Geoffrey R. Loftus

Using confidence intervals in within-subject designs

We argue that to best comprehend many data sets, plotting judiciously selected sample statistics with associated confidence intervals can usefully supplement, or even replace, standard hypothesis-testing procedures. We note that most social science statistics textbooks limit discussion of confidence intervals to their use in between-subject designs. Our central purpose in this article is to describe how to compute an analogous confidence interval that can be used in within-subject designs. This confidence interval rests on the reasoning that because between-subject variance typically plays no role in statistical analyses of within-subject designs, it can legitimately be ignored; hence, an appropriate confidence interval can be based on the standard within-subject error term—that is, on the variability due to the subject × condition interaction. Computation of such a confidence interval is simple and is embodied in Equation 2 on p. 482 of this article. This confidence interval has two useful properties. First, it is based on the same error term as is the corresponding analysis of variance, and hence leads to comparable conclusions. Second, it is related by a known factor (√2) to a confidence interval of the difference between sample means; accordingly, it can be used to infer the faith one can put in some pattern of sample means as a reflection of the underlying pattern of population means. These two properties correspond to analogous properties of the more widely used between-subject confidence interval.

Cognitive determinants of fixation location during picture viewing.

This experiment involved the question of where human observers look in a picture. The results indicated that observers fixate earlier, more often, and with longer durations on objects that have a low probability of appearing in a scene (e.g., an octopus in a farm scene) than on objects that have a high probability of appearing (e.g., a tractor in a farm scene). These findings (a) imply a role of cognitive factors in peripheral visual processing and (b) suggest a possible relationship between the nature of information initially acquired from a picture and subsequent recognition memory for that picture.

Some facts about “weapon focus”

Abstract“Weapon focus” refers to the concentration of acrime witnesss attention on a weapon, and the resultant reduction in ability to remember other details of the crime. We examined this phenomenon by presenting subject-witnesses with a series of slides depicting an event in a fast-food restaurant. Half of the subjects saw a customer point a gun at the cashier; the other half saw him hand the cashier a check. In Experiment 1, eye movements were recorded while subjects viewed the slides. Results showed that subjects made more eye fixations on the weapon than on the check, and fixations on the weapon were of a longer duration than fixations on the check. In Experiment 2, the memory of subjects in the weapon condition was poorer than the memory of subjects in the check condition: In Experiment 1 similar, though only marginally significant, performance effects were obtained. These results provide the first direct empirical support for weapon focus.

On interpretation of interactions

The principle focus of this paper is on interpretation of interactions that are obtained when response probability is used as a dependent variable. It is argued that results obtained with probability [or any dependent variable) are only interesting insofar as they reflect something about a corresponding theoretical component. It follows that the functional mapping of response probability [which is measured) onto the state of a theoretical component (which is inferred) must be somehow specified if conclusions are to be meaningful. Depending on the nature of such a mapping, various types of results, particularly results involving interactions, may or may not be interpretable.

Eye fixations and recognition memory for pictures

Abstract Three experiments were performed investigating the extent to which recognition memory for pictures can be predicted by eye-movement patterns on the picture at the time of study. In each experiment, 180 pictures were viewed followed by a yes-no recognition test on all the pictures. Eye movements were recorded at the time of study. Experiment I investigated payoff structure: It was found that higher-valued pictures both received more fixations and were remembered better than low-valued pictures, but when number of fixations was held constant, memory performance was independent of value. Experiment II showed that (a) when pictures are viewed for a fixed amount of time, memory performance is a positive function of number of fixations on the picture, (b) with number of fixations held constant, performance is independent of exposure time, and (c) there is no memory for pictures which were originally viewed only peripherally. In Expt. III, pictures were viewed either normally or while a distracting task (counting backward by threes) was being performed concurrently. The distracting task was found to reduce both number of fixations and memory performance for a picture. When number of fixations was held constant, performance was still better for normally viewed pictures, suggesting that the distracting task was doing more to inhibit encoding besides simply reducing the fixation rate.

Eye fixations and memory for emotional events

Subjects watched either an emotional, neutral, or unusual sequence of slides containing 1 critical slide in the middle. Experiments 1 and 2 allowed only a single eye fixation on the critical slide by presenting it for 180 ms (Experiment 1) or 150 ms (Experiment 2). Despite this constraint, memory for a central detail was better for the emotional condition. In Experiment 3, subjects were allowed 2.70 s to view the critical slide while their eye movements were monitored. When subjects who had devoted the same number of fixations were compared, memory for the central detail of the emotional slide was again better. The results suggest that enhanced memory for detail information of an emotional event does not occur solely because more attention is devoted to the emotional information.

