Comparative model fitting of relations among IAT versions , attitudes , and cultural knowledge

Nosek and Hansen (2008a) tested the contribution of attitudes and cultural knowledge to the Implicit Association Test and found that cultural knowledge had little or no relation to the IAT after accounting for their shared relationship with explicit attitudes. Nosek and Hansen (2008b) compared the original and personalized versions of the IAT and concluded that the personalized version encouraged explicit evaluation of target concepts, and that influence may account for the increased correlation between self-reported attitudes and the personalized IAT compared to the original IAT procedure. This supplement summarizes comparative model fitting testing whether the personalized and original tasks have distinct relations with cultural knowledge. This elaborates on the analyses reported in Nosek and Hansen (2008b) and shows that personalizing does not alter the (non) relationship between the IAT and cultural knowledge. This supplement assumes that the reader is familiar with at least one of Nosek and Hansen (2008a) or Nosek and Hansen (2008b). We recommend reviewing those articles to extract as much useful information from this report as possible. Hypothesis Testing Through Comparisons of Nested Structural Equation Models Comparing results of nested structural equation models allows us systematically to test specific hypotheses about the structure of relations between variables (McArdle, Johnson, Hishinuma, Miyamoto, & Andrade, 2001). For example, we can test whether the original and personalized IATs differ in their relation to evaluative knowledge by comparing the fits of two differently constrained models of the interrelationships among knowledge, explicit attitudes, and the IAT. The models are identical except that one constrains the functional relation between knowledge and each of the IAT versions to be equal, while the other model allows those relations to vary freely for the modified and original IATs. If the latter model demonstrates a significant improvement in overall model fit, then we can conclude that relations between the two versions of the IAT and knowledge are significantly different. This enables a direct test of the conceptual question without isolating that comparison from the interrelationships with other variables (as would be the case with a significance test of the difference in correlation coefficients). All models share a common structure in which explicit attitudes and evaluative knowledge are factors predicting the IAT. In the first two studies summarized, original and personalized IATs were collected within-subjects and are represented as two endogenous variables in a single model. In the last three studies summarized, original and personalized IATs were measured between-subjects and so we conducted two-group (original or modified) structural equation modeling with a single endogenous IAT variable (McArdle & Hamagami, 1996). Assessment of model fit was based on the root-meansquare error of approximation index (RMSEA or a; Browne & Cudeck, 1993; Steiger & Lind, 1980). This index weighs absolute fit, which declines whenever a parameter is removed from the model, against model complexity, such that the benefits of parsimony are considered along with fit (Steiger, 2000). Models fitting with a < . 05 are usually considered “close” fits, . 05 to . 08 as “fair” fits, . 08 to . 10 as “mediocre,” and above . 10 as “poor” (MacCallum, Browne, & Sugawara, 1996). Change in model fit from one proposed model to another was assessed by 2 / df