Several pending federal and state electoral-integrity bills specify hand audits of 1% to 10% of all precincts. However, percentage-based audits are usually inefficient, because they require large samples for large jurisdictions, even though the sample needed to achieve good accuracy is much more affected by the closeness of the contest than population size. Percentage-based audits can also be ineffective, since close contests may require auditing a large fraction of the total to provide confidence in the outcome. We present a plausible statistical frame-work that we have used in advising state and local election officials and legislators. In recent federal elections, this audit model would have required approximately the same effort and resources as the less effective percentage-based audits now being considered
Auditors are often faced with reviewing a sample drawn from special populations. One is the special population where invoices are divided into two categories, according to whether or not invoices are qualified. In other words, the qualified amount follows a nonstandard mixture distribution in which the qualified amount is either zero with a certain probability or the same as the known invoice amount with a certain probability. The other is the population where some invoices are partially qualified. In other words, some invoices have a qualified amount between zero and the full invoice amount. For these settings, the typical sample design is stratified random, with the estimation method employing a ratio type method. This paper focuses on efficient sample design for this setting and provides some guidelines in setting up stratum boundaries, calculating sample size and allocating sample size optimally across strata.
ObjectiveCompare mothers’ reports of injuries for infants and toddlers sleeping with crib-bumpers/mesh-liners/no-barriers and reasons for these sleep environment choices.MethodsA cross-sectional survey of mothers subscribing to a parenting magazine and using crib bumpers (n = 224), mesh liners (n = 262), and no barriers (n = 842). Analyses of four possible injuries (face-covered, climb-out/fall, slat-entrapment, hit-head) including multivariate logistic regression adjusted for missing data/demographics and Chi squared analyses of reasons for mothers’ choices.ResultsMaternal reports of finding infants/toddlers with face covered had 3.5 times higher adjusted odds (aOR) for crib bumper versus mesh liner use. Breathing difficulties and wedgings were reported for infants/toddlers using crib bumpers but not mesh liners. Climb-outs/falls showed no significant difference in aORs for crib bumpers versus no-barriers and mesh liners versus no barriers. Reports of slat-entrapment were less likely for mothers using crib bumpers and mesh liners than using no barrier (aOR = .28 and .32). Reports of hit-heads were less likely for crib bumpers vs no barrier (aOR = .38) with no significant difference between mesh liners versus no barrier use. Mothers using crib bumpers and mesh liners felt their choice prevented slat-entrapment (89%, 91%); 93.5% of crib bumper users felt their choice prevented hit-heads. Significantly more mesh liner than crib bumper users chose them because “There is no suffocation risk” (64.1% vs. 40.6%), while 83.6% of no-barrier users chose them because “I was concerned about suffocation risk.”Conclusions for PracticeMothers appeared to be more concerned about preventing minor risks than suffocation. Understanding reasons for mothers’ use of barriers/no-barriers is important in tailoring counseling for mothers with infants/toddlers.Electronic supplementary materialThe online version of this article (10.1007/s10995-019-02803-7) contains supplementary material, which is available to authorized users.
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