Robust ANCOVA using a smoother with bootstrap bagging

Many robust analogs of the classic analysis of covariance (ANCOVA) method have been proposed, some of which are based on some type of regression smoother. A method that first appeared in this journal, which is relatively simple and performs well in simulations, is based on a running interval smoother combined with comparing medians or 20% trimmed means. It makes no parametric assumption about the regression lines and does not assume that the regression lines are parallel. A possible way of improving the efficiency of the running interval smoother is to use bootstrap bagging and a minor goal here is to report some results supporting this approach. The major goal is to consider how ANCOVA might be performed when bootstrap bagging is used. Simple extensions of extant approaches that use some type of bootstrap method were found to be unsatisfactory. However, a basic percentile bootstrap method was found to perform well in simulations. And a reanalysis of data dealing with teachers' expectations about the cognitive ability of students illustrates that bootstrap bagging can make a practical difference.     

Comparing one-step m-estimators of location corresponding to two independent groups

Experience with real data indicates that psychometric measures often have heavy-tailed distributions. This is known to be a serious problem when comparing the means of two independent groups because heavy-tailed distributions can have a serious effect on power. Another problem that is common in some areas is outliers. This paper suggests an approach to these problems based on the one-step M-estimator of location. Simulations indicate that the new procedure provides very good control over the probability of a Type I error even when distributions are skewed, have different shapes, and the variances are unequal. Moreover, the new procedure has considerably more power than Welch's method when distributions have heavy tails, and it compares well to Yuen's method for comparing trimmed means. Wilcox's median procedure has about the same power as the proposed procedure, but Wilcox's method is based on a statistic that has a finite sample breakdown point of only 1/n, wheren is the sample size. Comments on other methods for comparing groups are also included.     

Patterns of reflex action,their autonomic components,and their behavioral significance

This is a discussion of the evidence that autonomic system reflexes are invariably triggered by stimuli that evoke both simple and complex somatic reflexes. Stimuli not only initiate reverberatory activity but sequences of reinforcements from higher centers. Reflexes come in chains, one reaction triggering another. Reflex actions are patterned, and these patterns are appropriate to the behavioral requirement indicated by stimuli. Reciprocal action produces a powerful braking or stimulatory action. Coactivation or synergic action of autonomie “antagonists” also occurs and can effect a greater cardiac output in certain vascular reflexes than can sympathetic action alone. Coactivation of vagus and sympathetic fibers occuring in reflex action or resulting from stimulation of specific areas in the hypothalamus has a physiologic importance to attainment of maximal cardiac function. Finally, two additional suggestions are made: (1) that the rhythmic reflex feedback discharge of the vagus from the baroreceptors aids in maintaining the regularity of cardiac rhythm as by interaaction of oscillators and (2) that the autonomic system, due to its early and often conditioned response, can be determinative as well as modulatory and supportive of behavior.     

Behaviors observed during S- in a simple discrimination learning task

Key pecking of pigeons was reinforced with food in the presence of a horizontal line and never reinforced in the presence of a vertical line. Highly stereotyped behaviors, as well as key pecking, were observed and recorded in the presence of both stimuli. Results showed that a high proportion of time spent in the presence of the horizontal line was occupied by key pecking, a high proportion of time in the presence of the vertical line was occupied by stereotyped nonkey-pecking behaviors, and intermediate proportions of time spent in the presence of intermediate stimuli were occupied by each class of behavior during generalization tests. Similar running rates (number of key pecks divided by observed key-pecking time) were obtained in the presence of all stimuli, indicating that changes in time rather than tempo accounted for the changes in overall rates of key pecking. An exception occurred in responding to the horizontal line as differential performance was developing. In addition to an increase in time spent key pecking, increased running rates occurred in seven of eight birds, suggesting that both time allocation and tempo play a role in behavioral contrast of overall rates of key pecking.     

Comparing examinees to a control

When comparing examinees to a control, the examiner usually does not know the probability of correctly classifying the examinees based on the number of items used and the number of examinees tested. Using ranking and selection techniques, a general framework is described for deriving a lower bound on this probability. We illustrate how these techniques can be applied to the binomial error model. New exact results are given for normal populations having unknown and unequal variances.The work upon which this publication is based was performed pursuant to a grant [Grant No. NIE-G-76-0083] with the National Institute of Education, Department of Health, Education and Welfare. Points of view or opinions stated do not necessarily represent official NIE position or policy.     

A microprocessor-based psychopathology laboratory: III. Hardware

The hardware configuration of a psychopathology research and clinical laboratory is described. Design prerequisites that guided hardware selection include: flexibility in experimental control, ease of data handling, system mobility, operational simplicity, and a method of providing clinical feedback. The microcomputer, mass storage, digital input/output, timers, and the auditory and visual modes of interacting with subjects/patients are described. Component costs are illustrated.     

Comparing one-step M-estimators of location when there are more than two groups

Methods for comparing means are known to be highly nonrobust in terms of Type II errors. The problem is that slight shifts from normal distributions toward heavy-tailed distributions inflate the standard error of the sample mean. In contrast, the standard error of various robust measures of location, such as the one-step M-estimator, are relatively unaffected by heavy tails. Wilcox recently examined a method of comparing the one-step M-estimators of location corresponding to two independent groups which provided good control over the probability of a Type I error even for unequal sample sizes, unequal variances, and different shaped distributions. There is a fairly obvious extension of this procedure to pairwise comparisons of more than two independent groups, but simulations reported here indicate that it is unsatisfactory. A slight modification of the procedure is found to give much better results, although some caution must be taken when there are unequal sample sizes and light-tailed distributions. An omnibus test is examined as well.     

An algorithm for comparing medians

An algorithm is presented for computing a test statistic for comparing medians based on a small-sample size estimate of the variance of the usual sample median.