The knowledge content of statistical data

An information-theoretic framework is used to analyze the knowledge content in multivariate cross classified data. Several related measures based directly on the information concept are proposed: the knowledge content (S) of a cross classification, its terseness (Zeta), and the separability (Gamma _X ) of one variable, given all others. Exemplary applications are presented which illustrate the solutions obtained where classical analysis is unsatisfactory, such as optimal grouping, the analysis of very skew tables, or the interpretation of well-known paradoxes. Further, the separability suggests a solution for the classic problem of inductive inference which is independent of sample size.     

Effects of lines of progress and semilogarithmic charts on ratings of charted data

The extent to which interrater agreement and ratings of significance on both changes in level and trend are affected by lines of progress and semilogarithmic charts was investigated. Thirteen graduate students rated four sets of charts, each set containing 19 phase changes. Set I data were plotted on equal interval charts. In Set II a line of progress was drawn through each phase on each chart. In Set III data points were replotted on semilogarithmic charts. In Set IV a line of progress was drawn through each phase of each Set III chart. A significant main effect on interrater agreement was found for lines of progress as well as a significant 2-way interaction between lines of progress and change type. Three main effects (chart type, lines of progress, and type of change) and a significant 3-way interaction were found for ratings of significance. Implications of these data for visual analysis of charted data are discussed.     

Statistical inference for false positive and false negative error rates in mastery testing

This paper describes an asymptotic inferential procedure for the estimates of the false positive and false negative error rates. Formulas and tables are described for the computations of the standard errors. A simulation study indicates that the asymptotic standard errors may be used even with samples of 25 cases as long as the Kuder-Richardson Formula 21 reliability is reasonably large. Otherwise, a large sample would be required.This work was performed pursuant to Grant No NIE-G-78-0087 with the National Institute of Education, Department of Health, Education and Welfare, Huynh Huynh, Principal Investigator. Points of view or opinions stated do not necessarily reflect NIE position or policy and no official endorsement should be inferred. The editorial assistance of Joseph C. Saunders is gratefully acknowledged.     

CRITICAL REALISM REDUX: A RESPONSE TO JOSH REEVES

This article combines an appreciation of several themes in Josh Reeves's Against Methodology in Science and Religion: Recent Debates on Rationality and Theology while arguing in favor of critical realism. The author holds that critical realism manages to combine the objective truth reached through inference and especially cognitive acts of judgment as well as the various, contingent historical contexts that also define where science is practiced. Reeves advocates a historical perspective, but this article claims that in order for critical realism to be credible, a philosophical perspective must be maintained.     

THEORIZING RELIGION AND QUESTIONING THE FUTURE OF ISLAM AND SCIENCE

Will there be any joint future for science and Islam? Although such questions have recently received considerable attention, more basic questions are often ignored. This article aims at addressing some of those more basic questions through exploring the assumptions that underlie different possible understandings of the question about the future of Islam and science. By investigating the relation between conceptualizations of religion and the question about the future of Islam and science, it will be argued that different understandings of the concept of religion (i.e., whether it denotes real objects, whether it is universal, and whether it is belief centered) lead to extremely different readings of the question. Besides, it will be argued that different answers to the question about the future of Islam and science can be understood in terms of the inference to best theological explanation; thus, the criteria that one assumes for the best theological explanation result in different criteria for evaluation of the answers.     

Valuing intervention and observation

Understanding causal relations is fundamental to effective action but causal data can be confounded. We examined the value that participants placed on data derived from a hypothetical intervention or observation. Our materials involved a possible cause (“bottled water”), a possible confound (“food”), and a context (“a restaurant”). We supposed that participants seek to draw as specific a causal inference as possible from presented data and value information sources more highly that allow them to do so. On this basis, we predicted that in circumstances where an intervention removed the confounding causal factor but observation did not, participants would prefer data derived from an intervention when the possible cause was present (the bottled water was drunk) but show the reverse preference when the possible cause was absent (the bottled water was not drunk). Experiment 1 confirmed this prediction. Using a between-subjects design, Experiment 2 tested for a difference in confidence in causal judgements given identical data, including data on the confound, as a function of method of data collection (intervention or observation). There was no significant difference in confidence ratings between the two methods but confidence ratings were sensitive to the probability of an effect (illness) given the cause. Using a within-subjects design, Experiment 3 revealed systematic individual differences in preference for the two methods. Participants were divided between those who considered intervention more confounded and those who considered observation more confounded. Our experiments point to the subtleties of participants' evaluation of data from studies of human beings.     

The influence of cognitive ability and instructional set on causal conditional inference

We report a large study in which participants are invited to draw inferences from causal conditional sentences with varying degrees of believability. General intelligence was measured, and participants were split into groups of high and low ability. Under strict deductive-reasoning instructions, it was observed that higher ability participants were significantly less influenced by prior belief than were those of lower ability. This effect disappeared, however, when pragmatic reasoning instructions were employed in a separate group. These findings are in accord with dual-process theories of reasoning. We also took detailed measures of beliefs in the conditional sentences used for the reasoning tasks. Statistical modelling showed that it is not belief in the conditional statement per se that is the causal factor, but rather correlates of it. Two different models of belief-based reasoning were found to fit the data according to the kind of instructions and the type of inference under consideration.     

Subjectivity and unconsciousness

Concepts of the unconscious were crucial to both Jung's and Freud's thinking. Psychoanalytic and analytical psychological views of the unconscious are compared and contrasted, and both are critically reviewed. It is suggested that we need to revise our conceptualization so as to take better account of the role of the analyst's expectations and inferences, and therefore of his or her subjectivity, whenever he or she makes a clinical judgement that unconscious mental processes are in operation. Some technical implications of a revised definition of unconsciousness are considered, especially indications for self-disclosure by an analyst of his or her own experience of events within the treatment.     

On aims and methods in the neuroimaging of derived relations

Ingenious and seemingly powerful technologies have been developed recently that enable the visualization in some detail of events in the brain concomitant upon the ongoing behavioral performance of a human participant. Measurement of such brain events offers at the very least a new set of dependent variables in relation to which the independent variables familiarly manipulated in the operant laboratory may be explored. Two related paradigms in which a start has been made in such research concern the derivation of novel or emergent relations from a baseline set of trained relations, and include the phenomenon of transitive inference (TI), observed in studies of stimulus equivalence (SE) and serial learning (SL) or seriation. This paper reviews some published and forthcoming neuroimaging studies of these and related phenomena, and considers how this line of research both demands and represents a welcome synthesis between types of question and levels of explanation in behavioral science that often have been seen as antithetical.     

Where do "constraints" come from? A comparison between inferences in biology and in word learning

In this paper, as a commentary on the papers in this special issue, the nature of constraints is discussed in terms of the comparison between inferences in biology and in word learning. Young children's inferences in biology could be constrained by three sources of information: factual knowledge, expectations based on a theory, and ontological knowledge. For example, young children's inference about the length of noses could be constrained by the facts the children know about the animals, the similarity between the animals and humans, and the ontological distinction between living things and nonliving things. In the same way, young children might figure out word meanings by linguistic and pragmatic knowledge, expectations of word meanings (e.g., the whole-object assumption), and ontological knowledge. Interactions among these sources of knowledge are documented by the papers in this special issue and related studies. It is argued that learning biases such as the whole-object assumption could not be induced only by linguistic and pragmatic cues in a social context, but should be regarded as a product of the interaction between a social context and children's theories.