Daily 10 - Feb 18

Class Performance

Students: 112 | Mean: 4.33 | Median: 4.5 | SD: 0.71

Scores ranged from 2.5 to 5 out of 5 points.

Score Distribution

Performance by Question

Questions

Q1: Classification measurement error independence

The error is not independent of the truth in the classification case — unlike classical measurement error where errors are independent of the true value.

  • Writing “is” instead of “is not” — Confusing classification error with classical error. Classification error depends on the true category.
  • Left blank — Some students did not provide an answer for this fill-in-the-blank question.
  • Adding extra words — Writing phrases beyond “is not” suggests uncertainty about the distinction between error types.

Q2: MCAR assumption — missingness is _____ of analysis variables

Missingness is independent of the analysis variables (\(Y\) and \(X\)s) under the MCAR assumption.

  • Writing “MAR” or “MCAR” — These are assumption names, not what fills the blank. The question asks about the property of missingness.
  • Writing “dependent” or “not included” — The opposite of the correct answer. MCAR means missingness does not depend on the variables.
  • Writing probability notation or variable names — Answers like “P(si),” “Si = 0,” “Y,” or “Xs” don’t answer the conceptual question.

Q3: Table 4 — wage gap and schooling gap for missing IQ

Young men with missing IQ scores earn roughly 19–24% lower wages and complete about 2 fewer years of schooling on average.

  • Percentage below range (15–18%) — Many students wrote 15%, 17%, or 18%, underestimating the wage gap shown in Table 4.
  • Percentage far outside range (5%, 47%) — Calculation errors leading to very different percentages.
  • Wrong years of schooling — Writing 1.2, 0.60, or 3 years instead of approximately 2.

Q4: Z is a _____ in the DAG

\(Z\) is a confounder — it affects both the treatment and the outcome in the DAG illustration.

  • Writing “proxy” — A proxy is not the same as a confounder, which directly causes both treatment and outcome.
  • Misspellings accepted — “Confound,” “confounding,” “confounding variable,” and similar variants all received full credit.
  • Writing “co-founder” — A misreading of “confounder.” The concept refers to a variable that confounds the causal relationship.

Q5: Rate of return to schooling and bias direction

Figure 2 shows 3.9% return, Figure 3 shows 2.6% after IQ adjustment, indicating the estimate is biased upward.

  • Writing “downward” instead of “upward” — The most common error. Since 3.9% drops to 2.6% after adjustment, the original was too high (biased upward).
  • Missing the bias direction entirely — Some provided percentages but omitted upward/downward. All three parts are needed.
  • Wrong adjusted return — Writing 1.6%, 2.4%, 2.8%, or 6% instead of 2.6%.

Key Takeaways

Strengths: Classification error not independent of truth | Z is a confounder | 3.9% and 2.6% returns widely known.

Review:

  • MCAR means “independent” — missingness is independent of analysis variables, not “MAR” or “dependent”
  • Table 4 wage gap is 19–24% — not 15% or 17%; review the calculation from Table 4 means
  • Bias is upward — the unadjusted estimate (3.9%) is higher than adjusted (2.6%), so the bias goes upward, not downward