Almost every real dataset has holes: a skipped survey question, a failed lab measurement, a participant who stopped showing up. The common reflex is to delete incomplete rows and move on. Whether that is harmless or seriously misleading depends on why the data are missing. Statisticians describe three broad mechanisms.
1. Missing completely at random (MCAR)
The chance that a value is missing has nothing to do with any characteristic of the person or the value itself. A test tube dropped on the floor; a page of a questionnaire lost in the mail.
Under MCAR, the complete cases are a random subset of everyone. Dropping incomplete rows wastes information and reduces power, but it does not bias the estimates.
MCAR is the easiest case and also the least common.
2. Missing at random (MAR)
The chance of missingness depends on things you have measured, but not on the missing value itself once those are accounted for. For example, older participants are more likely to skip an online follow-up questionnaire, and you know everyone's age.
The name is confusing: the data are not missing "randomly" in everyday terms. The point is that the pattern can be explained by observed variables. Methods such as multiple imputation or likelihood-based models can use those variables to give unbiased estimates. Simply deleting incomplete rows generally cannot.
3. Missing not at random (MNAR)
The chance of missingness depends on the missing value itself, even after accounting for everything observed. People with the most severe symptoms drop out of a trial because they feel too ill to attend. People with very high incomes decline to report income.
This is the hardest case. The observed data alone cannot tell you how different the missing values are. Any analysis has to rest on assumptions about the missing part.
Why it matters
Imagine a weight-loss trial where participants who are not losing weight tend to stop attending. If you analyse only those who completed the study, the program looks more effective than it is, because the disappointing results disappeared from the data.
What good practice looks like
- Report how much is missing, variable by variable and group by group.
- Compare people with and without missing values on what you do know. Big differences argue against MCAR.
- Avoid ad hoc fixes such as filling gaps with the mean or carrying the last observation forward; they can distort variances and trends.
- Use principled methods (multiple imputation, mixed models, inverse probability weighting) when MAR is plausible.
- Run sensitivity analyses that ask: if the missing values were systematically worse (or better), would the conclusion change?
Missing data are not just a technical nuisance. The reason values are missing is part of the story the data are telling.
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