How to Report Missing Data in APA 7

Your dataset has holes in it. Someone skipped the income question, three people left the last page of the battery blank, two dropped out between waves, and one scale total is missing because a single item is. Then your software quietly analyses 322 of your 412 participants, prints degrees of freedom that no longer match the sample described in the Method section, and warns you about none of it. That mismatch is the first arithmetic check a reviewer can run without your data, and it takes about four seconds. Here is what to report, how to argue a mechanism you cannot actually test, and how to describe listwise deletion, multiple imputation or full information maximum likelihood so someone else could run the same analysis. If you are building the section from scratch, the home article is how to report results in APA 7.

What goes in, and where

A reader has three questions and you answer them in order: how much is missing and where, why you think it is missing, and what you did about it. The APA Journal Article Reporting Standards ask for the frequency or percentage of missing data and for the method used to address it, so this is not a courtesy paragraph you add if there is room. Missing data are part of the description of your sample, in the same way that age and sex are.

The pieces live in two places. The Method section carries the counts and the plan: how many values were missing on each variable, how many participants had complete data, and the procedure you chose with its settings. The Results section carries the consequence: the N actually analyzed, and any sensitivity analysis you ran. If your analyzed sample is smaller than your recruited sample, say so at the point where the smaller number first appears, not three pages later.

The formatting rules are the ordinary ones, applied to the symbols that show up here. N, n, t, d, M, SD and m (the number of imputations) go in italics; the χ of Little's test stays roman because it is a Greek letter, and it carries the sample size inside the brackets like any chi-square: χ²(24, N = 412) = 31.06, p = .152. Leading zeros follow the can-it-exceed-one rule: p and the fraction of missing information lose theirs (p = .152, FMI = .18), d and unstandardised coefficients keep theirs (d = 0.33).

One distinction saves you from a meaningless summary figure: whole people and single values are not the same problem. Participants who withdrew, were excluded or never returned for wave 2 belong in the participant flow, with the reasons. Values left blank inside an otherwise complete protocol are item-level missingness. Averaging both into one percentage hides which of the two you have, and they are handled differently.

How many are missing, and where

Give the percentage and the raw count, variable by variable, and then the case-level figure. In a sample of 412 university students, that reads: missing values ranged from 1.9% (8) on the depression scale and 4.4% (18) on anxiety to 7.8% (32) on perceived social support and 15.0% (62) on household income; 322 participants (78.2%) had complete data on all analysis variables, and 90 (21.8%) were missing at least one value. Those two levels answer different questions. A variable missing 15% of its values is a measurement problem; 21.8% of cases incomplete is what listwise deletion would actually cost you.

The pattern matters as much as the amount. Say whether the holes are scattered across variables or concentrated in one block, whether they are monotone (once someone stops, they stop for good — the usual shape in longitudinal designs) or arbitrary, and whether a single item is dragging a whole scale total down with it. State your scoring rule explicitly if you used one: prorating a total when fewer than 10% of its items are missing is a defensible convention, but it is a decision, and an unstated decision looks like an accident.

The often-quoted threshold of 5% — below which most methods give much the same answer — comes from Schafer (1999) and it is a rule of thumb about consequences, not a permission slip. It says little when the missingness is systematic: 4% missing entirely among the participants with the highest symptom scores does more damage than 12% scattered at random. And 5% on each of six variables can leave a quarter of your cases incomplete, which is exactly why you report both the value-level and the case-level figures.

With more than three or four variables, this belongs in a table: one row per variable, columns for n observed, n missing and percentage missing, and a note giving the number of complete cases. In an intervention study, add a column per arm, because differential attrition between groups is a threat to the comparison itself and a single overall percentage conceals it. The universal APA table generator will lay out the rows and the note for you.

