Lecture 15a Activity

Unit E · Chapter 15

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. Writing a results section and judging one are different skills. This does the first, and then hands it to somebody whose only information is what you actually wrote down.

Format. About 15 minutes · threes · no laptop needed.

1. Write it (7 minutes)

Here is everything you have. A study of 94 university instructors asked whether student evaluation scores relate to a rated attractiveness composite, controlling for age and sex.

Parameter   | Coefficient |       SE |        95% CI | t(90) |      p
---------------------------------------------------------------------
(Intercept) |        3.76 |     0.23 | [ 3.29, 4.22] | 16.03 | < .001
beauty      |        0.13 |     0.06 | [ 0.01, 0.25] |  2.24 | 0.028
age         |    5.16e-05 | 4.86e-03 | [-0.01, 0.01] |  0.01 | 0.992
sex [male]  |        0.23 |     0.10 | [ 0.04, 0.42] |  2.46 | 0.016

R2 = 0.101,  adj. R2 = 0.071,  F(3, 90) = 3.36, p = .022
Standardized: beauty 0.24 [0.03, 0.45], sex [male] 0.51 [0.10, 0.92]

eval runs from 1 to 5. beauty is standardized. sex has female as the reference.

Write the results paragraph – actual sentences, five to eight of them. One person keeps a second list: every question you had to guess the answer to.

2. Break somebody else’s (5 minutes)

Swap with another group. Do not check theirs against a rubric. Try to break it:

  • One sentence that claims more than the output supports.
  • One number a reader would want that is not there.
  • One place a reader could not tell whether a coefficient is standardized.
  • The vaguest sentence – rewrite it to be specific.

Hand it back with those four marked.

3. Whole class (3 minutes)

  • Read out one entry from your “had to guess” list. These are what the real authors had to know and what most often goes missing.
  • Two groups made opposite decisions about the age coefficient. Both defend.

If you have more time: is \(R^2 = .10\) a sentence in your results or in your discussion? What is the difference?

If you were not in class

The “had to guess” list is the payoff. It usually includes whether assumptions were checked, whether the sample size was planned, whether these three predictors were the only ones tried, who rated attractiveness, and what the design was – none of it recoverable from a coefficient table. That is why a results section cannot stand alone, and why the reviewing questions from the lecture are mostly questions about what the table does not show.

Three things nearly every first draft gets wrong, and which the swap reliably catches:

  • Standardization. Unstandardized beauty is 0.13, standardized is 0.24. A sentence saying “0.13” without “points on the 1–5 scale per standard deviation of the composite” is unreadable; one saying “\(\beta = .24\)” without flagging it as standardized is worse.
  • Causal verbs. These are observational data. “Attractiveness improves evaluations” is not licensed; “was associated with higher evaluations” is.
  • The non-significant covariate. \(p = .99\) does not mean age is unrelated. It means this model with these 94 instructors cannot distinguish its coefficient from zero – and the interval, \([-0.01, 0.01]\), is the useful half of that sentence. Report the estimate and the interval.

On \(R^2\): the number belongs in the results, and what it means – that 90% of the variation is something other than these three variables – belongs in the discussion.