← Reading listKEEP IMPUTATION UNCERTAINTY IN THE COMBINED ANALYSIS
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Statistical analysis handoff workshop / 6 MIN READ

Keep imputation uncertainty in the combined analysis

Review the object being combined before accepting a single tidy result from several completed datasets.

Published by SNS Media Tech

AI-assisted research and analysis for the SNS Creative Fieldbook

Sources checked 2026-11-07

A supplied multiple-imputation analysis should preserve the uncertainty represented by its alternative completions. Review the analyst’s per-completion results and combination rule instead of accepting a convenient merged table as equivalent evidence.

What you will leave with: An analysis-pooling handoff with aligned estimands, per-completion estimates and uncertainty, a known-answer calculation and explicit unresolved assumptions.

Use this when

  • A research supplier delivers several completed versions of a dataset with missing values.
  • A dashboard receives one pooled result without an inspectable analysis handoff.

Not a guide to choosing an imputation model, proving missing-at-random assumptions or filling sensitive records. A qualified analyst owns the statistical method.

Identify the analysis object before combining anything

The mice pool() documentation describes analyzing each imputed dataset and then pooling model estimates. Pooling the datasets instead is not the same procedure. Its missing-data rule combines within-analysis and between-analysis variance; required model information includes estimates, standard errors and residual degrees of freedom. The technical owner must verify that this rule applies to the intended analysis rather than treating a software command as methodological approval.

Write the quantity the report should estimate in plain language, including its population, scale and reference category where relevant. Ask the supplier to identify every completed dataset and corresponding model run. All runs should address that same quantity. A coefficient named satisfaction can mean different things if a response scale was reversed in one file or if a reference group changed. Resolve such inconsistencies before considering any combined result.

Inspect the handoff as a collection of analyses

Request a compact table with completion identifier, analysis version, target estimate, associated uncertainty and any fit warning. Preserve the model formula and relevant coding beside it. Do not substitute the number of rows in a stacked export for the original number of participants. Alternative completions are different versions of incomplete information about the same study, not automatically additional independent respondents.

Track failed or incompatible runs explicitly. If a completion yields no usable result, ask why and what the analyst proposes to do; do not silently drop it until the remaining table looks stable. An absent standard error is not a zero standard error. Keep the source observations, completion identities and reporting outputs distinguishable so a later correction can be traced without guessing which analysis produced a displayed value.

Use a small known-answer calculation

Consider an invented three-completion fixture for one estimate: 10, 12 and 14 points, each with standard error two. The mean estimate is 12. The mean within-analysis variance is four. The sample variance of the three estimates is four: squared deviations total eight, divided by two. This very small fixture checks the arithmetic only; it is not a recommendation to use three imputations for a real study.

Under the documented missing-data pooling rule, total variance is the mean within-analysis variance plus (one plus one divided by the number of completions) times the between-analysis variance. Here it is four plus four-thirds times four, or about 9.333, giving a standard error of about 3.055. Merely retaining the common standard error of two would omit the visible disagreement among these supplied estimates. Have the analyst determine degrees of freedom and intervals separately; this example does not prescribe a normal approximation.

Keep numerical agreement separate from methodological validity

Compare the supplier’s output with the known-answer fixture before reviewing the substantive result. If the calculation disagrees, determine whether the supplied analysis uses another justified combination rule, a different variance convention or an implementation error. Record the explanation. A reproducible difference is more useful than repeatedly exporting the same unexplained number in a new file format.

After the mechanical check, request the analyst’s separate account of imputation assumptions, diagnostics and sensitivity to plausible alternatives. Correct pooling cannot establish that the missing information was modeled adequately, that the study design supports a causal statement or that its population is representative. Publish the approved estimate with its appropriate uncertainty and limitations. Keep unresolved method questions visible rather than presenting the clean combined table as a guarantee that missingness has been solved.

Make the reasoning concrete.

A fictional survey supplier provides three model summaries with estimates 10, 12 and 14 and standard errors of two. The receiving dashboard averages the estimates but displays two as the final standard error without identifying its combination rule.

Accept the familiar uncertainty

Opening: Keep two because every supplied summary has that value.

Hypothesis: The output resembles the individual analyses.

Risk: The displayed result ignores disagreement across the supplied completions.

Reconcile the numerical fixture

Opening: Ask the analyst to explain the combined variance and verify the known-answer example.

Hypothesis: The team can distinguish an implementation mismatch from a different justified method.

Risk: Passing the arithmetic still does not validate the imputation assumptions.

The receiver holds the uncertainty display until the analyst reconciles the rule and its applicability. No original record is overwritten and no inferential claim follows from the fixture alone.

Take the questions into your next brief.

Use these prompts in your own notes. Nothing is submitted from this page.

  1. Estimand

    Do all runs estimate the same quantity on the same scale?

  2. Inventory

    Can each completion be matched to its model result and warnings?

  3. Inputs

    Are estimate, uncertainty and relevant degrees of freedom available?

  4. Fixture

    Does the implementation reproduce the declared small calculation?

  5. Limits

    Which imputation assumptions and sensitivity questions remain unresolved?

Watch for the wrong conclusion.

  • Treating stacked completions as independent new participants.
  • Silently excluding failed analysis runs.
  • Confusing a correct numerical combination with validated missing-data assumptions.

Your next action

Recompute the fictional within, between and total variance, then request the corresponding fields and rule from a supplied analysis handoff.

Sources & scope

AI-assisted original analysis, fictional calculations and review procedures. Sources support the identified statistical mechanics, not validation of a real model or study. Qualified analysts retain method decisions; no personal data processing or deployment is performed.