Miguel A. García-Pérez

Forced-choice staircases with fixed step sizes: asymptotic and small-sample properties.

Visual detection and discrimination thresholds are often measured using adaptive staircases, and most studies use transformed (or weighted) up/down methods with fixed step sizes--in the spirit of Wetherill and Levitt (Br J Mathemat Statist Psychol 1965;18:1-10) or Kaernbach (Percept Psychophys 1991;49:227-229)--instead of changing step size at each trial in accordance with best-placement rules--in the spirit of Watson and Pelli (Percept Psychophys 1983;47:87-91). It is generally assumed that a fixed-step-size (FSS) staircase converges on the stimulus level at which a correct response occurs with the probabilities derived by Wetherill and Levitt or Kaernbach, but this has never been proved rigorously. This work used simulation techniques to determine the asymptotic and small-sample convergence of FSS staircases as a function of such parameters as the up/down rule, the size of the steps up or down, the starting stimulus level, or the spread of the psychometric function. The results showed that the asymptotic convergence of FSS staircases depends much more on the sizes of the steps than it does on the up/down rule. Yet, if the size delta+ of a step up differs from the size delta- of a step down in a way that the ratio delta-/delta+ is constant at a specific value that changes with up/down rule, then convergence percent-correct is unaffected by the absolute sizes of the steps. For use with the popular one-, two-, three- and four-down/one-up rules, these ratios must respectively be set at 0.2845, 0.5488, 0.7393 and 0.8415, rendering staircases that converge on the 77.85%-, 80.35%-, 83.15%- and 85.84%-correct points. Wetherill and Levitts transformed up/down rules--which require delta-/delta+ = 1--and the general version of Kaernbachs weighted up/down rule--which allows any delta-/delta+ ratio--fail to reach their presumed targets. The small-sample study showed that, even with the optimal settings, short FSS staircases (up to 20 reversals in length) are subject to some bias, and their precision is less than reasonable, but their characteristics improve when the size delta+ of a step up is larger than half the spread of the psychometric function. Practical recommendations are given for the design of efficient and trustworthy FSS staircases.

Cellwise Residual Analysis in Two-Way Contingency Tables

MacDonald and Gardner reported the results of a comparative study of two post hoc cellwise tests in 3 X 4 contingency tables under the independence and homogeneity models. Based on their results, they advised against the use of standardized residuals and in favor of adjusted residuals. Here the authors show that the comparison was biased in favor of adjusted residuals because of a failure to consider the nonunit variance of standardized residuals. The authors define a moment-corrected standardized residual that overcomes this bias and present the results of a thorough study including two-way tables of all dimensions between 2 X 2 and 8 X 12 that aimed at comparing moment-corrected standardized residuals with adjusted residuals. Across the entire set of table dimensions included in this study, the results reveal that both residuals yield essentially the same pat-tern of cell-by-cell and experimentwise Type I error rates when the data come from variables with uniform marginal distributions. When the data come from variables with peaked marginal distributions, adjusted residuals behave minimally better than moment-corrected residuals.

A Point Mutation in a Domain of Gamma Interferon Receptor 1 Provokes Severe Immunodeficiency

ABSTRACT Gamma interferon (IFN-γ) and the cellular responses induced by it are essential for controlling mycobacterial infections. Most patients bearing an IFN-γ receptor ligand-binding chain (IFN-γR1) deficiency present gross mutations that truncate the protein and prevent its expression, giving rise to severe mycobacterial infections and, frequently, a fatal outcome. In this report a new mutation that affects the IFN-γR1 ligand-binding domain in a Spanish patient with mycobacterial disseminated infection and multifocal osteomyelitis is characterized. The mutation generates an amino acid change that does not abrogate protein expression on the cellular surface but that severely impairs responses after the binding of IFN-γ (CD64 and HLA class II induction and tumor necrosis factor alpha and interleukin-12 production). A patients younger brother, who was also probably homozygous for the mutation, died from meningitis due toMycobacterium bovis. These findings suggest that a point mutation may be fatal when it affects functionally important domains of the receptor and that the severity is not directly related to a lack of IFN-γ receptor expression. Future research on these nontruncating mutations will make it possible to develop new therapeutical alternatives in this group of patients.

Luminance artifacts of cathode-ray tube displays for vision research

Phosphor persistence, video bandwidth, DC restoration and high-voltage regulation affect the appearance of images presented on cathode-ray tubes (CRTs), potentially resulting in differences between nominal and actual stimuli. We illustrate these effects by measuring physical parameters of horizontal and vertical static and counter-phase flickering gratings, and we illustrate problems for vision research by measuring contrast sensitivity to these gratings. We also measured the extent to which calibration protocols actually result in the monitor being calibrated over its entire area regardless of image size. The results of our physical measurements indicate substantial differences between gratings that nominally differ only as to orientation. Consistent with these differences, our psychophysical measurements indicate different sensitivities when the bars of the gratings are parallel or orthogonal to raster lines, regardless of the retinal orientation of the gratings. The results of our calibration check show that only a small region around the target area of calibration can be regarded as effectively linearized, and only if the size of the test image used during the check is similar to the size of the calibration patch. Overall, our results indicate potentially severe problems with the use of CRTs in vision research, and we discuss some published results that are likely to have been affected by these problems.

Yes-no staircases with fixed step sizes: psychometric properties and optimal setup.

