Alfred B. Kristofferson

Response delays and the timing of discrete motor responses

A model for the timing of repetitive discrete motor responses is proposed, and a prediction of negative dependency between successive interresponse intervals is confirmed by data from a Morse key tapping task. A method that makes use of the first-order serial correlation between interresponse intervals is used to distinguish between variance due to a timekeeping process and variance in motor response delays subsequent to the timekeeper. These two quantities are examined as a function of mean interresponse interval.

The timing of interresponse intervals

Analogs of models of duration discrimination are here related to the timing of discrete motor responses. The measure of interest is the variability in duration of intervals collected in short interval reproduction tasks. For data from a Morse key-tapping task, it is shown that, taken separately, neither of the models described can completely account for the relation between the mean and the variance of the interresponse intervals.

Psychophysical theories of duration discrimination

There are few quantitative theories of duration discrimination and few established empirical phenomena to guide theorizing. This paper discusses three such theories and several empirical findings. The theories assume that the discrimination is based only upon information extracted from the temporal extent of the stimulus pattern, and experimental evidence is presented that clearly supports this assumption for many stimulus patterns. Recent findings which indicate that duration information is analyzed in certain ways that are fundamentally different from other stimulus dimensions are reviewed, the duration discrimination psychometric function is examined, and the time-order error is discussed. The three theories are compared in terms of their ability to incorporate the empirical data.

A quantal step function in duration discrimination

The difference threshold for duration, for the case of empty time intervals bounded by brief auditory pulses, is an increasing function of base duration. For base durations between 100 and 1,480 msec, Weber’s law describes the function quite well and a Weber ratio of .05 is obtained. These results in the present paper conform closely to results that have been reported by others. However, it is further shown that the function changes as the amount of practice is increased at each specific base duration: steps unfold from the linear function, and these steps are clearly evident after 17 consecutive sessions at each base duration. Expressing threshold in terms of the apparent magnitude of the “time quantum,” it is found that q is about 13 msec when base duration is 100 msec and that it jumps to 25 at 200, to 50 at 400, and to 100 at 800. Between the abrupt risers in this step function, the treads are not quite flat, perhaps because the amount of practice was insufficient. It is concluded that the time quantum can be doubled and halved, at least within the doubles set 13, 25, 50, and 100 msec. It is not restricted to the single value of 50 msec as initially proposed (Kristofferson, 1967).

Duration discrimination of brief light flashes.

The data from four experiments indicate that when Os discriminate between light flashes of different durations, for durations for which Bloch’s law has been shown to hold, their discriminations are frequently made on the temporal information available in the flashes rather than on their apparent brightness. A model for duration discrimination which specifies that discriminability depends only on the difference in duration between the two brief flashes, and is independent of their durations, is presented and applied to the data.

A real-time criterion theory of duration discrimination

The common idea that a measure is taken of a duration stimulus over its temporal extent, and that the decision as to whether the stimulus is relatively long or short is based upon such a measure, is shown to be incorrect. Two experiments, which require speeded responding in duration discrimination and consider response latencies as well as response probabilities, demonstrate that the response that is made is determined by the outcome of a race between an internally timed interval, the criterion, and the presented stimulus. The onset of the stimulus triggers the criterion; if the criterion ends first, the response “long” is elicited. Duration discrimination is a matter of temporal order discrimination, and in the limit, “short” responses are simple reactions while “long” responses are time estimation responses. A specific model of the real-time criterion hypothesis is tested, and these initial tests generally confirm it. From this, it is concluded that errors in duration discrimination are due entirely to variability of the criterion and that afferent latencies are not necessarily variable. This adds additional evidence for the existence of deterministic afferent latencies.

Quantal and Deterministic Timing in Human Duration Discrimination

When we began to study duration discrimination, we expected it to give us rather direct information about time perception. That expectation has not been fulfilled. Instead, our “thresholds” for duration seem to be determined by our ability to produce a time interval, to time it out internally. The size of a threshold is wholly determined by the extent to which repeated attempts to time out a fixed time interval are variable.’ A set of duration stimuli is shown a t the top of FIGURE 1. Each stimulus consists of two 10-msec auditory pulses separated by the stimulus duration, D. The stimuli differ from each other only in D, and the values of D are symmetrically arranged around a midpoint value. The midpoint of the set is the base duration. A single stimulus is presented on a trial and the subject is asked to categorize it as “long” (RL) or “short” (Rs). Values of D greater than the midpoint are called long, and the decision on each trial is whether P, occurred before or after the midpoint value of D. In the experiments to be reported here, the subject is instructed to respond as quickly as possible, and the data consist of response probabilities and response latencies for each stimulus duration. The general hypothesis is pictured in FIGURE 1B. On each trial, PI triggers an internally timed interval, I, which terminates as the criterion event, C. P, triggers a sensory event B2. If, as shown here, C occurs before BZ, then a long response is determined. Short responses are triggered by B2 whenever it occurs first. The discrimination mechanism is a race between the two response triggers, Cand B2. The two kinds of responses, therefore, have different causal histories, as shown in FIGURE lC, RL being linked to P I and Rs being linked to P,. Long responses should be time-locked to P, and should occur a t the same time for all stimuli, that is, regardless of the time of occurrence of P2. Rs, on the other hand, should be time-locked to Pz . These time-locking predictions are a major test of the hypothesis and they have been confirmed experimentally.’ Since responding is speeded, short responses are direct reactions to P , and might resemble simple reaction times. Long responses are similar, except that the responses must be delayed, and RL latencies might resemble time estimation latencies. These expectations are also confirmed, and speeded duration discrimination appears to be a combination of simple reaction time and time estimation, in which one kind of response occurs on a trial, the other being countermanded. Practice with the stimulus set adjusts I so that C falls near the midpoint of the stimulus set. The lower panel in FIGURE 1 displays a specific model in which the times of occurrence of Care assumed to form an isosceles triangle. The variability in C i s due solely to variance in I, the afferent latencies having zero variance. Therefore, for each D, B, is a fixed point which divides the triangle into two parts. The proportion of the area under the triangle to the left of B, represents the probability of RL for that stimulus. Knowing the probability of RL for two different stimuli, both of which have a E2 within the triangle, enables one to calculate the quantum size, q, in msec, and also

Successiveness discrimination: Two models

Two models for successiveness discrimination, an attention-switching model and a duration-discrimination model, are described. Data are reported from a forced-choice successiveness discrimination task in which the standard stimulus assumed one of three values during a session. Of major interest is the ability of the models to account for the absence of observed variation in performance with changes in value of the standard. Conventional signal detection-type models or discrete state models would be unable to account for the data.

Complete recovery of a masked visual target

The experiment by Dember and Purcell (1967) was repeated and extended using four subjects over many sessions. When the time interval between target onset and the onset of the second mask was 116 msec, and that between the first mask and the second mask was 35 msec, complete recovery of the masked target was obtained for all subjects. Lengthening or shortening the 35-msec interval produced less than complete recovery.

Judgments about the duration of brief stimuli.

Visual duration discrimination data for durations between 70 and 1,020 msec are presented. A model for duration discrimination proposed by Allan, Kristofferson, and Wiens (1972) is elaborated, and the data are discussed in terms of the model. The data axe in agreement with the basic assumptions of the model. Differences between our data and duration discrimination data presented by others are discussed.