Accounts of the confidence-accuracy relation in recognition memory

Confidence and accuracy, while often considered to tap the same memory representation, are often found to be only weakly correlated (e.g., Bothwell, Deffenbacher, & Brigham, 1987; Deffenbacher, 1980). There are at least two possible (nonexclusive) reasons for this weak relation. First, it may be simply due to noise of one sort or another; that is, it may come about because of both within- and between-subjects statistical variations that are partially uncorrelated for confidence measures on the one hand and accuracy measures on the other. Second, confidence and accuracy may be uncorrelated because they are based, at least in part, on different memory representations that are affected in different ways by different independent variables. We propose a general theory that is designed to encompass both of these possibilities and, within the context of this theory, we evaluate effects of four variables—degree of rehearsal, study duration, study luminance, and test luminance—in three face recognition experiments. In conjunction with our theory, the results allow us to begin to identify the circumstances under which confidence and accuracy are based on the same versus different sources of information in memory. The results demonstrate the conditions under which subjects are quite poor at monitoring their memory performance, and are used to extend cue utilization theories to the domain of face recognition.

The functional visual field during picture viewing.

In four experiments, pictures of complex, naturalistic scenes were shown, followed by a two-alternative forced-choice recognition test in which the targets and distractors differed in only a single, critical detail. Eye movements were recorded at the time of study in the first two experiments. In Experiment 1 we investigated eye movements during short initial exposure times and found that if the nearest fixation to the critical detail was further than about 2 degrees of visual angle, performance was no better than chance. Experiment 2 replicated Experiment 1 using longer exposure times and an expanded set of pictures. Performance was still found to decrease with increase in distance of the nearest fixation to the critical detail, but not quite to chance. In Experiments 3 and 4 we controlled where the subjects first fixation occurred using a prefixation point of light. The results indicated that the performance again decreases with increasing distance from the critical detail; however, performances did not fall completely to chance levels. In Experiment 4 a verbal recognition test was included, and overall performance was still slightly better than chance at extreme distances. It was concluded that some information is stored from the visual periphery during picture viewing.

A picture is worth a thousandp values: On the irrelevance of hypothesis testing in the microcomputer age

Hypothesis testing, while by far the most common statistical technique for generating conclusions from data, is nonetheless not very informative. It emphasizes a banal and confusing question (“Is it true that some set of population means are not all identical to one another?”) whose answer is, in a mathematical sense, almost inevitably known (“No”). Hypothesis testing, as it is customarily implemented, ignores two issues that are generally much more interesting, important, and relevant: What is thepattern of population means over conditions, and what are the magnitudes of various variability measures (e.g., standard errors of the mean, estimates of population standard deviations)? The simple expedient of plotting relevant sample statistics with associated variability bars is a substantially better way of conveying the results of an experiment. In today’s microcomputer environment, there are many relatively cheap and easily available applications that allow one to do this. I make some brief, informal comments about some of these applications.

Why Is It Easier to Identify Someone Close Than Far Away

It is a matter of common sense that a person is easier to recognize when close than when far away. A possible explanation for why this happens begins with two observations. First, the human visual system, like many image-processing devices, can be viewed as a spatial filter that passes higher spatial frequencies, expressed in terms of cycles/degree, progressively more poorly. Second, as a face is moved farther from the observer, the face’s image spatial frequency spectrum, expressed in terms of cycles/ face, scales downward in a manner inversely proportional to distance. An implication of these two observations is that as a face moves away, progressively lower spatial frequencies, expressed in cycles/face—and therefore, progressively coarser facial details—are lost to the observer at a rate that is likewise inversely proportional to distance. We propose what we call thedistance-as-filtering hypothesis, which is that these two observations are sufficient to explain the effect of distance on face processing. If the distance-as-filtering hypothesis is correct, one should be able to simulate the effect of seeing a face at some distance, D, by filtering the face so as to mimic its spatial frequency composition, expressed in terms of cycles/face, at that distance. In four experiments, we measured face perception at varying distances that were simulated either by filtering the face as just described or by shrinking the face so that it subtended the visual angle corresponding to the desired distance. The distance-asfiltering hypothesis was confirmed perfectly in two face perception tasks: assessing the informational content of the face and identifying celebrities. Data from the two tasks could be accounted for by assuming that they were mediated by different low-pass spatial filters within the human visual system that have the same general mathematical description but that differ in scale by a factor of approximately 0.75. We discuss our results in terms of (1) how they can be used to explain the effect of distance on visual processing, (2) what they tell us about face processing, (3) how they are related to “flexible spatial scale usage,” as discussed by Schyns and colleagues, and (4) how they may be used in practical (e.g., legal) settings to demonstrate the loss of face information that occurs when a person is seen at a particular distance.