MCAR, MAR and MNAR are mechanisms
MCAR, MAR and MNAR describe how missingness happens. The observed counts alone do not prove which explanation is true.
| Mechanism | What must be true | Course story |
|---|---|---|
| MCAR | Missingness is independent of observed and unobserved values relevant to the mechanism. | Answers are independently lost with equal probability regardless of class or rating. |
| MAR given class | Once known class is accounted for, reply probability does not depend on the missing rating. | Day satisfied/dissatisfied both reply with probability 90%; Evening both with probability 40%. |
| MNAR | Missingness still depends on the missing value after conditioning on the observed information used. | Within Evening, satisfied reply with probability 40%, dissatisfied with probability 10%. |
MAR does not mean all students are equally likely to reply, and it does not mean complete-case estimates are automatically unbiased for the full population. MCAR removes systematic selection under the stated process but still leaves finite-sample variability and fewer observations.
Observed response rates do not identify the mechanism. Different rates can occur by chance or through dependence on known or unknown factors. Equal rates can hide strong bias: in two groups with half rating 1 and half rating 5, only the 5s might answer in one group and only the 1s in the other. Both have 50% response but observed means 5 and 1, despite true means both 3.
Follow up a random subset of nonrespondents using another channel. Their responses may inform the missingness story, but the people still not responding can differ, and contact mode can affect answers. State the remaining uncertainty.
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 connects nonresponse with representation. The survey separates group invitation shares from reply shares and asks what MCAR/MAR/MNAR mean.
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.
Answers independently lost with equal probability unrelated to group or rating fit what mechanism?
What must hold for MAR given group in the survey story?
2. Application
Apply the concept to a case or calculation.
A technical process independently loses answers unrelated to group or rating. Which label fits?
Within Evening, dissatisfied students reply less often even after accounting for group. Which label fits?
3. Interpretation and limitations
Evaluate assumptions and justify conclusions.
Does MAR given group make the unadjusted pooled respondent mean automatically unbiased for everyone?
Can observed response counts alone tell us which mechanism occurred?
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
Two groups might each have a 50% response rate, but only satisfied students reply in one group and only dissatisfied students reply in the other. Equal totals can hide different selection.
Check: did you answer the question, use evidence or working, and avoid claiming more than the evidence supports?
Show an example answer
Contact a sample of nonrespondents using another method and ask the same question. Compare their answers and known characteristics; some people may still not respond, so uncertainty remains.
Check: did you answer the question, use evidence or working, and avoid claiming more than the evidence supports?