Fourier analysis of reaction time data

The popularity of the assumption of stages in models of the reaction time process and the availability of fast and efficient means of computing approximations to the Fourier transform makes the Fourier analysis of reaction time data attractive. This paper indicates some problems associated with such analyses and suggests convenient ways to overcome some of the difficulties.     

A transit-signal methodology for studying reaction time

A new general method has been devised for measuring reaction time, which combines the traditional transit and signal methods. Some applications are described. Advantages over the traditional procedures are considered.     

The symbolic distance effect for alphabetic order judgements: A subjective report and reaction time analysis

The time needed to decide whether a pair of letters is in the correct alphabetic order varies inversely with alphabetic separation. This is an example of a phenomenon generally found with the comparison of ordered symbols or concepts, called the symbolic distance effect (Moyer and Bayer, 1976). It is argued that when letters are compared, an important determinant of this effect is the degree to which subjects subvocally run-through parts of the alphabet to determine the correctness of the order of a stimulus pair. A trial-by-trial introspection procedure coupled with reaction time measurements is used in the present experiment, in which letter order judgements were made over a range of separations. RTs increased with increasing number of letters in the reported run-through. At small letter separations, run-through occurred more frequently, and this was found to be the basis of the symbolic distance effect. For trials on which no run-through was reported the symbolic distance effect was absent. The data are summarized as a model in which comparisons are made from directly available order information from memory, or with an additional run-through process. The details of the run-through process suggest that groupings learned in childhood are probably involved in the selection of the starting letter for run-through.     

CDF-XL: computing cumulative distribution functions of reaction time data in Excel

In experimental psychology, central tendencies of reaction time (RT) distributions are used to compare different experimental conditions. This emphasis on the central tendency ignores additional information that may be derived from the RT distribution itself. One method for analysing RT distributions is to construct cumulative distribution frequency plots (CDFs; Ratcliff, Psychological Bulletin 86:446–461, 1979). However, this method is difficult to implement in widely available software, severely restricting its use. In this report, we present an Excel-based program, CDF-XL, for constructing and analysing CDFs, with the aim of making such techniques more readily accessible to researchers, including students (CDF-XL can be downloaded free of charge from the Psychonomic Society’s online archive). CDF-XL functions as an Excel workbook and starts from the raw experimental data, organised into three columns (Subject, Condition, and RT) on an Input Data worksheet (a point-and-click utility is provided for achieving this format from a broader data set). No further preprocessing or sorting of the data is required. With one click of a button, CDF-XL will generate two forms of cumulative analysis: (1) “standard” CDFs, based on percentiles of participant RT distributions (by condition), and (2) a related analysis employing the participant means of rank-ordered RT bins. Both analyses involve partitioning the data in similar ways, but the first uses a “median”-type measure at the participant level, while the latter uses the mean. The results are presented in three formats: (i) by participants, suitable for entry into further statistical analysis; (ii) grand means by condition; and (iii) completed CDF plots in Excel charts.     

Stage analysis of the reaction process using brain-evoked potentials and reaction time

Summary Motor processes partly determine reaction time (RT) in both choice reaction time and in binary classification tasks. These latter tasks are popular in cognitive psychology because the experimenter believes that he has kept the motor component simple and constant and therefore can attribute changes in RT to perceptual or cognitive processes. In this paper we used the P3 component of the event-related potential (ERP) as a time marker indicating the duration of perceptual and cognitive processes. The latency of this component is believed to reflect stimulus evaluation time independent of response selection and organization time.Two types of tasks were used: a choice-reaction time task and a binary classification task. Signal similarity and S-R compatibility additively affected RT, but only signal similarity affected P3 latency. The number of items in the positive set and response type affected both P3 latency and RT. Relative response frequency changed the bias in the cognitive evaluation of the stimulus, reflected in the latency of the P3 component, and affected RT only if the subjects preset their motor system (indexed by the late CNV). A model was presented which proposes that motor processes may partially overlap with the perceptual and cognitive evaluation of the stimulus. Both ERPs and RT are necessary tools in the study of the relative timing of these processes.     

Multiple visualisation in data analysis: a ViSta application for principal component analysis

Multiple visualisation (MV) is a statistic graphical method barely applied in data analysis practice, even though it provides interesting features for this purpose. This paper: (1) describes the application of the MV graphical method; (2) presents a number of rules related to the design of an MV; (3) introduces a general outline for developing MVs and shows how MV may be implemented in the ViSta statistical system; (4) illustrates this strategy by means of an example of MV oriented to principal component analysis; and, finally, (5) discusses some limitations of using and developing MVs.     

Eye-movement data: Cumulative fixation time and cluster analysis

This paper describes procedures for the visual presentation and cluster analysis of eye-movement data. Methods for two- and three-dimensional representation of cumulative fixation time (CFT) and ways of enhancing the peaks in CFT distributions are outlined and illustrated by reference to examples from eye-movement studies of cognitive processes. CFT distributions may also be partitioned using thek means clustering technique (MacQueen, 1967), and applications of variants of this technique to eye-movement data are discussed. Cluster analyses such ask means require the user to make initial estimates of the number and value of the means. One classification procedure (Wallace & Boulton, 1968a, 1968b), based on information theory, avoids these initial assumptions. This procedure is applied to a CFT distribution and has its solution compared with that ofk means for the same distribution. Finally, programs that implement these procedures on Macintosh computers are listed and offered on floppy disk.     

