Mathematical Psychology and Statistics

How prevalent is object-based attention?

by Sarah Creighton

Citation: Pilz KS, Roggeveen AB, Creighton SE, Bennett PJ, Sekuler AB (2012) How Prevalent Is Object-Based Attention? PLoS ONE 7(2): e30693. doi:10.1371/journal.pone.0030693

Previous research suggests that visual attention can be allocated to locations in space (space-based attention) and to... more Previous research suggests that visual attention can be allocated to locations in space (space-based attention) and to objects (object-based attention). The cueing effects associated with space-based attention tend to be large and are found consistently across experiments. Object-based attention effects, however, are small and found less consistently across experiments. In three experiments we address the possibility that variability in object-based attention effects across studies reflects low incidence of such effects at the level of individual subjects. Experiment 1 measured space-based and object-based cueing effects for horizontal and vertical rectangles in 60 subjects comparing commonly used target detection and discrimination tasks. In Experiment 2 we ran another 120 subjects in a target discrimination task in which rectangle orientation varied between subjects. Using parametric statistical methods, we found object-based effects only for horizontal rectangles. Bootstrapping methods were used to measure effects in individual subjects. Significant space-based cueing effects were found in nearly all subjects in both experiments, across tasks and rectangle orientations. However, only a small number of subjects exhibited significant object-based cueing effects. Experiment 3 measured only object-based attention effects using another common paradigm and again, using bootstrapping, we found only a small number of subjects that exhibited significant object-based cueing effects. Our results show that object-based effects are more prevalent for horizontal rectangles, which is in accordance with the theory that attention may be allocated more easily along the horizontal meridian. The fact that so few individuals exhibit a significant object-based cueing effect presumably is why previous studies of this effect might have yielded inconsistent results. The results from the current study highlight the importance of considering individual subject data in addition to commonly used statistical methods.

Information-sharing and aggregation models for interacting minds

by Piotr Migdal

Calculating and graphing within-subject confidence intervals for ANOVA

by Thom Baguley

Official/complete version:

Baguley, T. (2012). Calculating and graphing within-subject confidence intervals for ANOVA. Behavior Research Methods, 44, 158-175.

The psychological and statistical literature contains several proposals for calculating and plotting confidence... more The psychological and statistical literature contains several proposals for calculating and plotting confidence intervals for within-subject (repeated measures) ANOVA designs. A key distinction is between intervals supporting inference about patterns of means (and differences between pairs of means in particular) and those supporting individual means. It is argued that the former are best accomplished by adapting intervals proposed by Cousineau (2005) and Morey (2008) so that non-overlapping confidence intervals for individual means correspond to a confidence for their difference that does not include zero. The latter can be accomplished by fitting a multilevel model. In situations where both types of inference are of interest, the use of a two-tiered CI is recommended. Free open-source, cross-platform software for these interval estimates and plots (and for some common alternatives) is provided in the form of R functions for one-way within-subject and two-way mixed ANOVA designs. These functions provide an easy to use solution to the difficult problem of calculating and displaying within-subject confidence intervals.

Multiple groups of orientation-selective visual mechanisms underlying rapid orientated-line detection

by David Foster

Visual search for an edge or line element differing in orientation from a background of other edge or line elements... more Visual search for an edge or line element differing in orientation from a background of other edge or line elements can be performed rapidly and effortlessly. In this study, based on psychophysical measurements with ten human observers, threshold values of the angle between a target and background line elements were obtained as functions of background-element orientation, in brief masked displays. A repeated-loess analysis of the threshold functions suggested the existence of several groups of orientation-selective mechanisms contributing to rapid orientated-line detection; specifically, coarse, intermediate and fine mechanisms with preferred orientations spaced at angles of approximately 90 deg, 35-50 deg and 10-25 deg, respectively. The preferred orientations of coarse and some intermediate mechanisms coincided with the vertical or horizontal of the frontoparallel plane, but the preferred orientations of fine mechanisms varied randomly from observer to observer, possibly reflecting individual variations in neuronal sampling characteristics.

Approaching ideal observer efficiency in using color to retrieve information from natural scenes

by David Foster

Variations in illumination on a scene and trichromatic sampling by the eye limit inferences about scene content. The... more Variations in illumination on a scene and trichromatic sampling by the eye limit inferences about scene content. The aim of this work was to elucidate these limits in relation to an ideal observer using color signals alone. Simulations were based on 50 hyperspectral images of natural scenes and daylight illuminants with correlated color temperatures 4000 K, 6500 K, and 25,000 K. Estimates were made of the (Shannon) information available from each scene, the redundancies in receptoral and postreceptoral coding, and the information retrieved by an observer identifying corresponding points across image pairs. For the largest illuminant difference, between 25,000 K and 4000 K, a postreceptoral transformation providing minimum redundancy yielded an efficiency of about 80% in the information retrieved. This increased to about 89% when the transformation was optimized directly for information retrieved, corresponding to an equivalent Gaussian noise amplitude of 3.0% or to a mean of 3.6 x 10^4 distinct identifiable points per scene. Using color signals to retrieve information from natural scenes can approach ideal observer efficiency levels.

A new statistical power calculator

by Rory Allen

The website where you can find a working model of this calculator has moved from the one cited in the draft. It is now at:

http://homepages.gold.ac.uk/ps-tec/powercalculator

This short report describes a new graphical calculator of statistical power suitable for the simplest situation, of... more This short report describes a new graphical calculator of statistical power suitable for the simplest situation, of the two-group independent t-test. It overcomes the limitations of the power nomogram devised by Douglas Altman, and should be of value as a teaching tool.

An introduction to sphericity

by Thom Baguley