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Also known as: Missing Completely At Random
Missing completely at random: missingness unrelated to any observed or unobserved data.
DESCRIPTION
MCAR describes a missing data mechanism where the probability of missingness does not depend on observed or unobserved values. Analyses under MCAR are unbiased by the missingness, making simple methods like mean imputation or listwise deletion more defensible. MCAR is rare in practice; testing often relies on diagnostic heuristics. Understanding MCAR helps choose appropriate imputation strategies and assess inference risks.
ALTERNATIVE DEFINITIONS
Wikipedia
Data are missing completely at random (MCAR) if the probability of missingness is the same for all observations.
Emphasizes independence of missingness from data values.
UCLA Statistical Consulting
MCAR means that the probability of missingness is unrelated to the observed data or the missing values themselves.
Clarifies independence from both observed and unobserved data.
Penn State Eberly College of Science
Missing completely at random (MCAR) means the missingness does not depend on any measured or unmeasured variables.
Highlights measured versus unmeasured variable independence.
RELATED TERMS
Missing Data Multiple Imputation Listwise Deletion
COMPETING TERMS
KNOWLEDGE AREAS
Data Science AI Data Quality Mathematics
TARGET AUDIENCE
Data Scientist AI Engineer Data Steward Analytics Engineer
EXTERNAL SOURCES
- Wikipedia - Missing data
- UCLA Statistical Consulting - Explanation of missing data mechanisms
- Penn State Eberly College of Science - Lesson covering MCAR concept
- Wikipedia - General article on missing data
TOP QUESTIONS
Why is MCAR important for imputation decisions?
Under MCAR, simple methods like mean imputation or listwise deletion can yield unbiased estimates, simplifying preprocessing choices.
Category: Relevancy
How can you test whether missingness is MCAR?
Formal tests are limited; use diagnostics comparing distributions of observed versus missing groups and domain knowledge to assess plausibility.
Category: Validation
What is a common misunderstanding about MCAR?
Assuming MCAR without evidence; in practice missingness often depends on observed variables (MAR) or unobserved factors (MNAR).
Category: Misunderstanding
Which methods work well under MCAR?
Listwise deletion, simple imputation, and multiple imputation all produce unbiased estimates of means; variance still requires care.
Category: HowTo
What risks arise if MCAR is incorrectly assumed?
Biased estimates and misleading inference occur if missingness is MAR or MNAR but treated as MCAR.
Category: Risks
How does MCAR compare with MAR?
MCAR is stronger: missingness independent of all data; MAR allows dependence on observed variables only.
Category: Alternatives
Is MCAR common in real datasets?
Rare; many real-world processes drive missingness in relation to observed or unobserved factors.
Category: Opinion
How does MCAR affect model training?
It simplifies preprocessing; however, proper handling still matters to maintain variance and avoid information loss.
Category: Management
What hot topic around MCAR exists today?
Sensitivity analyses assess robustness of conclusions under alternative missingness mechanisms when MCAR is doubtful.
Category: Topic