The diamond ratio: A visual indicator of the extent of heterogeneity in meta-analysis

The result of a meta-analysis is conventionally pictured in the forest plot as a diamond, whose length is the 95% confidence interval (CI) for the summary measure of interest. The Diamond Ratio (DR) is the ratio of the length of the diamond given by a random effects meta-analysis to that given by a fixed effect meta-analysis. The DR is a simple visual indicator of the amount of change caused by moving from a fixed-effect to a random-effects meta-analysis. Increasing values of DR greater than 1.0 indicate increasing heterogeneity relative to the effect variances. We investigate the properties of the DR, and its relationship to four conventional but more complex measures of heterogeneity. We propose for the first time a CI on the DR, and show that it performs well in terms of coverage. We provide example code to calculate the DR and its CI, and to show these in a forest plot. We conclude that the DR is a useful indicator that can assist students and researchers to understand heterogeneity, and to appreciate its extent in particular cases.     

From Modal Discourse to Possible Worlds

The possible-worlds semantics for modality says that a sentence is possibly true if it is true in some possible world. Given classical prepositional logic, one can easily prove that every consistent set of propositions can be embedded in a ‘maximal consistent set’, which in a sense represents a possible world. However the construction depends on the fact that standard modal logics are finitary, and it seems false that an infinite collection of sets of sentences each finite subset of which is intuitively ‘possible’ in natural language has the property that the whole set is possible. The argument of the paper is that the principles needed to shew that natural language possibility sentences involve quantification over worlds are analogous to those used in infinitary modal logic.     

Knowledge to Wisdom: We Need a Revolution

Introduction The following document is a very brief summary of a thesis and argument that I have devoted the last 30 years of my life to trying to get across to my fellow human beings. It was first spelled out in What’s Wrong With Science? (Bran’s Head Books, 1976) and subsequently in From Knowledge to Wisdom (Blackwell, 1984), Is Science Neurotic? (Imperial College Press, 2004) and numerous articles, references to which can be found on . Three years ago an international group was formed, called Friends of Wisdom, which seeks to get across to academics and the public the compelling arguments and urgent need to transform academic inquiry so that its basic aim becomes to seek and promote wisdom. The document below is taken from the website of Friends of Wisdom, the URL of which is . It is the mission statement of Friends of Wisdom. You are invited to join.     

Cognitive demands of error processing associated with preparation and execution of a motor skill

Maxwell et al. [Maxwell, J. P., Masters, R. S. W., Kerr, E., & Weedon, E. (2001). The implicit benefit of learning without errors. The Quarterly Journal of Experimental Psychology, 54A, 1049–1068. The implicit benefit of learning without errors. The Quarterly Journal of Experimental Psychology, 54A, 1049–1068] suggested that, following unsuccessful movements, the learner forms hypotheses about the probable causes of the error and the required movement adjustments necessary for its elimination. Hypothesis testing is an explicit process that places demands on cognitive resources. Demands on cognitive resources can be identified by measuring probe reaction times (PRT) and movement times. Lengthened PRT and movement times reflects increased cognitive demands. Thus, PRT and movement times should be longer following errors, relative to successful, movements. This hypothesis was tested using a motor skill (golf putting). Furthermore, the association between error processing and the preparation and execution phases of movement was examined. The data confirmed that cognitive demand is greater for trials following an error, relative to trials without an error. This effect was apparent throughout learning and in both the preparatory and execution phases of the movement. Cognitive effort also appeared to be higher during movement preparation, relative to movement execution.     

Peers,Social Control,or Guilt? Self-Conscious Emotions as Explanation for Antisocial Behavior

Criminologists rarely include self-conscious emotions like guilt or shame to explain delinquency. Instead, factors external to the individual are often used, such as social institutions, the family, or peers. This study uses a longitudinal sample of 526 youth from two waves of survey data to assess the effects of peer influences, social control, and the self-conscious emotion of guilt on youth problem behaviors. Problem behavior is measured using teacher assessments at Time2. All other variables are baseline youth self-report measures that were collected at Time1. The results show that guilt statistically predicted teacher-assessed problem behaviors. Further work is needed to develop this measure in criminology.     

Maternal Prenatal Stress and Other Developmental Risk Factors for Adolescent Depression: Spotlight on Sex Differences

Maternal stress during pregnancy has been linked to premorbid abnormalities associated with depression (e.g., difficult temperament, cognitive deficits) in offspring. However, few studies have looked across developmental periods to examine maternal stress during pregnancy and offspring depression during adolescence and whether these associations differ by sex. The current study used data from 1711 mother-offspring dyads (offspring sex: 49.8% male) in a longitudinal birth cohort study. Maternal narratives collected during pregnancy were qualitatively coded for stress-related themes by independent raters. Latent class analysis (LCA) identified distinct subgroups of offspring based on exposure to maternal prenatal stress and other developmental factors from the prenatal, childhood, and adolescent periods that have been associated with depression and/or maternal prenatal stress. LCA identified subgroups that were compared to determine whether and to what extent they differed on adolescent depressive symptoms. LCA revealed a subgroup of “high-risk” individuals, characterized by maternal factors during pregnancy (higher ambivalence/negativity and lower positivity towards the pregnancy, higher levels of hassles, lower maternal education and higher maternal age at birth, higher pre-pregnancy BMI) and offspring developmental factors (decreased cognitive functioning during childhood and adolescence, lower perceived parental support during adolescence, and higher levels of maternal depression during adolescence). High-risk females exhibited elevated conduct symptoms and higher birth order, while high-risk males exhibited decreased internalizing symptoms and lower birth order. Both high-risk males and females reported elevated depressive symptoms during adolescence relative to their “low-risk” counterparts.     

Inspection Times and the Selection Task: Are They Relevant?

Five experiments are reported based upon Evans' (1996) inspection time paradigm in which subjects are required to solve computer-presented Wason Selection Task problems while simultaneously using a mouse to indicate which card is currently under consideration. It had previously been found that selected cards were inspected for considerably longer than were non-selected cards, and this was taken as support for the existence of pre-conscious heuristics that direct attention towards relevant aspects of a problem. The first experiment reported here fully replicated this effect. However, by systematically varying the task format in subsequent experiments, the effect was found to diminish, disappear, or even reverse. The change in effect size and direction was not accompanied by any systematic variations in the subjects' card choices, indicating that the changes in taskformat had not altered the operation of the relevance-determining heuristics. On balance, it is suggested that the inspection time effect appears to be artefactual, and the inspection time paradigm therefore does not constitute satisfactory evidence for the existence of pre-conscious heuristics.     

Predicting belief in paranormal phenomena: a comparison of conditional and probabilistic reasoning

Previous studies, using student participants, have investigated conditional reasoning (Wierzbicki, 1985) and probabilistic reasoning (Blackmore and Troscianko, 1985) separately as predictors of belief in paranormal phenomena. Findings show that the fewer reasoning errors made, the less likely people are to believe. The current study investigated both types of reasoning within the same analysis in order to find the extent to which each would predict paranormal belief by itself. Sixty‐five non‐undergraduate participants completed two self‐report questionnaires to ascertain their degree of belief in the paranormal, and a reasoning test. The expected negative correlation between reasoning ability and paranormal belief was found. However, while conditional reasoning scores predicted paranormal belief (r=−0.27), probabilistic reasoning scores did not (r=0.01). It was noted that the sample used was possibly biased, due to a lack of sufficiently sceptical participants, and that future studies may need to target people with different degrees of belief. Copyright © 1999 John Wiley & Sons, Ltd.