Missing values filled in several times over, and the results pooled. Why that beats filling them in once, how to choose the predictors, and how to report a pooled estimate.
Single imputation replaces each missing value with one number: the mean, the median, or a regression prediction. Quanta offers all three, and they are appropriate for quick exploratory work.
They share a serious defect for inference. They treat a guess as though it were an observation. The imputed value carries no uncertainty, so standard errors come out too small, confidence intervals too narrow, and p values too optimistic. Mean substitution additionally shrinks the variance of the variable and attenuates its correlations with everything else, because every imputed case sits exactly at the centre.
Multiple imputation solves this by filling the gaps several times, each with different plausible values drawn from a model. You then analyse every completed dataset and pool the results. The variation between imputations is what carries the uncertainty that single imputation throws away.
MICE, multiple imputation by chained equations, does this variable by variable in sequence, cycling until the imputations stabilise. It handles mixed variable types, which is why it is the standard approach in applied research.
Include the outcome in the imputation model. This feels wrong and is correct. Omitting the outcome biases the relationship you are about to study toward zero. Quanta's predictor selector says so explicitly: include the outcome plus auxiliaries.
Include auxiliary variables that predict either the missing values or the missingness itself, even if they are not in your analysis model. They make the MAR assumption more plausible and they cost nothing.
More imputations than you think. The old advice of five came from an era of expensive computation. A reasonable rule is to use at least as many imputations as your percentage of incomplete cases: 30% incomplete means at least 30 imputations. On Apple silicon the run time is not the constraint it used to be.
Do not impute the variable that defines your sample. If a case is missing the grouping variable, it does not belong in a group comparison, and imputing it manufactures membership.
You cannot average the results of several analyses naively, because that would ignore how much they disagreed. Rubin's rules combine them properly: the pooled estimate is the average across imputations, and the pooled variance combines the within-imputation variance, the ordinary uncertainty in each analysis, with the between-imputation variance, the disagreement across them.
Quanta pools means, correlations, and regression coefficients, reporting the pooled estimate with its standard error. Correlations are pooled through the Fisher-z transformation rather than averaged directly, which is the correct handling and a detail many implementations get wrong.
The between-imputation component is the whole point. It is the honest acknowledgement that you did not observe those values, and it is precisely what single imputation omits.
Open Data Quality and find the imputation and cleaning section. Choose MICE rather than one of the single methods for anything you intend to report inferentially.
Select the variables to impute, then the predictors, remembering to include your outcome.
Set the number of imputations against your proportion of incomplete cases.
Run the pooled analysis rather than analysing one imputed dataset. Quanta pools the mean, correlation, or regression you specify across imputations using Rubin's rules; picking a single completed dataset discards the entire benefit.
Check Little's MCAR first. If missingness is completely random and minimal, complete-case analysis may be simpler and equally defensible.
Report the amount of missing data, the method, the number of imputations, the predictors, and the pooled estimates.
Missing values (4.8% of cells) were handled by multiple imputation by chained equations with 40 imputations, including the outcome and three auxiliary variables in the imputation model. Estimates were pooled using Rubin's rules; the pooled regression coefficient for autonomy was B = 2.31, SE = 0.58, p < .001.
State the number of imputations and the predictors. Without them the analysis is not reproducible.
Report the fraction of missing information if available. It tells a reader how much the conclusion rests on imputed rather than observed data.
Name the MAR assumption. Multiple imputation assumes missing at random, and saying so is the difference between applying a method and understanding it.
Every result carries a ReliCheck Intelligence card with one action: explain this result in plain language. It runs entirely on your Mac with Apple Intelligence. No upload, no API key, nothing to configure. The model only explains the result Quanta has already computed and validated. It never computes a statistic, and it never applies a decision on your behalf.
From the action bar you can add the result to a report, copy the table, or copy the APA text. Exported reports carry the APA table, its note, and a caution specific to that analysis beneath it.
Quanta's multiple imputation is validated against R's mice package with Rubin's rules, matching pooled estimates, variance, and the fraction of missing information. The engine is pure Swift with no R or Python at runtime. Full record on the validation page.
Data Quality is part of every Quanta subscription, $9.99 a month or $79.99 a year after the 30-day trial. One price for everyone. See pricing.
The analysis, the report builder, and the on-device explanations all work with the network off. Your dataset is never uploaded.
Little's MCAR test whether you need imputation at all · Representation checks who the missing data belongs to · Multiple linear regression pooled across imputations · the complete list on the analyses page.