Listwise vs. Pairwise Deletion for Missing Data

Listwise deletion decides, case by case, whether that respondent has every variable the analysis needs; if even one value is missing, the whole case is dropped before any statistic is computed, so every number in the output — every correlation, every regression coefficient — is calculated from the identical subsample. Pairwise deletion never removes a case outright. For each individual correlation or covariance, it uses whichever cases happen to have both of those two variables observed, ignoring whatever else might be missing on that case. A three-variable correlation matrix built this way can end up drawing on three different subsamples, one per pair, that don't fully overlap.

Because each cell of the matrix is estimated independently, from whichever cases happen to have that particular pair observed, the correlations don't have to be mutually consistent the way they would be if they all came from one shared sample. In a reproducible worked example (30 hypothetical survey respondents reporting weekly study hours (X), self-rated exam preparedness (Y), and a test-anxiety score (Z), with missingness that clusters by which item a respondent skipped), only 8 of the 30 cases have all three items — those give a valid listwise correlation matrix: r(X,Y)=0.950, r(X,Z)=0.886, r(Y,Z)=0.843, determinant 0.021, all three eigenvalues positive (0.045, 0.168, 2.787). Computed pairwise instead, each correlation draws on more cases (16, 16, and 14 respectively) but returns r(X,Y)=0.952, r(Y,Z)=0.849, and r(X,Z)=−0.182. Given the first two values, basic correlation algebra requires r(X,Z) to be at least 0.646 — no real dataset with the same X, Y, and Z throughout could produce anything lower. The pairwise result of −0.182 violates that floor, and the resulting matrix has a determinant of −0.954 with one negative eigenvalue (−0.369): it is not positive semi-definite, meaning it cannot be a genuine correlation matrix at all. Feed a matrix like this into a factor analysis or structural equation model and it will either fail to converge or return nonsensical estimates.

No — most of the time a pairwise-deleted matrix is still valid, especially with little missing data or missingness that's genuinely unrelated to the variables involved. The risk grows with more variables, more missing data, and missingness that even loosely tracks the variables themselves, which is common and hard to rule out with survey non-response. Because the failure is silent — most software will not warn that the matrix it just handed you is invalid — it's worth checking a pairwise-deleted correlation or covariance matrix for positive semi-definiteness (a smallest eigenvalue below zero is the tell) before using it in any downstream model that assumes a valid matrix, such as factor analysis, SEM, or matrix-based simulation.

Both are unbiased only under the strongest missing-data assumption, MCAR (missing completely at random) — meaning whether a value is missing has nothing to do with any variable, observed or not. Under MAR (missingness predictable from other observed variables, the far more common real-world case) or MNAR (missingness related to the unobserved value itself), both listwise and pairwise deletion can produce biased estimates. Pairwise deletion is not inherently more robust to non-random missingness than listwise deletion — it simply uses more of the available data under the same strong assumption.

If your sample stays large enough after complete-case selection and missingness is plausibly close to MCAR, listwise deletion is the safer default: it produces one coherent dataset, one N, and no risk of an invalid matrix. Pairwise deletion is defensible mainly for quick exploratory correlation work, provided you check the resulting matrix's validity before relying on it. Neither is the current methodological recommendation for a primary analysis once more than a small share of values is missing — multiple imputation and full information maximum likelihood (FIML) are both built to use every observed value from a single internally consistent model, without dropping cases or risking an incoherent matrix.

Defaults vary by procedure, not just by package, so it’s worth checking the specific command rather than assuming. SPSS’s regression procedures default to listwise deletion; its Bivariate Correlations procedure defaults to pairwise deletion but exposes a listwise option in the same dialog. R’s base cor() function takes a use argument, with "complete.obs" for listwise deletion and "pairwise.complete.obs" for pairwise deletion. Because the default differs by procedure within the same software, confirm which one a given command is actually applying before trusting the output.

No. Both deletion methods discard information — either whole cases or specific data points from specific calculations. Multiple imputation instead creates several complete, filled-in versions of the dataset, analyzes each one, and pools the results using Rubin's rules, using every observed value in the process. FIML takes a different route to the same goal, estimating model parameters directly from each case's available data without ever creating a filled-in dataset. Under MAR, both are generally preferred to either deletion method once missingness is more than trivial.