An eyewitness paradox

Two methods of analysing data from an identification parade give rise to seemingly contradictory outcomes, both of which reach statistical significance. The traditional method is based on the first choices of eyewitnesses, whereas the paired-comparison method takes account of each eyewitness's full rank ordering of the lineup participants. The person that most eyewitnesses pick out as the perpetrator of an offence (according to the first-choice method) may in fact be the person that those same eyewitnesses as a group regard as least likely to have committed the act (according to the paired-comparison method). Implications of the paradox for the analysis of lineup data are considered.     

Determination of a behavioral transfer function: White-noise analysis of session-to-session response-ratio dynamics on concurrent VI VI schedules

Six pigeons were exposed to concurrent variable-interval schedules in which the programmed reinforcer ratios changed from session to session according to a pseudorandom binary sequence. This procedure corresponded to the stochastic identification paradigm (“white-noise experiment”) of systems theory and enabled the relation between log response ratios in the current session and log reinforcer ratios in all previous sessions to be determined. Such dynamic relations are called linear transfer functions. Both nonparametric and parametric representations of these, in the form of “impulse-response functions,” were determined for each bird. The session-to-session response ratios resulting from the session-to-session pseudorandom binary variations in reinforcer ratios were well predicted by the impulse-response functions identified for each pigeon. The impulse-response functions were well fitted by a second-order dynamic model involving only two parameters: a time constant and a gain. The mean time constant was 0.67 sessions, implying that the effects of abrupt changes in log reinforcer ratios should be 96% complete within about five sessions. The mean gain was 0.53, which was surprisingly low inasmuch as it should equal the sensitivity to reinforcement ratio observed under steady-state conditions. The same six pigeons were subjected to a similar experiment 10 months following the first. Despite individual differences in impulse-response functions between birds within each experiment, the impulse-response functions determined from the two experiments were essentially the same.     

Molecular maximizing characterizes choice on Vaughan's (1981) procedure

Pigeons keypecked on a two-key procedure in which their choice ratios during one time period determined the reinforcement rates assigned to each key during the next period (Vaughan, 1981). During each of four phases, which differed in the reinforcement rates they provided for different choice ratios, the duration of these periods was four minutes, duplicating one condition from Vaughan's study. During the other four phases, these periods lasted six seconds. When these periods were long, the results were similar to Vaughan's and appeared compatible with melioration theory. But when these periods were short, the data were consistent with molecular maximizing (see Silberberg & Ziriax, 1982) and were incompatible with melioration, molar maximizing, and matching. In a simulation, stat birds following a molecular-maximizing algorithm responded on the short- and long-period conditions of this experiment. When the time periods lasted four minutes, the results were similar to Vaughan's and to the results of the four-minute conditions of this study; when the time periods lasted six seconds, the choice data were similar to the data from real subjects for the six-second conditions. Thus, a molecular-maximizing response rule generated choice data comparable to those from the short- and long-period conditions of this experiment. These data show that, among extant accounts, choice on the Vaughan procedure is most compatible with molecular maximizing.     

Choice between reliable and unreliable outcomes: mixed percentage-reinforcement in concurrent chains.

Pigeons' choices between alternatives that provided different percentages of reinforcement in mixed schedules were studied using the concurrent-chains procedure. In Experiment 1, the alternatives were terminal-link schedules that were equal in delay and magnitude of reinforcement, but that provided different percentages of reinforcement, with one schedule providing, reinforcement twice as reliably as the other. All pigeons preferred the more reliable schedule, and their level of preference was not systematically affected by variation in the absolute percentage values, or in the magnitude of reinforcement. In Experiment 2, preference for a schedule providing 100% reinforcement over one providing 33% reinforcement increased systematically with increases in the duration of the terminal links. In contrast, preference decreased systematically with increases in the duration of the initial links. Experiment 3 examined choice with equal percentages of reinforcement but unequal delays to reinforcement. Preference for the shorter delay to reinforcement was not systematically affected by variation in the absolute percentage of reinforcement. The overall pattern of results supported predictions based on an extension of the delay-reduction hypothesis to choice procedures involving mixed schedules of percentage reinforcement.     

Reply to silberberg and ziriax

Silberberg and Ziriax (1985) report that a modification of Vaughan's (1981) procedure produces results inconsistent with melioration (the position advocated by Vaughan) but consistent with a process they term molecular maximizing. Here it is argued that the theory of molecular maximization is not sufficiently unambiguous that researchers other than the developers can test its predictions, and that in any case none of the data presented by Silberberg and Ziriax are both clearly consistent with molecular maximization and inconsistent with melioration.     

Comparing the effects of two correction procedures on human acquisition of sequential behavior patterns

Thirty-one college undergraduates learned to touch abstract stimuli on a computer screen in arbitrarily designated “correct” sequential orders. Four sets of seven stimuli were used; the stimuli were arrayed horizontally on the screen in random sequences. A correct response (i.e., touching first the stimulus designated as first) resulted in that stimulus appearing near the top of the screen in its correct sequential position (left to right), and remaining there until the end of the trial. Incorrect responses (i.e., touching a stimulus out of sequence) terminated the trial. New trials displayed either the same sequence as the one on which an error had occurred (same-order correction procedure), or a new random sequence (new-order correction procedure). Whenever all responses occurred in the correct sequence, the next trial displayed a new random sequence. Each phase ended when five consecutive correct response sequences occurred. Initially, the same-order correction procedure increased control by the position as well as by the shape of the stimuli; also, it produced more errors, more total trials, more trials to mastery, and more individual patterns of reacquisition than were produced by the new-order procedure.     

More on concurrent interval-ratio schedules: a replication and review.

It has been suggested that the failure to maximize reinforcement on concurrent variable-interval, variable-ratio schedules may be misleading. Inasmuch as response costs are not directly measured, it is possible that subjects are optimally balancing the benefits of reinforcement against the costs of responding. To evaluate this hypothesis, pigeons were tested in a procedure in which interval and ratio schedules had equal response costs. On a concurrent variable time (VT), variable ratio-time (VRT) schedule, the VT schedule runs throughout the session and the VRT schedule is controlled by responses to a changeover key that switches from one schedule to the other. Reinforcement is presented independent of response. This schedule retains the essential features of concurrent VI VR, but eliminates differential response costs for the two alternatives. It therefore also eliminates at least one significant ambiguity about the reinforcement maximizing performance. Pigeons did not maximize rate of reinforcement on this procedure. Instead, their times spent on the alternative schedules matched the relative rates of reinforcement, even when schedule parameters were such that matching earned the lowest possible overall rate of reinforcement. It was further shown that the observed matching was not a procedural artifact arising from the constraints built into the schedule.