The mechanism: MCAR, MAR, MNAR — and how you argue it

Rubin's (1976) three-way classification is about what the probability of being missing depends on. Data are missing completely at random (MCAR) when that probability is unrelated to anything, observed or not: the holes are a coin toss. They are missing at random (MAR) when the probability depends on things you did measure — men skip the income question more often, and you have sex in the file. They are missing not at random (MNAR) when the probability depends on the missing value itself: the highest earners are the ones who leave income blank. The names are unhelpfully similar, so define the one you claim in a clause rather than trusting the acronym to carry it.

Only MCAR is testable, and only partially. Little's MCAR test compares the means of the observed variables across the missingness patterns and reports a chi-square: χ²(24, N = 412) = 31.06, p = .152. Two limits are worth knowing before you lean on it. A non-significant result is not proof of MCAR — it is a failure to reject, and with modest samples the test has little power. And with a large sample almost anything reaches significance: χ²(38, N = 1,204) = 61.44, p = .009 can reflect a difference of a couple of scale points. The test also looks only at means, so it is blind to missingness related to variances or to associations.

The argument that actually persuades is a set of comparisons between the participants with and without missing values on everything you observed. Report them: missingness on income was unrelated to sex, χ²(1, N = 412) = 0.84, p = .359, and to age, t(410) = 0.62, p = .536, d = 0.09, but participants missing income scored higher on depression, t(402) = 2.41, p = .016, d = 0.33 (the degrees of freedom drop to 402 because eight people have no depression score). Read that correctly: a significant difference is evidence against MCAR, and it is an argument for MAR precisely because the variable that predicts missingness is one you measured and can therefore put in the imputation model.

MAR is an assumption, and the honest sentence says so: «Data were assumed to be missing at random, conditional on the analysis variables and two auxiliary variables». No test can distinguish MAR from MNAR, because doing so would require the values you do not have. What you can do is make MAR more plausible — include auxiliary variables correlated with missingness or with the incomplete variable, even if they never appear in the substantive model — and, when MNAR is genuinely on the table (dropout driven by the symptom you are measuring), run a sensitivity analysis that shifts the imputed values by a plausible amount and report whether your conclusion survives.

What you did, and why

Listwise deletion is defensible when very little is missing and MCAR is plausible, and it is what your software does by default whether you decided on it or not. Report it as a decision: «Analyses used complete cases (n = 322); 90 participants were excluded for missing data on at least one analysis variable». It costs you power, and it buys you bias whenever the mechanism is not MCAR. Pairwise deletion costs more than it looks: each correlation is computed on a different subsample, the Ns in your table stop agreeing with each other, and the resulting matrix can fail to be positive definite, which then breaks the factor analysis you were about to run on it.

Multiple imputation needs five details or it is not reproducible: the software and package, the number of imputations m and how you chose it, the imputation method, which variables entered the imputation model, and the fact that estimates were pooled using Rubin's rules. The old default of m = 5 is generous only to the computer; a workable convention (White, Royston and Wood, 2011) is to set m at least equal to the percentage of incomplete cases, which with 21.8% incomplete gives m = 25. The imputation model must include the dependent variable and every variable in the analysis, plus the auxiliaries — leave the outcome out and you impute predictors that are unrelated to it, which attenuates exactly the effect you are testing. Reporting the fraction of missing information (FMI = .18) tells the reader how much of your uncertainty comes from the holes. The mechanics in SPSS and R are laid out in imputing missing data in SPSS and R.

Full information maximum likelihood (FIML) produces no imputed datasets at all: it estimates the model using every case that contributes any information, under the same MAR assumption. It is what SEM software gives you as soon as you ask for it — the default in Mplus, one argument in lavaan (missing = 'fiml') — and it is usually one line in the Method: «Models were estimated with full information maximum likelihood, which uses all available data under a missing-at-random assumption (N = 412)». The N you report is the full one, which is the point. If you want auxiliary variables, they enter as saturated correlates rather than as predictors, and say which ones. With non-normal indicators the estimator becomes robust maximum likelihood, and that is worth naming too.

