Illusory correlation,group size and memory

Two studies were conducted to test the predictions of a multi-component model of distinctiveness-based illusory correlation (IC) regarding the use of episodic and evaluative information in the production of the phenomenon. Extending on the standard paradigm, participants were presented with 4 groups decreasing in size, but all exhibiting the same ratio of positive to negative behaviours. Study 1 (N = 75) specifically tested the role of group size and distinctiveness, by including a zero-frequency cell in the design. Consistent with predictions drawn from the proposed model, with decreasing group size, the magnitude of the IC effect showed a linear increase in judgments thought to be based on evaluative information. In Study 2 (N = 43), a number of changes were introduced to a group assignment task (double presentation, inclusion of decoys) that allowed a more rigorous test of the predicted item-specific memory effects. In addition, a new multilevel, mixed logistic regression approach to signal-detection type analysis was used, providing a more flexible and reliable analysis than previously. Again, with decreasing group size, IC effects showed the predicted monotonic increase on the measures (group assignment frequencies, likability ratings) thought to be dependent on evaluative information. At the same time, measures thought to be based on episodic information (free recall and group assignment accuracy) partly revealed the predicted enhanced episodic memory for smaller groups and negative items, while also supporting a distinctiveness-based approach. Additional analysis revealed that the pattern of results for judgments though to be based on evaluative information was independent of interpersonal variation in behavioral memory, as predicted by the multi-component model, and in contrast to predictions of the competing models. The results are discussed in terms of the implications of the findings for the proposed mechanisms of illusory correlation.     

Efficiency in data gathering: Set size effects in the selection task

Two experiments were conducted with variants of Wason's (1966 Wason, P. C. 1966. “Reasoning”. In New horizons in psychology, Edited by: Foss, B. M. Harmondsworth, , UK: Penguin.  [Google Scholar]) selection task. The common focus was the effect of differences in the sizes of the sets represented by P and not-Q in assertions of the form If P then Q (conditional) or All P are Q (categorical). Results support the conclusion that such set size differences affect the strategies people adopt when asked to determine, efficiently, the truth or falsity of such assertions, but they do not entirely negate the tendency to select the term represented by P (the antecedent of the conditional or the subject of the categorical) in preference to the term represented by not-Q (the complement of the consequent of the conditional or the complement of the predicate of the categorical). Several possible explanations of this perseverance are considered. Results also support the conclusion that people find it easier to assess categorical assertions than logically equivalent conditional assertions.     

Point-biserial correlation: Interval estimation,hypothesis testing,meta-analysis,and sample size determination

The point-biserial correlation is a commonly used measure of effect size in two-group designs. New estimators of point-biserial correlation are derived from different forms of a standardized mean difference. Point-biserial correlations are defined for designs with either fixed or random group sample sizes and can accommodate unequal variances. Confidence intervals and standard errors for the point-biserial correlation estimators are derived from the sampling distributions for pooled-variance and separate-variance versions of a standardized mean difference. The proposed point-biserial confidence intervals can be used to conduct directional two-sided tests, equivalence tests, directional non-equivalence tests, and non-inferiority tests. A confidence interval for an average point-biserial correlation in meta-analysis applications performs substantially better than the currently used methods. Sample size formulas for estimating a point-biserial correlation with desired precision and testing a point-biserial correlation with desired power are proposed. R functions are provided that can be used to compute the proposed confidence intervals and sample size formulas.     

The occurrence of an increase in correlation by restriction of range

Given three variables,x, y, z, univariate selection onx, usually reduces the correlationr _{y z} . However, in some cases, whenr _{x y} orr _{x z} assumes extreme values,r _{y z} may increase. This reversal is explained by comparison to the effects of suppressor variables and predictors of predictability.     

