive, interaction zero. A constant difference is exactly what no interaction looks like.

With three programs, each interaction coefficient compares one program’s duration slope to the reference program’s; the comparison between the two non-reference programs is not in the table. So “the effect differed for joggers but not swimmers” is the wrong sentence – neither coefficient is about a single group. For an overall test, use the omnibus \(F\) for the interaction term.