Investigating the quantity–quality relationship in scientific creativity: an empirical examination of expected residual variance and the tilted funnel hypothesis

Abstract

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.

Scientific Research in Ecuador: A Bibliometric Analysis

“…One issue that has caused debate in the academic world is the relationship between the number of scientific publications and their perceived quality, which allows us to understand how these publications can influence the field of study [285,286]. These investigations allow the generation of new knowledge valuable for the academy and the socio-economic growth of a region or country [287,288].…”

Quantity and Quality in Scientific Productivity: The Tilted Funnel Goes Bayesian

“…Yet, it has been highlighted that the equal odds baseline also suggests other propositions and characteristics concerning the relationship between quantity and quality of ideas ( Forthmann et al 2020b , 2020c , 2021b ). First, the correlation between the number of papers and average paper quality is proposed to be zero, such that individual scientists’ ‘hit-rate’ is not dependent on their quantity of work ( Simonton 1988 , 2003 , 2004 ).…”

“…What this means in a linear regression model in which quantity predicts quality of production is that the equal odds baseline implies heteroscedasticity and model residuals are hypothesized to display the shape of a tilted funnel that increases across the scale of quantity ( Forthmann et al 2020c ). In order to test the EOB in general and this ‘tilted funnel hypothesis’ of the EOB, statistical methods such as structural equation modeling ( Forthmann et al 2020b , 2021a ) and quantile regression ( Forthmann et al 2020c ) have been proposed and employed. The current work extends these previous efforts to test the EOB by transitioning to Bayesian statistical inference within a regression framework that encompasses and, hence, unifies existing approaches.…”

Understanding ideational fluency as a survival process

“…Current evidence suggests that, to generate a relatively original or novel idea, individuals must first generate several quotidian ideas that might be useful or practical but are not very original (Hass, 2017). In addition, individuals who posit the largest number of creations (i.e., the most ideationally fluent artists or scientists) are also the most likely to produce the ideas that are socially considered to be highly creative (Forthmann, Leveling, Dong, & Dumas, 2020). Extending this pattern further to a period of time (e.g., career span) suggests that the relation between overall productivity and creative successes may be positive, linear, stochastic and stable: a description of creative production known as the equal‐odds rule (Simonton, 1997).…”