The asymptotic distribution of commonality components

Commonality components have been defined as a method of partitioning squared multiple correlations. In this paper, the asymptotic joint distribution of all 2 ^k – 1 squared multiple correlations is derived. The asymptotic joint distribution of linear combinations of squared multiple correlations is obtained as a corollary. In particular, the asymptotic joint distribution of commonality components are derived as a special case. Simultaneous and nonsimultaneous asymptotic confidence intervals for commonality components can be obtained from this distribution.This work was supported in part by the Spencer Foundation and the National Science Foundation.The authors are grateful to Bryna Siegel-Gorlick for her help in obtaining the data used in Example 4.3, and to the referees for their comments and suggestions.     

Effect sizes in ANCOVA and difference-in-differences designs

It is common practice in both randomized and quasi-experiments to adjust for baseline characteristics when estimating the average effect of an intervention. The inclusion of a pre-test, for example, can reduce both the standard error of this estimate and—in non-randomized designs—its bias. At the same time, it is also standard to report the effect of an intervention in standardized effect size units, thereby making it comparable to other interventions and studies. Curiously, the estimation of this effect size, including covariate adjustment, has received little attention. In this article, we provide a framework for defining effect sizes in designs with a pre-test (e.g., difference-in-differences and analysis of covariance) and propose estimators of those effect sizes. The estimators and approximations to their sampling distributions are evaluated using a simulation study and then demonstrated using an example from published data.     

White Jesus and Antisemitism: Toward an Antiracist and Decolonial Christology

This article argues that traditional Christology is intimately bound up with a triumphalist agenda that denies Jesus’ Jewishness and is structurally antisemitic. Taking an antiracist stance, the article argues that systemic rethinking of Christianity’s theological resources is needed, which must be anti-antisemitic and antiracist. This involves reconfiguring how we take on board Jesus’ Jewishness in a post-Holocaust context and recognizing Jesus as a Jewish prophet. From this, it is tentatively suggested that rethinking the role of the Messiah involves understanding a Levinasian Messiah who does not come, but rather calls upon us to act in a Messianic role before the Other as an ethical imperative.     

Stimulus Generalization and the Peak Shift with Movement Stimuli

Stimulus generalization is suggested as an alternative method for examination of the “novelty? problem in motor learning. These experiments demonstrated that stimulus generalization occurs using simple movements as stimuli. The phenomenon of the “peak shift? in post-discrimination generalization gradients was also examined. The first experiment demonstrated that a peak shift occurred using linear movements as stimuli and that the magnitude of the peak shift increased as the difference between the training stimuli decreased. The second experiment showed similar results when the stimuli consisted of a range of movements rather than a single movement length. The final experiment provided evidence that perception of movement length is influenced by the magnitude of an immediately preceding movement. The relevance of these studies to current motor-learning theory is discussed.     

Reviews

The Catalpa Bow: A Study of Shamanistic Practices in Japan Carmen Blacker Richmond: Curzon Press. 1999. 382 pp. ISBN 1–873410–85–9 (pbk.)

Beyond Phenomenology: Rethinking the Study of Religion Gavin Flood London: Cassell. 1999. 311pp. ISBN 0 304 70131 9 (hbk), 70570 5 (pbk).     

Correcting an analysis of variance for clustering

A great deal of educational and social data arises from cluster sampling designs where clusters involve schools, classrooms, or communities. A mistake that is sometimes encountered in the analysis of such data is to ignore the effect of clustering and analyse the data as if it were based on a simple random sample. This typically leads to an overstatement of the precision of results and too liberal conclusions about precision and statistical significance of mean differences. This paper gives simple corrections to the test statistics that would be computed in an analysis of variance if clustering were (incorrectly) ignored. The corrections are multiplicative factors depending on the total sample size, the cluster size, and the intraclass correlation structure. For example, the corrected F statistic has Fisher's F distribution with reduced degrees of freedom. The corrected statistic reduces to the F statistic computed by ignoring clustering when the intraclass correlations are zero. It reduces to the F statistic computed using cluster means when the intraclass correlations are unity, and it is in between otherwise. A similar adjustment to the usual statistic for testing a linear contrast among group means is described.     

Some Cautions for Research on Personality and Health

This article comments on three conceptualizations of the relationship between personality and disease as they relate to the papers in this issue. Despite the sophistication and promise of recent research in this area, conceptual and methodological difficulties present in earlier psychosomatic research have persisted. In this area, robust and convincing associations between traits and disease remain largely elusive, and stable, valid measures of psychological factors are relatively rare. In addition, the mechanisms relating behavior to health are sometimes sketchy or overstated. We suggest that the most productive research strategies will focus on mechanisms linking behavior to health, rather than merely correlating traits with measures of disease. Needed are continued close attention to these pitfalls by researchers as well as the maintenance of a critical attitude by readers.     

Adaptation level as an explanation of the peak shift in generalization with movement stimuli

Two experiments examine the value of adaptation level theory as an explanation of the peak shift phenomenon in stimulus generalization using linear arm movements. The first experiment manipulates the differences in adaptation levels during training by varying the frequency of experience of the training stimulus. Significant shifts in the peaks of generalization gradients were subsequently identified. The peak shifts were in the direction predicted by adaptation level theory. The second experiment manipulates testing adaptation levels by biasing the generalization test movements. Three groups of subjects performed differentially weighted test sequences in which the relative number of short, medium, or long movements was manipulated. Significant peak shifts of generalization gradients were observed in the direction predicted by adaptation level theory.     

Preschool children's mathematical knowledge: The effect of teacher "math talk."

This study examined the relation between the amount of mathematical input in the speech of preschool or day-care teachers and the growth of children's conventional mathematical knowledge over the school year. Three main findings emerged. First, there were marked individual differences in children's conventional mathematical knowledge by 4 years of age that were associated with socioeconomic status. Second, there were dramatic differences in the amount of math-related talk teachers provided. Third, and most important, the amount of teachers' math-related talk was significantly related to the growth of preschoolers' conventional mathematical knowledge over the school year but was unrelated to their math knowledge at the start of the school year.     

Trends in Gender Differences in Academic Achievement from 1960 to 1994: An Analysis of Differences in Mean,Variance, and Extreme Scores

Gender differences in academic achievement have been studied extensively. While it is generally agreed that females have a slight advantage on average in verbal abilities and males have a slight advantage on average in mathematics, it is unclear whether these differences have changed over time. In this paper evidence from seven surveys representative of the United States twelth grade student population and the National Assessment of Educational Progress(NAEP) long term trend data is brought to bear on the magnitude of gender differences in achievement, the level of agreement among different indices of difference, and the stability of these differences over time. These data provide the unique opportunity to not only empirically estimate mean differences, differences in variance, and differences in extreme scores, but also to estimate change over time in all three indices using both the same and different tests over time. Results show that gender differences in mean and variance are small, while differences in extreme scores are often substantial. None of these differences have changed significantly since 1960, with the possible exception of mean differences in mathematics and science. Each of the datasets reflects the racial composition of the national population when properly weighted (i.e. White = 70%, Black = 15%,Hispanic = 10%, Other = 5%).