The effects of degree of learning,meaning, and invidual differences on the feeling-of-knowing

Research on the feeling-of-knowing (FOK) phenomenon has established it as a valid indicator of the contents of memory and a reliable predictor of subsequent performance. It has been shown that degree of prior learning of items is one factor upon which FOK is based — the ‘overlearning’ effect. The present study was designed to determine, firstly, whether the overlearning effect is due to different numbers of presentations of physical attributes during learning, to encoding variability, or to both, and secondly, whether individual differences in the cognitive style variable of category width affect FOK judgments or accuracy. Using a delayed recall-FOK judgment-recognition paradigm, measures on these tests were obtained from narrow and broad categorizers, who learned paired-associate items to a criterion of 1 or 3 correct recalls. The target item, a homograph, to be produced in response to the cue, a number, was learned either as a word of single or multiple meaning. Results showed that a greater degree of learning did not increase FOK magnitude or accuracy, although it did increase recall and overall recognition. On the other hand, category width and encoding variability did not affect recall and recognition, but did influence magnitude and accuracy of FOK: Broad categorizers gave higher FOK ratings than narrow, and when single meanings of the target only were learned, broad categorizers gave higher ratings than narrow. This finding was not replicated in the accuracy of FOK responses: Broad categorizers were more accurate for multiple target encoding but less accurate for single. Thus FOK is influenced by semantic aspects of the target in different ways by subjects exhibiting different cognitive styles. The study places FOK firmly in the metamemory domain.     

Mental comparison of size and magnitude: size congruity effects

Paivio (1975) found that the latency to choose the larger of two named objects does not depend on congruity between the object sizes and the sizes of the object names. Because size congruity does affect latencies for pictorially presented objects, Paivio interpreted this result as support for the dual coding hypothesis. However, Experiment 1 demonstrated that Paivio's results were an artifact of his experimental design. Size congruity does affect latencies to choose the larger of two named objects when object pairs are not repeated. When the same object pairs are used repeatedly, as in Paivio's experiment, the effect disappears. In this case the response is probably remembered, so that the objects need not be compared. To determine the processing stages affected by size congruity, both the distance between stimulus sizes and the size congruity were manipulated in Experiment 2. Three groups of subjects chose either the greater Arabic digit, the greater named digit, or the larger named object. Size congruity interacted with distance only for Arabic digits. For both Arabic digits and named digits, the interference caused by size incongruity was greater than the facilitation caused by size congruity, whereas for object names, the facilitation was greater than the interference. A model of the interaction between physical size comparisons and conceptual size comparisons is proposed to account for these results.     

The proper sequence for correcting correlation coefficients for range restriction and unreliability

Corrections of correlations for range restriction (i.e., selection) and unreliability are common in psychometric work. The current rule of thumb for determining the order in which to apply these corrections looks to the nature of the reliability estimate (i.e., restricted or unrestricted). While intuitive, this rule of thumb is untenable when the correction includes the variable upon which selection is made, as is generally the case. Using classical test theory, we show that it is the nature of the range restriction, not the nature of the available reliability coefficient, that determines the sequence for applying corrections for range restriction and unreliability.We would like to thank Malcolm James Ree for his encouragement and helpful comments as well as those of the editors, associate editor, and reviewers.     

Multiple correlation: exact power and sample size calculations

This article discusses power and sample size calculations for observational studies in which the values of the independent variables cannot be fixed in advance but are themselves outcomes of the study. It reviews the mathematical framework applicable when a multivariate normal distribution can be assumed and describes a method for calculating exact power and sample sizes using a series expansion for the distribution of the multiple correlation coefficient. A table of exact sample sizes for level .05 tests is provided. Approximations to the exact power are discussed, most notably those of Cohen (1977). A rigorous justification of Cohen's approximations is given. Comparisons with exact answers show that the approximations are quite accurate in many situations of practical interest. More extensive tables and a computer program for exact calculations can be obtained from the authors.     

Prehension in children and adults: The effects of object size

Studies of visually goal-directed arm movements in adults have shown that various task constraints such as intention, context, and object properties affect different kinematic characteristics of the movement components (Jeannerod, 1984; MacKenzie et al., 1987; Marteniuk et al., 1987, 1990; Paulignan et al., 1991; Soechting, 1984). The purpose of the present study was to compare the effects of varying object size on the kinematics of reaching and grasping in both children and adults. Five children aged 9–10 years and five adults aged 18–24 years reached for and grasped three different sized cubes. Results revealed that object size had the same effect on the planning and control of reaching and grasping movements in children as in adults. Unlike adults, however, children in this age range spent more time in deceleration and reached peak aperture much later in the movement trajectory. The results were interpreted as immature integration of the visual and proprioceptive systems in 9–10 year olds. The implications of these findings for further examining developmental trends in prehension are discussed.PsycINFO classification: 2330     

