Little's MCAR Test

Little's MCAR test is a chi-square test of whether the means of observed variables differ across missing-data patterns, which they should not if values are missing completely at random.

Little의 MCAR 검정은 결측 유형별로 관측된 변수의 평균이 전체 평균과 다른지를 카이제곱으로 검정해, 결측이 완전히 무작위(MCAR)인지 판단하는 방법이다.

How can I test whether the missing values in my survey variables are missing completely at random?

설문 문항의 결측값이 완전히 무작위로 빠진 것인지 어떻게 검정하나요?

Little's MCAR test estimates the overall means and covariances with the EM algorithm and compares each missing-data pattern's observed means against them. A significant result rejects MCAR, while a non-significant result is consistent with MCAR but does not prove it or rule out MNAR.

When to use Little's MCAR Test

• You must justify listwise deletion or a complete-case analysis
• Several continuous variables have missing values in different patterns
• You want a formal check before choosing an imputation strategy

When to use something else

• Variables are mostly categorical; inspect missingness with logistic models of a missingness indicator instead
• You need to distinguish MAR from MNAR; use sensitivity analysis such as pattern-mixture models instead

Assumptions and requirements

• Variables are approximately multivariate normal
• Each missing-data pattern has enough cases for the chi-square approximation
• Rows are independent

What the analysis reports

• Chi-square statistic d²
• Degrees of freedom (sum of observed variables per pattern minus the number of variables)
• p value
• EM estimates of means
• Per-pattern contribution table

How to report it

Little's MCAR test was [not] significant, χ²([df]) = [value], p = [value], suggesting the data were [not] missing completely at random.

Related methods

• Missing Data Pattern Analysis
• Multiple Imputation (MICE) with Pooled Regression

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