Tests of symmetry in three-way contingency tables

Three-dimensional contingency tables are analyzed, with one variable (e.g., sex) as a factor, and with a natural relation between the other variables (e.g. left and right eye vision). Models of special interest, like symmetry and proportional symmetry between the related variables, and homogeneity across the factor levels, are investigated. Maximum likelihood estimators of parameters and partitions of chi-square goodness-of-fit statistics are explicitly presented; the independence of certain models is noted, and an example is discussed.     

Robust estimation of ability in the Rasch model

Estimating ability parameters in latent trait models in general, and in the Rasch model in particular is almost always hampered by noise in the data. This noise can be caused by guessing, inattention to easy questions, and other factors which are unrelated to ability. In this study several alternative formulations which attempt to deal with these problems without a reparameterization are tested through a Monte Carlo simulation. It was found that although no one of the tested schemes is uniformly superior to all others, a modified jackknife stood out as the best one in general, it was also super efficient (more efficient than the asymptotically optimal estimator) for tests with forty or fewer items. It is proposed that this sort of jackknifing scheme for estimating ability be considered for practical work.This research was funded through a grant from the Law Enforcement Assistance Administration (78-NI-AX-0047) to the Bureau of Social Science Research, Howard Wainer, Principal Investigator. We would like to thank Ronald Mead, Anne Morgan and James Ramsay for kind, generous, and invaluable help at various stages of the project.     

Delay or rate of food delivery as determiners of response rate

Pigeons were confronted with two keys: a green food key and a white changeover key. Food became available for a peck to the green key after variable intervals of time (mean = 113 seconds). A single peck on the changeover key changed the color of the food key to red for a fixed period of time during which the timing of the variable-interval schedule in green was suspended and the switching option eliminated and after which the conditions associated with green were reinstated. In Experiment 1 a single food presentation was obtainable during each red-key period after a minimum delay timed from the switch. This delay and the duration of the red-key period were held constant during a condition but varied between conditions (delay = 2.5, 7.5, 15, or 30 seconds; red-period duration = 30, 60, 120, 240, or 480 seconds). In Experiment 2 additional food presentations were scheduled during a 240-second red-key period with the delay to the first food delivery held constant at 30 seconds, and the delays to later food deliveries varied over conditions. Considering the data from both experiments, the rate of switching to red was a decreasing function of the delay to the first food, the delay to the second food, and perhaps the delay to the third food after a switch. There was no clear evidence that the rate of food in the red-key period made an independent contribution. The ordering of response rates among conditions was consistent with the view that each food presentation after a response adds an incremental effect to the rate of the response and that each food presentation's contribution is a decreasing function of its delay timed from the response.     

The effects of modifying consummatory behavior on the topography of the autoshaped pecking response in pigeons

The autoshaped responses of two debeaked pigeons that had developed modified eating behavior were compared to the autoshaped responses of three control subjects that ate grain normally. The control subjects exhibited keylight responding that was judged normal by two independent raters. The debeaked subjects pecked the key and ate grain with both normal and modified responses. The results of this study demostrate that an autoshaping procedure using grain as an appetitive stimulus may be used to establish a response that is not biologically preorganized.     

Evaluation of a coaching strategy to reduce swimming stroke errors with beginning age-group swimmers

A coaching strategy to decrease errors in swimming strokes with swimmers who had not improved under "standard" coaching procedures was investigated using a multiple baseline design across subjects and swimming strokes. The procedure resulted in a large decrease in errors on swimming strokes during sessions in a training pool. Stimulus generalization of improved performance to normal practice conditions in the regular pool was observed with all but one swimmer. This improvement was maintained during two maintenance phases lasting approximately 2 weeks, as well as under standard coaching conditions during at least a 2-week follow-up. For two swimmers, error rates on one of the strokes showed a gradual increase between the third and fifth week of follow-up, but brief remedial prompting sessions immediately corrected their performance. Some beneficial response generalization to other components of the stroke being trained was observed, but no improvements were found on untrained strokes. The error correction package did not disrupt practice, require excessive amounts of the coach's time, or necessitate the use of cumbersome apparatus. In addition, the coach and the swimmers considered the procedures to be effective, and expressed their willingness to participate in them again in the future.     