The representation of multiplication facts: developmental changes in the problem size, five, and tie effects

In this study, we investigated the development of basic effects that have been found in single-digit multiplication arithmetic: the problem size, five, and tie effects. Participants (9-, 10-, and 11-year-olds and adults) performed a production task on simple multiplication. The procedure replicated study [Canadian Journal of Psychology, Vol. 39, pp. 338-366], but the results show that the gradual decrease of the problem size effect ends in sixth grade. We report analyses on raw latencies and state trace analyses that take into account reaction time scaling as a function of age. The results show that 11-year-olds do not differ significantly from adults on any of the three effects. Before 11 years of age, interesting developmental changes occur.     

The occurrence of an increase in correlation with explicit selection

It is generally believed that correlations and standard deviations measured within an explicitly selected group must be smaller than those within an applicant population. A small data set is used to show that this is not always true, and that both validity and reliability estimates within a selected group can exceed those within the applicant population. The increase in correlation within the explicitly selected group is tied to an increase in standard deviation of the predictor in the selected group. This conclusion extends Levin's (1972) result for the case of incidental selection, selection on an unmeasured third variable. If possible, theoretical derivations should not be limited to the case where the predictor standard deviation in the applicant population exceeds that in the selected group. When such a situation occurs in observed data, it cannot be immediately dismissed as an artifact.The author would like to thank Mark L. Davison and other reviewers for their comments on earlier drafts of the paper. An anonymous reviewer provided a better example than the original one, resulting in a more general conclusion.This work was supported in part by a Dissertation Fellowship from the University of Minnesota.     

The effects of size,clutter, and complexity on vanishing-point distances in visual imagery

Summary The portrayal of vanishing-point distances in visual imagery was examined in six experiments. In all experiments, subjects formed visual images of squares, and the squares were to be oriented orthogonally to subjects' line of sight. The squares differed in their level of surface complexity, and were either undivided, divided into 4 equally sized smaller squares, or divided into 16 equally sized smaller squares. Squares also differed in stated referent size, and ranged from 3 in. to 128 ft along each side. After subjects had formed an image of a specified square, they transformed their image so that the square was portrayed to move away from them. Eventually, the imaged square was portrayed to be so far away that if it were any further away, it could not be identified. Subjects estimated the distance to the square that was portrayed in their image at that time, the vanishing-point distance, and the relationship between stated referent size and imaged vanishing-point distance was best described by a power function with an exponent less than 1. In general, there were trends for exponents (slopes on log axes) to increase slightly and for multiplicative constants (y intercepts on log axes) to decrease as surface complexity increased. No differences in exponents or in multiplicative constants were found when the vanishing-point was approached from either sub-threshold or suprathreshold directions. When clutter in the form of additional imaged objects located to either side of the primary imaged object was added to the image, the exponent of the vanishing-point function increased slightly and the multiplicative constant decreased. The success of a power function (and the failure of the size-distance invariance hypothesis) in describing the vanishing-point distance function calls into question the notions (a) that a constant grain size exists in the, imaginal visual field at a given location and (b) that grain size specifies a lower limit in the storage of information in visual images.     

The effects of selection in factor analysis

Factorial results are affected by selection of subjects and by selection of tests. It is shown that the addition of one or more tests which are linear combinations of tests already in a battery causes the addition of one or more incidental factors. If the given test battery reveals a simple structure, the addition of tests which are linear combinations of the given tests leaves the structure unaffected unless the number of incidental factors is so large that the common factors become indeterminate.     

Some multiple correlation and predictor selection methods

The Doolittle, Wherry-Doolittle, and Summerfield-Lubin methods of multiple correlation are compared theoretically as well as by an application in which a set of predictors is selected. Wherry's method and the Summerfield-Lubin method are shown to be equivalent; the relationship of these methods to the Doolittle method is indicated. The Summerfield-Lubin method, because of its compactness and ease of computation, and because of the meaningfulness of the interim computational values, is recommended as a convenient least squares method of multiple correlation and predictor selection.