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It is increasingly common to collect pre-post data with pseudonyms orself-constructed identifiers. On survey responses from sensitive populations,identifiers may be made optional to encourage higher response rates. Theability to match responses between pre- and post-intervention phases for everyparticipant may be impossible in such applications, leaving practitioners witha choice between the paired t-test on the matched samples and the two-samplet-test on all samples for evaluating mean differences. We demonstrate theinadequacies with both approaches, as the former test requires discardingunmatched data, while the latter test ignores correlation and assumesindependence. In cases with a subset of matched samples, an opportunity toachieve limited inference about the correlation exists. We propose a noveltechnique for such `partially matched' data, which we refer to as theQuantile-based t-test for correlated samples, to assess mean differences usinga conservative estimate of the correlation between responses based on thematched subset. Critically, our approach does not discard unmatched samples,nor does it assume independence. Our results demonstrate that the proposedmethod yields nominal Type I error probability while affording more power thanexisting approaches. Practitioners can readily adopt our approach with basicstatistical programming software.

Mistaken identities lead to missed opportunities: Testing for mean differences in partially matched data