Three things do not belong in the paper unannounced. Mean substitution puts every missing case at the center of the distribution, which shrinks the variance and pulls the correlations toward zero. Single regression or EM imputation gives a plausible value but treats it as if it had been observed, so the standard errors come out too small and the confidence intervals too narrow. And any decision you took after seeing the results — dropping a variable because its missingness was inconvenient — needs to be reported as what it was. The way to defuse all of this is a sensitivity analysis: run the model both ways and put both numbers in. Complete cases gave B = -0.41, SE = 0.11, 95% CI [-0.63, -0.19], and multiple imputation gave B = -0.34, SE = 0.09, 95% CI [-0.52, -0.16], p < .001 — same conclusion, and now nobody has to wonder.

What the 78.4% gives away

A review of 37 dissertations that analyzed NHANES data found that 78.4% did not state even whether they had missing values. Not that they had none — NHANES, like every large health survey, is full of them, and some of its measures are collected on subsamples by design. Twenty-nine of those 37 documents simply never mentioned the subject, in the section where the sample is described, in a dataset whose documentation devotes pages to it.

Silence is not neutral, because the reader fills it with the default. No statement means listwise deletion, and listwise deletion in a large survey can quietly remove a third of the sample and, with it, the people whose data are hardest to collect. Then comes the arithmetic: your Method says N = 412, your regression prints F(4, 317) = 12.44, p < .001, and those degrees of freedom mean 322 cases were analyzed. Ninety people disappeared and the paper never said so. That is one query in a review report, and one revision round.

The fix is two sentences and numbers you already have on screen. Write them before you run the analysis, in the analysis plan, where the decision is still a methodological one rather than a way of rescuing a p value: which cases you will exclude, what you will impute and with which model, and what you will do if the two approaches disagree. That belongs in the same document as the rest of your decisions — see how to write a data analysis plan for a thesis.

The part that buys you credibility is the last one. If complete-case and imputed analyses agree, one sentence says so and the reader stops worrying. If they disagree, that disagreement is a finding about your data, not an accident to be hidden: it means the missingness is doing work, and the discussion has something real to say about who is not in your sample and what that does to the estimate.

The whole thing, written out

The Method version, multiple imputation: «Of the 412 participants, 90 (21.8%) were missing at least one value on the analysis variables. Missing values ranged from 1.9% (8) on the depression scale to 15.0% (62) on household income. Little's MCAR test was non-significant, χ²(24, N = 412) = 31.06, p = .152, but participants missing income data reported higher depression scores than those with complete data, t(402) = 2.41, p = .016, d = 0.33; missingness was unrelated to sex, χ²(1, N = 412) = 0.84, p = .359, and to age, t(410) = 0.62, p = .536. Data were therefore assumed to be missing at random and handled with multiple imputation by chained equations (R, mice package), with m = 25 imputations, predictive mean matching for continuous variables, and an imputation model containing all analysis variables — including the outcome — plus two auxiliary variables (perceived stress and years of study). Estimates were pooled using Rubin's rules; the pooled degrees of freedom follow Barnard and Rubin (1999) and are reported rounded.»

The Results version, with the sensitivity analysis attached: «In the imputed data (N = 412), social support predicted lower depressive symptoms, B = -0.34, SE = 0.09, 95% CI [-0.52, -0.16], p < .001, FMI = .18. The complete-case analysis (n = 322) produced an estimate of the same sign and magnitude, B = -0.41, SE = 0.11, 95% CI [-0.63, -0.19], F(4, 317) = 12.44, p < .001, R² = .14, so the conclusion does not depend on how missing data were handled.» For where this paragraph sits relative to the rest, there is a full worked section in the APA 7 Results section, written out.

And the short version, for when the problem really is small: «Missing values affected 1.2% of the data points and no variable had more than 2.4% missing. Little's MCAR test was non-significant, χ²(9, N = 412) = 11.83, p = .223, and analyses were conducted on complete cases (n = 401).» Three sentences, three numbers, no imputation, and nothing left for a reviewer to ask. The difference between this and the 78.4% is not sophistication — it is having written the sentences down.

