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      Development and Testing of an Abbreviated Numeracy Scale: A Rasch Analysis Approach

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          ABSTRACT

          Research has demonstrated that individual differences in numeracy may have important consequences for decision making. In the present paper, we develop a shorter, psychometrically improved measure of numeracy—the ability to understand, manipulate, and use numerical information, including probabilities. Across two large independent samples that varied widely in age and educational level, participants completed 18 items from existing numeracy measures. In Study 1, we conducted a Rasch analysis on the item pool and created an eight‐item numeracy scale that assesses a broader range of difficulty than previous scales. In Study 2, we replicated this eight‐item scale in a separate Rasch analysis using data from an independent sample. We also found that the new Rasch‐based numeracy scale, compared with previous measures, could predict decision‐making preferences obtained in past studies, supporting its predictive validity. In Study, 3, we further established the predictive validity of the Rasch‐based numeracy scale. Specifically, we examined the associations between numeracy and risk judgments, compared with previous scales. Overall, we found that the Rasch‐based scale was a better linear predictor of risk judgments than prior measures. Moreover, this study is the first to present the psychometric properties of several popular numeracy measures across a diverse sample of ages and educational level. We discuss the usefulness and the advantages of the new scale, which we feel can be used in a wide range of subject populations, allowing for a more clear understanding of how numeracy is associated with decision processes. Copyright © 2012 John Wiley & Sons, Ltd.

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          Most cited references28

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          Development and testing of a short form of the patient activation measure.

          The Patient Activation Measure (PAM) is a 22-item measure that assesses patient knowledge, skill, and confidence for self-management. The measure was developed using Rasch analyses and is an interval level, unidimensional, Guttman-like measure. The current analysis is aimed at reducing the number of items in the measure while maintaining adequate precision. We relied on an iterative use of Rasch analysis to identify items that could be eliminated without loss of significant precision and reliability. With each item deletion, the item scale locations were recalibrated and the person reliability evaluated to check if and how much of a decline in precision of measurement resulted from the deletion of the item. The data used in the analysis were the same data used in the development of the original 22-item measure. These data were collected in 2003 via a telephone survey of 1,515 randomly selected adults. Principal Findings. The analysis yielded a 13-item measure that has psychometric properties similar to the original 22-item version. The scores for the 13-item measure range in value from 38.6 to 53.0 (on a theoretical 0-100 point scale). The range of values is essentially unchanged from the original 22-item version. Subgroup analysis suggests that there is a slight loss of precision with some subgroups. The results of the analysis indicate that the shortened 13-item version is both reliable and valid.
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            Construct validity in psychological tests.

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              On the practice of dichotomization of quantitative variables.

              The authors examine the practice of dichotomization of quantitative measures, wherein relationships among variables are examined after 1 or more variables have been converted to dichotomous variables by splitting the sample at some point on the scale(s) of measurement. A common form of dichotomization is the median split, where the independent variable is split at the median to form high and low groups, which are then compared with respect to their means on the dependent variable. The consequences of dichotomization for measurement and statistical analyses are illustrated and discussed. The use of dichotomization in practice is described, and justifications that are offered for such usage are examined. The authors present the case that dichotomization is rarely defensible and often will yield misleading results.
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                Author and article information

                Journal
                J Behav Decis Mak
                J Behav Decis Mak
                10.1002/(ISSN)1099-0771
                BDM
                Journal of Behavioral Decision Making
                John Wiley & Sons, Ltd (Chichester, UK )
                0894-3257
                1099-0771
                15 March 2012
                April 2013
                : 26
                : 2 ( doiID: 10.1002/bdm.v26.2 )
                : 198-212
                Affiliations
                [ 1 ] Decision Research Eugene OR USA
                [ 2 ] Department of Psychology The Ohio State University Columbus OH USA
                Author notes
                [*] [* ]Correspondence to: Joshua Weller, Decision Research, 1201 Oak Street, Suite 200, Eugene, OR 97401, USA. E‐mail: jweller@ 123456decisionresearch.org
                Article
                BDM1751
                10.1002/bdm.1751
                7161838
                32313367
                1d7739e1-0c6d-4ddb-904b-2e6ef8be5510
                Copyright © 2012 John Wiley & Sons, Ltd.

                This article is being made freely available through PubMed Central as part of the COVID-19 public health emergency response. It can be used for unrestricted research re-use and analysis in any form or by any means with acknowledgement of the original source, for the duration of the public health emergency.

                History
                Page count
                Pages: 15
                Funding
                Funded by: National Science Foundation
                Award ID: SES‐0820197
                Award ID: SES‐0517770
                Award ID: SES‐0901036
                Award ID: SES‐0925008
                Award ID: SES‐082058
                Funded by: National Institute on Aging
                Award ID: R01AG20717
                Award ID: P30AG024962
                Categories
                Research Article
                Research Articles
                Custom metadata
                2.0
                April 2013
                Converter:WILEY_ML3GV2_TO_JATSPMC version:5.8.0 mode:remove_FC converted:15.04.2020

                numeracy,decision making,individual differences,rasch analysis,cognitive reflection test

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