Mixed-modality psychophysical scaling: Sequential dependencies and other properties

J. C. Stevens and Marks’s (1980) method of magnitude matching and a derivative, category matching, are examined in two experiments. Category matching produces highly similar matching functions to those of magnitude matching. The two methods are both subject to significant sequential dependencies, which, however, should not affect exponents of matching functions. Such mixed-modality scaling methods are also useful for theory testing. In the present case, responses were assimilated to the immediately previous response (different modality stimulus) but contrasted with the stimulus (same modality) two trials back in the sequence. The dependency of the response-response dependency on Sn-S_n-k was independent of stimulus modality. However, the usual dependency of the coefficient of variation of ratios of successive responses on Sn-S_n-k was not found. These results support the class of theories in which assimilative response-response dependencies and contrastive response-stimulus dependencies arise from different mechanisms, and disconfirm those in which both effects arise in a linked fashion from a single mechanism.     

Consistency of magnitude estimations with conceptual data dimensions used for sonification

In two experiments listeners assessed how sounds represented data, as might be used in sonification. In Experiment 1, 209 undergraduates used magnitude estimation to define the relationship between three sound attributes (frequency, tempo, modulation index) and 10 data dimensions (size, temperature, pressure, velocity, number of dollars, urgency, proximity, attractiveness, danger, mass). Polarities and slopes (i.e. power function exponents) are reported and compared to predictions from the literature. In Experiment 2, 226 new participants demonstrated polarities and slopes are stable across a direct replication. Results show that listener expectations depend on both sound and data dimensions in use. While there are some unanimous expectations across listeners, there are also differences due to different mental models formed by participants, which may relate to listening experience. Copyright © 2006 John Wiley & Sons, Ltd.     

Power functions of loudness magnitude estimations and auditory brainstem evoked responses

The correspondence between subjective and neural response to change in acoustic intensity was considered by deriving power functions from subjective loudness estimations and from the amplitude and latency of auditory brainstem evoked response components (BER). Thirty-six subjects provided loudness magnitude estimations of 2-sec trains of positive polarity click stimuli, 20/sec, at intensity levels ranging from 55 to 90 dB in 5-dB steps. The loudness power function yielded an exponent of .48. With longer trains of the same click stimuli, the exponents of BER latency measures ranged from -.14 for wave I to -.03 for later waves. The exponents of BER amplitude-intensity functions ranged from .40 to .19. Although these exponents tended to be larger than exponents previously reported, they were all lower than the exponent derived from the subjective loudness estimates, and a clear correspondence between the exponents of the loudness and BER component intensity functions was not found.     

Size,convexity, and curvature magnitude estimations of curvilinear forms

Groups of Os made magnitude estimates of size, convexity, and curvature of patterns along a shape continuum. College Os repeated the procedure for a given physical measure in three successive sessions, but high school Os made only one set of estimates. The apparent size for the patterns was found to grow with an exponent between .700 and .755 for high school and college Os. The magnitude estimates for convexity and curvature were less reliable than the size estimates both between college and high school Os and within college Os over successive sessions. The magnitude estimates from the high school and college Os showed a faster apparent growth of curvature than of convexity.     

Fixed-ratio pausing: Joint effects of past reinforcer magnitude and stimuli correlated with upcoming magnitude

Pigeons responded on fixed-ratio schedules ending in small or large reinforcers (grain presentations of different duration) interspersed within each session. In mixed-schedule conditions, the response key was lit with a single color throughout the session, and pausing was directly related to the past reinforcer (longer pauses after large reinforcers than after small ones). In multiple-schedule conditions, different colors accompanied the ratios ending in small and large reinforcers, and pausing was affected by the upcoming reinforcer as well as the past one. Pauses were shorter before large reinforcers than before small ones, but they continued to be longer after large reinforcers than after small ones. The influence of the past reinforcer was modulated by the magnitude of the upcoming reinforcer; in the presence of the stimulus before the small reinforcer, the effect of the past reinforcer was enhanced relative to its effect in the stimulus before the large reinforcer. These results show that pausing between ratios is jointly determined by two competing factors: past conditions of reinforcement and stimuli correlated with upcoming conditions.     

