Confusing Statistical Term #13: Missing at Random and Missing Completely at Random

Stage 2One of the important issues with missing data is the missing data mechanism. You may have heard of these: Missing Completely at Random (MCAR), Missing at Random (MAR), and Missing Not at Random (MNAR).

The mechanism is important because it affects how much the missing data bias your results. This has a big impact on what is a reasonable approach to dealing with the missing data.  So you have to take it into account in choosing an approach.

The concepts of these mechanisms can be a bit abstract.missing data

And to top it off, two of these mechanisms have really confusing names: Missing Completely at Random and Missing at Random.

Missing Completely at Random (MCAR)

Missing Completely at Random is pretty straightforward.  What it means is what is says:  the propensity for a data point to be missing is completely random.

There’s no relationship between whether a data point is missing and any values in the data set, missing or observed.

The missing data are just a random subset of the data.

So for example if someone accidentally skips one page of your survey because the pages stuck together, the missingness mechanism isn’t about any of the values.

Missing at Random (MAR)

This is where the unfortunate names come in.

Missing at Random means  the propensity for a data point to be missing is not related to the missing data, but it is related to some of the observed data.

Whether or not someone answered #13 on your survey has nothing to do with the missing values, but it does have to do with the values of some other variable.

So for example if older people are more likely to skip survey question #13 than younger people, the missingness mechanism is based on age, a different variable.

A better name would actually be Missing Conditionally at Random, because the missingness is conditional on another variable.  But that’s not what Rubin originally picked, and it would really mess up the acronyms at this point.

The idea is, if we can control for this conditional variable, we can get a random subset.

Why it’s Important

As it turns out, keeping these two terms straight is important. Which mechanism you have in your data will affect which methods you can use to deal with that missing data without biasing your results.

You can imagine that good techniques for data that are MAR need to incorporate variables that are related to the missingness. Other, simpler techniques will work for MCAR data, as long as you have a large enough sample.

Go to the next article or see the full series on Easy-to-Confuse Statistical Concepts

Approaches to Missing Data: the Good, the Bad, and the Unthinkable
Learn the different methods for dealing with missing data and how they work in different missing data situations.

Reader Interactions


  1. Harry says

    Thank you – I have been struggling with the semantics of the term MAR for a while and thought it was me going crazy. This is the first time I have finally seen someone point out how confusingly inaccurate the name MAR is because it certainly isnt random

    My preference would be that they were called MNAR with a suffix denoting whether it is based directly on the missing data variable or indirectly due to another another – so MAR would be MNAR-AV (another variable) or MNAR-I (indirect) and MNAR would be MNAR-TV (this variable) or MNAR-D (direct)

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