What Proportion of People Are Gifted? Examining the Consequences of Theoretical Definitions

• In Event: Leveraging Nonempirical Quantitative Analysis for Theory Development and Exploration: A New Paradigm for Giftedness Research

Abstract

Substantial attention has been devoted to cultivating sophisticated verbal definitions of giftedness. However, the operationalization of such definitions is the ultimate assessment of their consequence (i.e., how schools apply the definition to identify gifted students). This presentation reviews some of the most commonly used conceptions of giftedness (IQ only, NAGC's definition, Renzulli's Three Ring Conception, and a sample of state definitions) and quantifies the definitions to provide estimates for the number of students each definition identifies as gifted. The number of students identified as gifted depends on: the number of necessary and sufficient criteria (e.g., test scores, nominations, etc), how the criteria are combined, the number of domains included, and the correlation between domains.

Identification decisions made on the basis of multiple criteria must use the "and", "or", or "mean" combination rules or a composite of these (McBee, Peters, & Waterman, 2014). The "and" rule requires qualification standards to be met on every criterion whereas the "or" rule, requires students to meet the qualification standard on only one assessment. For example, the NAGC definition is an "or" combination rule because it requires individuals to fall into the top 10% of performance with respect to one and only one symbol system or psychomotor skill area in order to be considered gifted. If we assume that distribution roughly follows a multivariate normal distribution, we can calculate the probability that an individual possesses any skill at or above the 90th percentile by numerically integrating the multivariate normal distribution into each relevant domain. However, how many students will be identified as gifted also depends on the correlation across the different relevant domains.

Determining the correlations between the variables.

Ad hoc "guesstimation" of correlations between the variables is indefensible and is unlikely to result in a mathematically acceptable correlation matrix. A better method for arriving at an acceptable and defensible correlation matrix is based on confirmatory factor analysis (CFA). Due to space limitations, calculation specifics are omitted.

Example Analysis

The NAGC definition of giftedness specifies both symbol systems and sensorimotor skills as domains of giftedness. When only ten domains (e.g., five symbol system and five sensorimotor) are considered, the gifted percentage of the population ranges from about 32% if the correlations between factors is high and the factor loadings are high (r = .6 and Λi=.9) to 65% if the correlations between factors and the factor loadings are low (r = .0 and Λi=.1). This pattern is consistent with the properties of an "or" combination rule as outlined in McBee, Peters, and Waterman (2014). The more domains that one considers "worthy" for inclusion in the construct of giftedness, and the lower the correlations between those domains, the more people will qualify.

We hope that the results of these analyses illustrate why quantitative or psychometric analysis must accompany quantitative or psychometric arguments. Many of the common practices in gifted education that make intuitive sense end up having unanticipated effects.

Authors

• Matthew C. Makel, Duke University

• Matthew McBee, East Tennessee State University