Modification of magnitude estimations in thermotactile perception during self-generated and externally generated movements

Fourteen participants felt a 'cold' stimulus move across a fingertip. When movement was self-controlled, the stimulus was reported as feeling less 'cold' than when movement was externally generated.     

Sequential effects in naming: a time-criterion account

S. J. Lupker, P. Brown, and L. Colombo (1997) reported that target naming latencies are strongly affected by the difficulty of the other stimuli in a trial block, an effect they attributed to readers' strategic use of a time criterion to guide responding. In the present research, the authors asked whether there are also trial-by-trial ("sequential") effects by examining naming latency as a function of the difficulty of the preceding stimulus. In Experiment 1, both nonwords and high-frequency regular words were named more rapidly following a word than a nonword. Experiments 2, 3, and 4 were parallel experiments involving a variety of stimulus types (e.g., high- and low-frequency inconsistent words, easy and hard nonwords). In all cases, similar sequential effects were observed (i.e., all stimulus types had shorter latencies following an easier-to-name than a harder-to-name stimulus). In terms of the time-criterion account, criterion placement appears to be affected by the relative difficulty of the preceding stimulus in a way that is independent of stimulus type.     

Concurrent schedules: reinforcer magnitude effects

Five pigeons were trained on pairs of concurrent variable-interval schedules in a switching-key procedure. The arranged overall rate of reinforcement was constant in all conditions, and the reinforcer-magnitude ratios obtained from the two alternatives were varied over five levels. Each condition remained in effect for 65 sessions and the last 50 sessions of data from each condition were analyzed. At a molar level of analysis, preference was described well by a version of the generalized matching law, consistent with previous reports. More local analyses showed that recently obtained reinforcers had small measurable effects on current preference, with the most recently obtained reinforcer having a substantially larger effect. Larger reinforcers resulted in larger and longer preference pulses, and a small preference was maintained for the larger-magnitude alternative even after long inter-reinforcer intervals. These results are consistent with the notion that the variables controlling choice have both short- and long-term effects. Moreover, they suggest that control by reinforcer magnitude is exerted in a manner similar to control by reinforcer frequency. Lower sensitivities when reinforcer magnitude is varied are likely to be due to equal frequencies of different sized preference pulses, whereas higher sensitivities when reinforcer rates are varied might result from changes in the frequencies of different sized preference pulses.     

A comparison of methods to test mediation and other intervening variable effects

A Monte Carlo study compared 14 methods to test the statistical significance of the intervening variable effect. An intervening variable (mediator) transmits the effect of an independent variable to a dependent variable. The commonly used R. M. Baron and D. A. Kenny (1986) approach has low statistical power. Two methods based on the distribution of the product and 2 difference-in-coefficients methods have the most accurate Type I error rates and greatest statistical power except in 1 important case in which Type I error rates are too high. The best balance of Type I error and statistical power across all cases is the test of the joint significance of the two effects comprising the intervening variable effect.     

Children and adults' distance estimations in a large-scale environment: effects of time and clutter

In two experiments adults (mean age = 19-5), sixth graders (mean age = 11-8), fourth graders (mean age = 9-8), and second graders (mean age = 7-8) walked a straight line distance through a large-scale environment. Subjects were then asked to estimate the time taken to traverse each half of the walk and to estimate the distance between objects seen along the walk. In Experiment 1 each half of the walk was traversed in the same amount of time but contained a different number of objects (clutter). Time and distance estimates were related, but were not affected by the number of intervening objects encountered between locations. In Experiment 2 subjects again encountered a different number of objects along each half of the walk but each half was traversed in varying amounts of time. Again, time and distance estimates were related, and there was no clutter effect. There were no consistent developmental differences across the two experiments. It was concluded that (1) Thorndyke's clutter effect does not occur across all types of spatial cognition tasks, and (2) children and adults tend to relate time and distance across a variety of distance estimation tasks.     

