Why the missing data is the most informative column

The salary column is eighty-one per cent complete and the analysis quietly uses those rows. The nineteen per cent are not scattered at random: they are the contractors, the recent joiners and the two grades where disclosure is optional, and the reported average now describes a different company.

What everyone sees

Missing values are treated as a nuisance affecting precision — a smaller effective sample, handled by excluding incomplete rows. Exclusion is not neutral. If whether a value is present depends on what the value is, then complete-case analysis selects the sample on the variable of interest, which is the one operation guaranteed to bias it.

What is actually happening

Little and Rubin set out the distinction that governs this: under data missing completely at random, dropping incomplete cases costs precision only, whereas under data missing not at random the estimate itself is biased, and the pattern of missingness is informative about the omitted values. Schafer and Graham reviewed practice and found that the two most common approaches — deleting incomplete cases and substituting the column mean — perform poorly under realistic assumptions, with mean substitution actively understating variance and manufacturing false precision. The instructive move is to treat missingness as data: model which records are incomplete, because that indicator often predicts the outcome better than the surviving values do.

Why it stays hidden

The bias hides because software handles it silently. The default is to drop incomplete rows, no warning is printed, and the output reports an n that looks like the sample. Anyone reading the results sees a clean table, and the only trace of the excluded population is a number that was never shown.