Timing the second response in two-response avoidance.

Rats were trained on a free-operant avoidance task requiring two lever presses within R seconds, with the opportunity for each response distinguished by differing stimuli. Response latencies at a variety of response-shock intervals were found to be proportional to the time available for the response. These results are shown to be consonant with a scalar expectancy model of timing behavior.     

Concurrent schedules: Effects of time- and response-allocation constraints

Five pigeons were trained on concurrent variable-interval schedules arranged on two keys. In Part 1 of the experiment, the subjects responded under no constraints, and the ratios of reinforcers obtainable were varied over five levels. In Part 2, the conditions of the experiment were changed such that the time spent responding on the left key before a subsequent changeover to the right key determined the minimum time that must be spent responding on the right key before a changeover to the left key could occur. When the left key provided a higher reinforcer rate than the right key, this procedure ensured that the time allocated to the two keys was approximately equal. The data showed that such a time-allocation constraint only marginally constrained response allocation. In Part 3, the numbers of responses emitted on the left key before a changeover to the right key determined the minimum number of responses that had to be emitted on the right key before a changeover to the left key could occur. This response constraint completely constrained time allocation. These data are consistent with the view that response allocation is a fundamental process (and time allocation a derivative process), or that response and time allocation are independently controlled, in concurrent-schedule performance.     

The acquisition of observing.

Pigeons were exposed to stimuli correlated with the presence or absence of a variable-interval 60-second schedule of reinforcement only while they depressed a crossbar or "perch." In the first experiment, the stimuli were different tilts of a line displayed on the key. When the difference in brightness between the line and the background (salience) was maximal, seven of eight birds acquired the discrimination, but when the difference was reduced by 50%, only one succeeded. In the second experiment, wavelength of chamber illumination served as the relevant dimension. Neither experiment showed a large effect attributable to the magnitude of the difference (disparity) between the positive and the negative stimulus. Individual differences in time spent observing were positively correlated with level of discrimination in the presence of the stimuli. All birds produced the positive stimulus for a greater proportion of the available time than they did the negative stimulus. This may be the mechanism that provides selective reinforcement of observing. Finally, the formation of a discrimination was analyzed in terms of changes in the proportion of time spent in contact with the discriminative stimuli.     

RITALIN VS. RESPONSE COST IN THE CONTROL OF HYPERACTIVE CHILDREN: A WITHIN-SUBJECT COMPARISON

A within-subject comparison was made of the effects of methylphenidate (Ritalin) and response cost in reducing the off-task behavior of two boys, 7 and 8 years of age, who had been diagnosed as having an attentional deficit disorder with hyperactivity. Several dosages of Ritalin (5 to 20 mg/day) were evaluated with the results indicating varying effects of the drug for both children. Response cost (with free-time as the reinforcer) was superior to Ritalin in raising levels of on-task behavior and in improving academic performance.     

TEACHING COIN EQUIVALENCE TO THE MENTALLY RETARDED1

A program was designed to teach coin equivalence to mentally retarded adolescents. Coin equivalence was defined as choosing several different combinations of coins to equal specified target values. A pretest-posttest matched-groups design was employed with an experimental group receiving the monetary training, and a no-training control group. A multiple baseline across coin-counting responses was also incorporated in the experimental group. Training was divided into six stages, each teaching one specific method of combining coins to equal 10 target values from 5¢ through 50¢. A three-component response chain was used, requiring (a) naming, (b) selecting and counting, and (c) depositing target monetary values into a coin machine. Experimental subjects improved significantly in coin equivalence performance and maintained their skill on follow up tests; control subjects did not.