Reliability of multiple classifications

Cohen's kappa index is reformulated for multiple classifications based on exchangeable random variables. It is found that kappa is between 0 and 1 inclusive. Two characterizations for kappa are stated in terms of the relationship between such random variables. Within the normal test score model, kappa increases with test reliability and test length. Furthermore, when based on binary classifications, kappa is an inverse U-shaped function of the cutoff score. These trends also hold for the beta-binomial test score model.Paper read at the Spring meeting of the Psychometric Society, Bell Laboratories (Murray Hill, New Jersey), March 1976.The editorial assistance and helpful comments of Leonard S. Feldt, Sarah P. Seaman-Huynh, and the three referees are gratefully acknowledged.     

On the discriminability of stimulus duration.

The performance of pigeons trained to detect differences in the duration of stimuli was analysed using a matching model of signal detection. Two white stimuli, S1 and S2, differing in duration, were arranged with equal probability on the center key of a three-key chamber. S1 was systematically varied from 5 seconds to 25 seconds while S2 remained constant at 30 seconds. On completion of the center-key stimulus, a peck on the center key turned on the two red side keys. A left-key response was "correct" when S1 had been in effect on the center key and a right-key response was "correct" on S2 trials. A correct response produced a 3-second magazine light accompanied intermittently by food. Incorrect responses produced 3-second blackouts. Detection performance was measured under two procedures. In the first, the obtained reinforcement ratio was uncontrolled by allowing the number of food reinforcements obtained for correct left- and right-key responses to vary as the stimuli were changed. In the second procedure, the presentation of food reinforcement was controlled by holding the obtained reinforcement ratio constant. Discriminability changed as a function of stimulus differences under both procedures. No such trend was found in response bias.     

Alternative fixed-ratio fixed-interval schedules of reinforcement

Five rats were trained under alternative fixed-ratio fixed-interval schedules, in which food reinforcement was provided for the completion of either a fixed-ratio or a fixed-interval requirement, whichever was met first. Overall response rate and running rate (the rate of responding after the postreinforcement pause) decreased for all subjects as the fixed-ratio value increased. As the proportion of reinforcements obtained from the fixed-ratio component increased and the alternative schedule approached a simple fixed ratio, overall response rate and running rate both increased; conversely, as the proportion of reinforcements obtained from the fixed-interval component increased and the alternative schedule approached a simple fixed interval, response rates decreased. Postreinforcement pause length increased linearly as the average time between reinforcements increased, regardless of the schedule parameters. A break-run pattern of responding was predominant at low- and medium-valued fixed ratios. All subjects displayed at least occasional positively accelerated responding within interreinforcement intervals at higher fixed-ratio values.     

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.     

Effects of signaled and unsignaled shock on schedule-controlled lever pressing and schedule-induced licking: Shock intensity and body weight

Schedule-controlled lever pressing and schedule-induced licking were studied in rats under a multiple fixed-interval fixed-interval schedule of food reinforcement. Following acquisition of stable rates of pressing and licking, a multiple variable-time variable-time schedule of electric-shock delivery was superimposed upon the baseline schedule. In only one component of the multiple schedule, a 5-sec stimulus preceded each shock (signaled shock). In the other component shock was unsignaled. Several shock intensities (Experiment 1) and body weights (Experiment 2) were studied. Lever pressing and licking were affected similarly by experimental manipulations, although with parametric differences. Depending upon shock intensity and body weight, rates of lever pressing and licking were hardly suppressed, suppressed primarily in the unsignaled shock component (differential suppression), or markedly suppressed in both components. Differential suppression during components with signaled and unsignaled shock and conditioned suppression of responding during the preshock stimulus appeared not to be functionally related. Differential suppression depended more on the discriminability of shock-free time, and on shock intensity, body weight, and the type of response than on the “preparatory” behavior preceding shock.     

Dynamic equilibrium on a cyclic-interval schedule with a ramp

Five human subjects pressed a panel for money on a cyclic-interval schedule that arranged recurring periods of linearly increasing reinforcement rates (ramps). Response rate versus time functions for all subjects showed recurring periods of linearly increasing response rates. The responding of four of the five subjects was in phase with the reinforcement input. The remaining subject showed a two-minute phase shift. These results suggest that organisms may act like simple amplifiers on cyclic-interval schedules, that is, the form of the input signal is not changed by the organism, but is returned with amplification. By analogy with the variable-interval case, the controlling variable on cyclic-interval schedules with rate ramps may be the constant reinforcement acceleration that is arranged by the schedule.     

Self-control in pigeons under the Mischel paradigm

Walter Mischel studied self-control in preschool children in the following manner: if the child waited for an interval to end, he or she received the more preferred of two reinforcers; if the child responded to terminate the interval by ringing a bell, the less preferred reinforcer was given. We used an analogous procedure to study self-control in pigeons: if the bird waited for a trial to end, it received the more preferred reinforcer; if the bird terminated the trial by pecking a key, the less preferred reinforcer was given. We explored the effects on self-control of a number of variables analogous to those studied by Mischel and co-workers, e.g., presence versus absence of reinforcers, of alternative responses, and of stimuli during the wait interval; prior experience of the subjects; and test paradigm. The results obtained with pigeons paralleled the results obtained by Mischel with human children.     

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.