Track 13 · Resampling and Statistical Reasoning · Lesson 5 of 10
Missing data
Classify missing-data mechanisms (MCAR, MAR, MNAR), explain when complete-case analysis and simple imputation give biased answers, and report missingness honestly.
An income survey finds an average monthly income of 12 000 SAR — among the people who answered the income question. If high earners are the most likely to skip it, the true average is higher, and no amount of careful arithmetic on the answers that were given will reveal by how much.
Almost every real dataset has holes. What matters is not only how many values are missing but why. Rubin's classification describes how the probability that a value is missing relates to the data:
- MCAR — missing completely at random. Missingness is unrelated to anything, observed or not (a lab sample dropped on the floor; a random subset of forms lost in the post).
- MAR — missing at random. Missingness depends only on observed variables (older respondents skip the income question more often, and age is recorded). Within groups of equal age, the missing incomes are like the observed ones.
- MNAR — missing not at random. Missingness depends on the missing value itself or on something unobserved (high earners skip the income question because their income is high).
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It has 8 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Classify missingness as MCAR, MAR or MNAR from how the data were collected
- Calculate how complete-case analysis distorts a mean when response depends on the value
- Explain why mean imputation understates variability and standard errors
- Report missing data honestly: how much, why, what was done and how sensitive the results are