Literature Index

Statistics is taught in all Singapore schools as part of the compulsory subject mathematics. Only at the university level may statistics be offered as a subject by itself, in the Department of Economics and Statistics. In attempting to make every school-leaver numerate and literate the statistics taught at the school level is meant to equip an individual with the ability to interpret and understand correctly the data presented in tables, diagrams, charts, and graphs. It is the concern of every mathematics teacher in school that pupils should know enough about simple statistics to be able to interpret them correctly and not be deceived by them.

Attribution theory, in its broadest sense, is concerned with the attempts of ordinary people to understand the causes and implications of the events they witness. It deals with the "naive psychology" of people as they interpret their own behavior and the actions of others. The current ascendancy of attribution theory in social psychology thus culminates a long struggle to upgrade that discipline's conception of man. No longer the stimulus-response (S-R) automation of radical behaviorism, promoted beyond the rank of information processor and cognitive consistency seeker, psychological man has at last been awarded a status equal to that of the scientist who investigates him. For in the perspective of attribution theory, people are intuitive psychologists who seek to explain behavior and to draw inferences about actors and about their social environments. The intuitive scientist's ability to master his social environment, accordingly, will depend upon the accuracy and adequacy of his hypotheses, evidence, and analyses. Conversely, any systematic errors in existing theories, biases in available data, or inadequacies in methods of analysis, yield serious consequences - both for the lay psychologist and for the society that he builds and perpetuates. These shortcomings, explored from the vantage point of contemporary attribution theory, provide the focus of this chapter.

Several editorial and institutional interventions in psychology have aimed to improve statistical reporting in journals. These efforts have sought to de-emphasise statistical significance and encourage alternative analyses, especially effect sizes and confidence intervals (CIs), but the interventions to date have had short-lived and superficial impact-if any impact at all. I review some of these interventions in psychology and discuss possible reasons for lack of success. I give an inter-disciplinary context by discussing reform efforts in medicine-in which useful reform has already been achieved-and ecology. I then identify statistics education as the next major challenge for reformers, and report data on students' understanding of CIs, and difficulties they have making appropriate interpretation of CIs. I explain the need for further evidence on which to base improved statistics education in psychology.

We present a critique showing the flawed logical structure of statistical significance tests. We then attempt to analyze, why, in spite of this faulty reasoning the use of significance tests persists. We identify the illusion of probabilistic proof by contradiction as a central stumbling block, because it is based on a misleading generalization of reasoning from logic to inference under uncertainty. We present new data from a student sample and examples from the psychological literature showing the strength and prevalence of this illusion. We identify some intrinsic cognitive mechanisms (similarity to modus tollens reasoning; verbal ambiguity in describing the meaning of significance tests; and the need to rule out chance findings) and extrinsic social pressures which help to maintain the illusion. We conclude by mentioning some alternative methods for presenting and analyzing psychological data, none of which can be considered the ultimate method.