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The Most Dangerous Profession: A Note on Nonsampling Error

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Abstract

Nonsampling errors are subtle, and strategies for dealing with them are not particularly well known within psychology. This article provides a compelling example of an incorrect conclusion drawn from a nonrandom sample: H. C. Lombard's (1835) mortality data. This example is augmented by a second example (A. Wald, 1980) that shows how modeling the selection mechanism can correct for the bias introduced by nonsampling errors. These 2 examples are then connected to modern statistical methods that through the method of multiple imputation allow researchers to assess uncertainty in observational studies. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
... The biggest flaw in their methodology, it seems to me, is their treatment of missing data. Missing data are an enormous problem in all observational studies (see Rosenbaum [2002] for a lucid description of what can be done, Little and Rubin [1987] for a more general discussion of dealing with missing data, and Wainer [2000] for a lively discussion on the impact of missing data on inferences), and its pernicious effects enters into this problem in an interesting way. Avery et al. (2004) suggest that by using a preference ranking they eliminate many of the possible ways that schools can manipulate the rankings. ...
... These were somewhat younger than those found by Madden, but this was expected since Lombard was dealing with ordinary people rather than the "geniuses" in Madden's (the positive correlation between fame and longevity was well known even then). But Lombard's study yielded one surprise; the most dangerous profession-the one with the shortest longevity-was that of "student," with an average age of death of only 20.7! Lombard recognized the reason for this anomaly, but apparently he did not connect it to his other results, which he interpreted as if they reflected real danger (for more details, see Wainer [1999]). ...
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The cost of attending a 4-yr. private university can easily top $150,000, making education one of the most expensive purchases we make. Unfortunately, the sorts of informed opinions and objective comparisons that are widely available for other large consumer purchases, like automobiles, are lacking in education. Instead we must make due with ad hoc indexes like that published annually by U.S. News and World Report. A recent alternative to this index using preference rankings was proposed. In this essay I discuss the challenges facing this index, and other survey instruments, caused by nonignorable missing data. My conclusion is not optimistic. (c) 2005 by JOURNAL OF CONSUMER RESEARCH, Inc..
... Reasons for Meditating Indeed Change Over Time There was some indication in previous studies that reasons for meditating may change over time, but the evidence is largely correlational, that is, the importance of a given reason for meditating covaried with meditators' amount of practice (see above). But, as one of the meditation teachers in study 1 remarked, beginning meditators who see their initial goals unfulfilled might just stop meditating after some time, so these correlations suffer from the potential problem of nonsampling error (Wainer, 1999). Our data strongly indicate that long-term meditators might indeed consist of a systematically selected subsample of all people who begin to meditate (see Table 3). ...
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... Wald was able to solve the dilemma of bomber armor largely because he recognized that a selection effect was at work within his sample: he was able to study only those aircraft that had survived previous bombing runs (Wainer, 1999). He recognized how the missing data in his sample could inform on the conditions affecting the total population of bombers, rather than just those that had survived. ...
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... Johnson & Christensen, 2012: 217). Moreover, whereas nonresponse may not necessarily bias a study's data, a single nonresponse renders a probability sample nonrandom and, thus, introduces ambiguity into the inferences that can be made (Wainer, 1999). ...
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While he was a member of the Statistical Research Group (SRG), Abraham Wald worked on the problem of estimating the vulnerability of aircraft, using data obtained from survivors. This work was published as a series of SRG memoranda and was used in World War II and in the wars in Korea and Vietnam. The memoranda were recently reissued by the Center for Naval Analyses. This article is a condensation and exposition of Wald's work, in which his ideas and methods are described. In the final section, his main results are reexamined in the light of classical statistical theory and more recent work.
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Nonsampling errors are subtle, and strategies for dealing with them are not particularly well known within psychology. This article provides a compelling example of an incorrect conclusion drawn from a nonrandom sample: H. C. Lomard's (1835) mortality data. This example is augmented by a second example (A. Wald, 1980) that shows how modeling the selection mechanism can correct for the bias introduced by nonsampling errors. These 2 examples are then connected to modern statistical methods that through the method of multiple imputation allow researchers to assess uncertainty in observational studies. The APA's task force on Statistical Inference has received comments and suggestions from interested parties throughout the entire time I have served on it. These comments have always been treated by the task force with careful attention. In the most recent batch was a one-page missive from John Tukey containing seven suggestions. In the course of my professional life I have made many errors, but happily, ignoring statistical advice from John Tukey is not one of them. Tukey's fifth suggestion, in its entirety, is, "non-.ampling errors deserve greater attention, especially when randomization is absent. The formal statistical analysis treats only some of the uncertainties" (J. W. Tukey, personal communication, June 16, 1997). Indeed, but nonsampling errors are subtle, and strategies for dealing with them are not particularly well known within psychology. Thus, I think it would be worthwhile to provide a particularly interesting illustration of one and point the way toward alternative methodologies for interested readers.
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There is no safety in numbers. When data are gathered from a sample in which the selection criteria are unknown, many problems can befall the unwary investigator. In this paper we explore some of these problems and discuss some solutions. Our principle example is drawn from data from students who choose to take the College Board's Scholastic Aptitude Test (SAT). We explore methods of covariance adjustment as well as more explicitly model-based adjustment methods. Among the latter we discuss Heckman's Selection Model, Rubin's Mixture Model, and Tukey's Simplified Selection Model.
De l'influence des professions sur la durée de la vie [On the influence of profession on the length of life]
  • H. C. Lombard