Four responses to missing data
Recovering a source measurement and guessing a replacement are different actions. Choose the action that fits the analysis.
Recover: copy a verified score from the exact student's exact exam, recording provenance. Keep missing: use other valid fields and report coverage. Exclude for a stated analysis: define the analysis population, number excluded and potential selection bias. Impute: use an explicit estimate or model, mark replacements and report assumptions and uncertainty.
The Week 3 final registry stays unfilled. Week 4 later introduces imputation for predictive inputs fitted on training data. These serve different tasks. Neither treats an imputed value as observed truth.
In [2,4,missing,missing,missing], the observed mean is 3 and sample SD is sqrt(2), about 1.414. Fill each blank with 3: the mean stays 3, numeric count increases from 2 to 5, but sample SD falls to sqrt(0.5), about 0.707. The number of observed answers remains two. Mean filling reduces visible spread and can distort relationships; it does not automatically represent uncertainty about the missing values.
Source: W3 PDF pp. 4-55. The 14-row registry example below comes from the Week 3 lab code you previously pasted in this conversation; it is separate from the lecture's smaller examples.
The lecture separates recovered observations from assumed replacements. The mean-fill demonstration and sensitivity table show different consequences of assumptions.
Practice problems
Supplementary study questions on the lecture concepts — not verbatim exam questions. Each answer counts toward spaced review.
1. Conceptual understanding
Definitions and distinctions.
A verified sheet contains the exact missing exam score. Which action is supported?
Mean-fill [2,4,missing,missing,missing]. How many answers were genuinely observed?
2. Application
Apply the concept to a case or calculation.
Which action creates a newly recovered observed score?
Mean-filling [2,4,missing,missing,missing] produces which values?
3. Interpretation and limitations
Evaluate assumptions and justify conclusions.
In that mean-fill demonstration, what happens to sample SD?
Reporting scores only for students with recorded scores is acceptable when what is clear?
Explain it in writing
Self-checked, not marked. Write a few sentences, then compare with the example answer. Your writing is saved as you type.
Show an example answer
Programme counts need programme membership, not a score. Removing students for an unrelated missing field changes who is counted and can distort programme sizes.
Check: did you answer the question, use evidence or working, and avoid claiming more than the evidence supports?
Show an example answer
State the replacement rule, how many cells were filled, how many values were actually observed, and the fact that results depend on an assumption. Keep the final registry unfilled when required.
Check: did you answer the question, use evidence or working, and avoid claiming more than the evidence supports?