Already drafted it? Paste your Results section into Review one section and you get the first objection a reviewer would raise, quoting the exact sentence from your text. Free, no sign-up.

Frequently asked questions

How do you report missing data in APA 7?

In three moves. The amount, as percentage plus raw count for each variable and for complete cases: «missing values ranged from 1.9% (8) to 15.0% (62); 322 participants (78.2%) had complete data». The mechanism you are assuming, with the evidence for it: Little's MCAR test, χ²(24, N = 412) = 31.06, p = .152, plus comparisons between complete and incomplete cases. And the method, with its settings: multiple imputation with m = 25, FIML, or complete cases with the n excluded. Counts and plan go in the Method section, the analyzed N and any sensitivity analysis in the Results.

How much missing data is acceptable?

There is no threshold that makes an analysis valid or invalid, and the widely quoted 5% (Schafer, 1999) is a rule of thumb about when methods start to diverge, not a limit. What matters more than the amount is the pattern: 4% missing concentrated among the most symptomatic participants biases your estimate more than 12% scattered at random. Report the value-level percentage per variable and the case-level figure — 5% missing on each of six variables can leave a quarter of your cases incomplete — and bear in mind the working convention: once a key variable is missing more than about 10% of its values, few reviewers accept complete cases, and the expected move is multiple imputation or FIML.

What are MCAR, MAR and MNAR, and how do I know which one I have?

MCAR means the probability of a value being missing is unrelated to anything, observed or unobserved. MAR means it depends on variables you measured (men skip the income item more often, and you have sex in the file). MNAR means it depends on the missing value itself (the highest earners are the ones who skip it). You can test MCAR, imperfectly, with Little's test; you cannot distinguish MAR from MNAR with your data, because that would require the values you do not have. In practice you argue for MAR: show which observed variables predict missingness, put them in the imputation model, and state the assumption as an assumption.

How do you report Little's MCAR test in APA style?

As a chi-square, with the sample size inside the brackets: χ²(24, N = 412) = 31.06, p = .152. The χ stays roman because it is a Greek letter, the N is italic, and p takes no leading zero. Interpret it with care: a non-significant result does not prove MCAR, it only fails to reject it, and with a large sample the test flags trivial differences — χ²(38, N = 1,204) = 61.44, p = .009 may amount to two scale points. It also compares means only, so missingness tied to variances or to associations goes undetected.

How many imputations (m) should I run?

More than the classic 5. A workable convention (White, Royston and Wood, 2011) is to set m at least equal to the percentage of incomplete cases: with 21.8% of cases incomplete, m = 25. Running more costs computing time and nothing else, and it makes your results reproducible to more decimal places, since each set of imputations carries its own random variation. Report m, the imputation method (predictive mean matching, chained equations), the variables in the imputation model — including the outcome — and the fact that estimates were pooled with Rubin's rules.

Is listwise deletion ever acceptable?

Yes: when very little is missing and MCAR is plausible, complete-case analysis is unbiased and the loss of power is small. It stops being defensible when a fifth of your cases disappear or when missingness is related to your variables, because then you are analyzing a self-selected subsample. Two rules apply either way. Report it as a decision with the numbers («complete cases, n = 322; 90 excluded»), rather than letting the software do it silently. And if the excluded cases differ from the retained ones on anything you measured, run the analysis both ways and report both estimates.

With the counts per variable, the complete-case figure, a mechanism stated as an assumption and backed by comparisons, and the method with its settings, your missing data are reported the way APA 7 asks — and the reader can reconcile every N in the paper. When the problem gets harder — dropout driven by the symptom you are measuring, a longitudinal file where the imputation model needs the time structure in it, or an MNAR sensitivity analysis you have to defend — that is what my statistical consulting is for.