Interest in the use of adaptive staircase methods in clinical practice is increasing, but time limitations require that they be based on yes-no trials. The psychometric properties of yes-no staircases with fixed step sizes (FSS staircases) in small-sample situations have never been studied in depth. As a result, information is lacking as to what is the optimal setup for an FSS staircase. To determine this optimal setup, we used simulation techniques to study the asymptotic and small-sample convergence of yes-no FSS staircases as a function of the up/down rule, the size of the steps up or down, the starting stimulus level, the spread of the psychometric function, and the lapsing rate. Our results indicate that yes-no FSS staircases with steps up and down of the same size are unstable because with these settings, the staircases yield different results across variations in irrelevant parameters such as the spread of the psychometric function or the starting level. Our study also identified settings with which the properties of estimates are unaffected by these factors. With these optimal settings, yes-no FSS staircases can provide very quick and accurate estimates in 7 to 8 trials. Practical recommendations are given to get the best out of yes-no FSS staircases.

Shifts of the psychometric function: Distinguishing bias from perceptual effects

Morgan, Dillenburger, Raphael, and Solomon have shown that observers can use different response strategies when unsure of their answer, and, thus, they can voluntarily shift the location of the psychometric function estimated with the method of single stimuli (MSS; sometimes also referred to as the single-interval, two-alternative method). They wondered whether MSS could distinguish response bias from a true perceptual effect that would also shift the location of the psychometric function. We demonstrate theoretically that the inability to distinguish response bias from perceptual effects is an inherent shortcoming of MSS, although a three-response format including also an “undecided” response option may solve the problem under restrictive assumptions whose validity cannot be tested with MSS data. We also show that a proper two-alternative forced-choice (2AFC) task with the three-response format is free of all these problems so that bias and perceptual effects can easily be separated out. The use of a three-response 2AFC format is essential to eliminate a confound (response bias) in studies of perceptual effects and, hence, to eliminate a threat to the internal validity of research in this area.

The Role of Parametric Assumptions in Adaptive Bayesian Estimation.

Variants of adaptive Bayesian procedures for estimating the 5% point on a psychometric function were studied by simulation. Bias and standard error were the criteria to evaluate performance. The results indicated a superiority of (a) uniform priors, (b) model likelihood functions that are odd symmetric about threshold and that have parameter values larger than their counterparts in the psychometric function, (c) stimulus placement at the prior mean, and (d) estimates defined as the posterior mean. Unbiasedness arises in only 10 trials, and 20 trials ensure constant standard errors. The standard error of the estimates equals 0.617 times the inverse of the square root of the number of trials. Other variants yielded bias and larger standard errors.

Statistical conclusion validity: some common threats and simple remedies.

The ultimate goal of research is to produce dependable knowledge or to provide the evidence that may guide practical decisions. Statistical conclusion validity (SCV) holds when the conclusions of a research study are founded on an adequate analysis of the data, generally meaning that adequate statistical methods are used whose small-sample behavior is accurate, besides being logically capable of providing an answer to the research question. Compared to the three other traditional aspects of research validity (external validity, internal validity, and construct validity), interest in SCV has recently grown on evidence that inadequate data analyses are sometimes carried out which yield conclusions that a proper analysis of the data would not have supported. This paper discusses evidence of three common threats to SCV that arise from widespread recommendations or practices in data analysis, namely, the use of repeated testing and optional stopping without control of Type-I error rates, the recommendation to check the assumptions of statistical tests, and the use of regression whenever a bivariate relation or the equivalence between two variables is studied. For each of these threats, examples are presented and alternative practices that safeguard SCV are discussed. Educational and editorial changes that may improve the SCV of published research are also discussed.

A multidimensional extension to Hirsch’s h-index

The h-index is becoming a reference tool for career assessment and it is starting to be considered by some agencies and institutions in promotion, allocation, and funding decisions. In areas where h indices tend to be low, individuals with different research accomplishments may end up with the same h. This paper proposes a multidimensional extension of the h index in which the conventional h is only the first component. Additional components of the multidimensional index are obtained by computing the h-index for the subset of papers not considered in the immediately preceding component. Computation of the multidimensional index for 204 faculty members in Departments of Methodology of the Behavioral Sciences in Spain shows that individuals with the same h can indeed be distinguished by their values in the remaining components, and that the strength of the correlation of the second and third components of the multidimensional index with alternative bibliometric indicators is similar to that of the first component (i.e., the original h).

Interval bias in 2AFC detection tasks: sorting out the artifacts

Proportion correct in two-alternative forced choice (2AFC) detection tasks often varies when the stimulus is presented in the first or in the second interval. Reanalysis of published data reveals that these order effects (or interval bias) are strong and prevalent, refuting the standard difference model of signal detection theory. Order effects are commonly regarded as evidence that observers use an off-center criterion under the difference model with bias. We consider an alternative difference model with indecision whereby observers are occasionally undecided and guess with some bias toward one of the response options. Whether or not the data show order effects, the two models fit 2AFC data indistinguishably, but they yield meaningfully different estimates of sensory parameters. Under indeterminacy as to which model governs 2AFC performance, parameter estimates are suspect and potentially misleading. The indeterminacy can be circumvented by modifying the response format so that observers can express indecision when needed. Reanalysis of published data collected in this way lends support to the indecision model. We illustrate alternative approaches to fitting psychometric functions under the indecision model and discuss designs for 2AFC experiments that improve the accuracy of parameter estimates, whether or not order effects are apparent in the data.