Among scientists who study scientific production, the relationship between the quantity of a scientist’s production and the quality of their work has long been a topic of empirical research and theoretical debate. One principal theoretical perspective on the quantity–quality relationship has been the equal odds baseline, which posits that a scientist’s number of high-quality products increases linearly with their total number of products, and that there is a zero correlation between a scientist’s total number of products and the average quality of those products. While these central tenets of the equal odds baseline are well known, it also posits a number of more specific and less discussed aspects of the quality–quantity relation, including the expected residual variance and heteroscedastic errors when quality is regressed on quantity. After a careful examination of the expected variance by means of a non-parametric bootstrap approach, we forward a further prediction based on the heteroscedasticity implied by the equal-odds baseline that we term the tilted funnel hypothesis, that describes the shape of a bivariate scatterplot when quality is regressed on quantity, as well as the change in the strength of slope coefficients at different conditional quantiles of the quality distribution. In this study, we empirically test the expected residual variance and the tilted funnel hypothesis across three large datasets (including approximately 1.5 million inventors, 1800 psychologists, and 20,000 multidisciplinary scientists). Across all of the data sets, the results empirically supported the tilted funnel hypothesis, and therefore the results provided further evidence of the utility of the equal odds baseline.

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Purpose To explore how registered nurses (certified, noncertified, and managers) value certification as determined by the Perceived Value of Certification Tool, review the psychometric properties of the instrument, and ascertain the benefits and barriers to nursing specialty certification. Design Systematic review (without meta‐analysis) of 18 studies representing 26,534 registered nurses. Methods Rigorous processes were used to minimize bias; to identify, appraise, and synthesize studies to explore how registered nurses value certification; and to ascertain the benefits and barriers to nursing specialty certification. Psychometric properties of the Perceived Value of Certification Tool were also reviewed and evaluated. Methods and results are presented in accordance with the Preferred Reporting Items for Systematic reviews and Meta‐Analyses guidelines. Findings All studies included in the review were cross‐sectional studies with observational, descriptive designs published between 2003 and 2019. The average study participant was a 49‐year‐old Caucasian woman with a bachelor of science in nursing degree and 20 years of experience working as a staff nurse in a hospital. In accordance with the results reported in all studies included in the systematic review, the highest level of agreement and strong agreement occurred with the intrinsic value statements of enhances feeling of personal accomplishment (n = 16,697; 97.8%), provides personal satisfaction (n = 16,607; 92.7%), and validates specialized knowledge (n = 16,697; 97%). The lowest levels of agreement and strong agreement occurred with the extrinsic value statements of promotes recognition from employers (n = 16,607; 78.6%), increases consumer confidence (n = 16,607; 73.3%), and increases salary (n = 16,607; 41.9%). Conclusions The vigorous statistical work completed on the developmental study for the instrument conducted in 2003 has yet to be duplicated in the multiple studies published subsequently. The chiefly descriptive studies detailed in this systematic review are of limited usefulness in guiding future research. The Perceived Value of Certification Tool has proven useful in stimulating interest; however, a revision of the instrument is now required to promote research and patient outcome studies regarding the self‐perceived value of certification in nursing specialties. Clinical Relevance This report systematically reviews 18 studies that have used the Perceived Value of Certification Tool, a tool that has been widely used since 2003, to measure the perceptions of registered nurses regarding specialty certification. This review provides evidence that the instrument has potential for expanded use in patient outcomes studies and should be revised to better serve the needs of researchers.