A free, easy-to-use, computer-based simple and four-choice reaction time programme: the Deary-Liewald reaction time task

Reaction time tasks are used widely in basic and applied psychology. There is a need for an easy-to-use, freely available programme that can run simple and choice reaction time tasks with no special software. We report the development of, and make available, the Deary-Liewald reaction time task. It is initially tested here on 150 participants, aged from 18 to 80, alongside another widely used reaction time device and tests of fluid and crystallised intelligence and processing speed. The new task’s parameters perform as expected with respect to age and intelligence differences. The new task’s parameters are reliable, and have very high correlations with the existing task. We also provide instructions for downloading and using the new reaction time programme, and we encourage other researchers to use it.     

On measuring the minimum detection time: A simple reaction time study in the time estimation paradigm

Kornblum's time estimation paradigm, together with the so‐called ‘race model’, provides an appealing alternative for measuring the ‘cut‐off’ which separates ‘true’ reaction times from anticipatory reaction times. However, the model is not precise enough to reveal the relation between the signal intensity and the ‘cut‐off’. Accordingly, Kornblum's model is extended with an emphasis on the measure of the ‘cut‐off’. Another aspect of the extension is to use a parametric method to analyse the data. In particular, it is assumed that the time estimation‐induced latency is gamma distributed and the signal‐induced latency is Weibull distributed, with the latter shifted by the ‘cut‐off’. The rationale behind the parametric assumption is discussed. For illustrative purposes, two pieces of experimental work are presented. Since the core of the race model is the assumption of an independent race between the time estimation process and the detection process, the first experiment tests whether, for the same signal intensity, the signal‐induced latency distribution is invariant across different time intervals; the second experiment tests whether, for the same time interval, the time estimation‐induced latency distribution is invariant across different signal intensity conditions. The data from the second experiment are also used to test various parametric assumptions in the model, which include the signal effect on the ‘cut‐off’. The new model fits the data well.     

Obtaining meaningful results from Fourier deconvolution of reaction time data

The technique of Fourier deconvolution is a powerful tool for testing distributional predictions of stage models of reaction time. However, direct application of Fourier theory to reaction time data has sometimes produced disappointing results. This article reviews Fourier transform theory as it applies to the problem of deconvolving a component of the reaction time distribution. Problems encountered in deconvolution are shown to be due to the presence of noise in the Fourier transforms of the sampled distributions, which is amplified by the operation of deconvolution. A variety of filtering techniques for the removal of noise are discussed, including window functions, adaptive kernel smoothing, and optimal Wiener filtering. The best results were obtained using a window function whose pass band was determined empirically from the power spectrum of the deconvolved distribution. These findings are discussed in relation to other, nontrigonometric approaches to the problem of deconvolution.     

A microprocessor reaction time laboratory

The hardware and software required to implement a multiple-subject microprocessor-based laboratory are described. A basic stimulus-probe reaction time paradigm encompasses a wide range of cognitive psychology experiments and requires little or no sophistication to use.     

Payoff: A neglected factor in reaction time measurement

The aim of this paper is to point out some implications of implicit or explicit payoffs in reaction time experiments. In any psychophysical task the subject is given a set of instructions which define the desired performance, as it were the rules of the game. Instructions may be supplemented by knowledge of results which further define the required performance. When performance admits of being “good” or “bad,” however wide these limits, the instructions may be said to define, explicitly or implicitly, a system of payoffs. In reaction time experiments the subject is instructed, amongst other things, to respond as soon as possible after the stimulus but never before it. These instructions could equally well be represented by a system of payoffs and Figure 1 illustrates the kind of payoff system normally implied in these instructions. If S represents the time at which the physical stimulus occurs the graph shows a fixed penalty for anticipations (response before S), maximum positive score for responses immediately following S declining at an arbitrary rate as a function of elapsed time between S and the response until an unacceptably long time involves a constant maximum penalty. Some experimenters choose to treat very short RT's as anticipations. This is represented by the dashed line in Figure 1, but it should be clear that payoff values are, to a certain extent, arbitrary.     

A latent markov model for the analysis of longitudinal data collected in continuous time: states, durations, and transitions

Markov models provide a general framework for analyzing and interpreting time dependencies in psychological applications. Recent work extended Markov models to the case of latent states because frequently psychological states are not directly observable and subject to measurement error. This article presents a further generalization of latent Markov models to allow for the analysis of rating data that are collected at arbitrary points in time. This extension offers new ways of investigating change processes by focusing explicitly on the durations that are spent in latent states. In an experience sampling application the author shows that such duration analyses can provide valuable insights about chronometric features of emotions.     

A comparison of sequential sampling models for two-choice reaction time

The authors evaluated 4 sequential sampling models for 2-choice decisions--the Wiener diffusion, Ornstein-Uhlenbeck (OU) diffusion, accumulator, and Poisson counter models--by fitting them to the response time (RT) distributions and accuracy data from 3 experiments. Each of the models was augmented with assumptions of variability across trials in the rate of accumulation of evidence from stimuli, the values of response criteria, and the value of base RT across trials. Although there was substantial model mimicry, empirical conditions were identified under which the models make discriminably different predictions. The best accounts of the data were provided by the Wiener diffusion model, the OU model with small-to-moderate decay, and the accumulator model with long-tailed (exponential) distributions of criteria, although the last was unable to produce error RTs shorter than correct RTs. The relationship between these models and 3 recent, neurally inspired models was also examined.     

VideoNoter: A productivity tool for video data analysis

The software described in this paper, VideoNoter, addresses the need for tools that support annotation and retrieval of video data and organize the presentation of multiple analyses of the same data. Video is widely perceived as an important medium for psychological research, because video recording makes the fleeting particulars of human interaction available as data for detailed analysis, while retaining much of the context of the event. Though the benefits of using video data are high, the process can be prohibitively time-consuming. We have developed a prototype computer-based video analysis tool that can enhance the productivity of the video analysis process. In this paper, we report on the design and implementation of VideoNoter, and we discuss how it facilitates video data analysis.