Correcting the t statistic for measurement error
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Correcting the t statistic for measurement error Srinivas Durvasula & Subhash Sharma & Kealy Carter
Published online: 5 April 2012 # Springer Science+Business Media, LLC 2012
Abstract Studies in marketing often involve application of multi-item scales to measure latent constructs. Once the psychometric properties of a scale have been assessed, responses to individual scale items are often summed to form a composite score, which then is compared across groups by performing statistical tests such as a t test. In this note, we draw researchers’ attention to an often overlooked fact that the t test is attenuated by imperfect measures. As a solution, we propose the disattenuated t statistic and discuss how it would increase accuracy of estimates and affect decisions in the marketing discipline. Keywords Methodology, testing of group means . Disattenuated t statistic . Composite scale scores . t statistic
1 Introduction Many marketing constructs are measured by multi-item scales. When using such scales, researchers first assess the psychometric properties (e.g., reliability and validity) and then form composite scores, before proceeding to examine between-
S. Durvasula College of Business Administration, Marquette University, Milwaukee, WI 53233, USA e-mail: [email protected] S. Sharma (*) Moore School of Business, University of South Carolina, Columbia, SC 29208, USA e-mail: [email protected] K. Carter Moore School of Business, University of South Carolina, Columbia, SC 29208, USA e-mail: [email protected]
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Mark Lett (2012) 23:671–682
group mean differences. Typically, for a two-group case, examination of betweengroup mean differences is assessed using the t statistic or the equivalent F statistic. Consider, for example, an experiment where we manipulate nutritional information on the package of a ready-to-eat food item, measure attitude toward the label using a multi-item rating scale, obtain the composite label attitude score, and use the score to compare gender differences. Or consider the studies on self-construal. In these studies, typically a sample is drawn from a country in which consumers have an independent self-construal (typically western cultures), and another sample is drawn from another country where the consumers have an interdependent self-construal (typically eastern cultures). Hypotheses related to between-group mean differences are then tested using the t test. Sometimes the statistical tests show significant mean differences while in other cases they do not. We rely on the statistical test results and related effect sizes to derive major implications. What if the t statistic shows that the mean differences are not significant? What if there is a statistically significant mean difference, but barely so? Is it accurate for the researchers to conclude that no group differences exist? Unfortunately, making accurate inferences based on the t statistic will be a problem because of measurement error or imperfect reliability (i.e., coefficient alpha is
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