Pervasiveness and magnitude of context effects: evidence for the relativity of absolute magnitude estimation

To test the assertion that absolute magnitude estimation serves to minimize context effects, two experiments were conducted in which area stimuli were judged under differing conditions. In Experiment 1, four groups of subjects made magnitude estimations of triangles ranging in area from 1.5 to 3,072 cm2. No standard or modulus was used, and instructions were similar to those used in absolute magnitude estimation experiments. Each group first judged a different subrange of the stimuli (1.5-24; 48-768; 6-96; or 192-3,072 cm2) before making judgments of the remaining stimuli. In Experiment 2, two groups of subjects made magnitude estimations of triangles ranging in area from 1.5 to 12,288 cm2, with each group first judging a different subrange of stimuli (1.5-24 cm2 or 768-12,288 cm2). The design and instructions were virtually identical to those used in absolute magnitude estimation experiments. Our results indicate that the wording of the instructions is not crucial and that judgments are influenced in two ways that are not predicted by proponents of absolute magnitude estimation. First, the power functions fit to the initially presented subranges (e.g., 1.5-24 cm2), which were judged without contextual effects produced by previously presented stimuli, were inconsistent with one another. Second, judgments of the remaining stimuli were influenced by the subrange of stimuli judged initially. The prevalence of context effects in both experiments, in spite of instructional differences, suggests that although one should avoid using a standard and modulus, there is little else to be gained by adopting the absolute magnitude estimation procedure.     

Sequential contrast effects with human subjects

Institutionalized retardates were exposed to a multiple variable-interval: extinction schedule of reinforcement in which 5-min periods of variable-interval reinforcement and 5-min periods of extinction were presented in a random order. This schedule was found to generate sequential contrast effects: response rates during variable-interval reinforcement were higher when a variable-interval period followed an extinction period than when it followed another variable-interval period. The rate of responding within a variable-interval period also was affected by the number of extinction periods preceding a variable-interval period. As the number of successive extinction periods that preceded a variable-interval period increased, the rate of responding during that variable-interval period increased. The sequential contrast effects were transient, being most evident during the early sessions and generally disappearing by the tenth session.     

In touch with numbers: Embodied and situated effects in number magnitude comparison

The idea of embodied numerosity denotes that seemingly abstract number concepts (e.g., magnitude) are rooted in bodily experiences and situated action. In the present study we evaluated whether there is an embodied representation of the place–value structure of the Arabic number system and if so whether this representation is influenced by situated aspects. In a two-digit number magnitude comparison task participants had to directly touch the larger of two numbers. Importantly, pointing responses were systematically biased toward the decade digit of the target number. Additionally, this leftward bias towards the tens digit was reduced in unit–decade incompatible number pairs. Thereby, we demonstrated an influence of place–value processing on manual pointing movement. Our results therefore corroborate the notion of an embodied representation of the place–value structure of Arabic numbers which is modulated by situated aspects.     

The role of spatial attention and other processes on the magnitude and time course of cueing effects

We are quite often exposed to multiple objects present in the visual scene, thus attentional selection is necessary in order to selectively respond to the relevant information. Objects can be selected on the basis of the location they occupy by orienting attention in space. In this paper, we review the evidence showing that attention can be oriented in space either endogenously, on the basis of central cues, predictive of the relevant location, or exogenously, automatically triggered by the salient properties of visual stimuli (peripheral cues). Several dissociations observed between orienting on the basis of the two types of cues have led to the conclusion that they do not represent just two modes of triggering the orienting of the very same attentional mechanism, but rather they modulate processing differently. We present a theoretical framework according to which endogenous predictive cues facilitate target processing by orienting attention, thus amplifying processing at the attended location. In contrast, apart from attentional orienting, peripherally presented discrepant cues might trigger additional cue-target event-integration and event-segregation processes, which modulate processing in a different way, thus leading to cueing effects that are exclusively triggered by peripheral cues.     

Sequential effects on speeded information processing: a developmental study

Two experiments were performed to assess age-related changes in sequential effects on choice reaction time (RT). Sequential effects portray the influence of previous trials on the RT to the current stimulus. In Experiment 1, three age groups (7-9, 10-12, and 18-25 years) performed a spatially compatible choice task, with response-to-stimulus intervals (RSIs) of 50 and 500 ms varied between trial blocks. In Experiment 2, three age groups (7-9, 15-16, and 18-25 years) performed the task with spatial stimulus-response (S-R) mappings (compatible versus incompatible) varied between participants. For adults, the experiments yielded a pattern of sequential effects suggestive of "automatic facilitation" (i.e., a first-order repetition effect and a higher order benefit-only pattern for short RSIs) and "subjective expectancy" (i.e., a first-order alternation effect and a higher order cost-benefit pattern for long RSIs). Automatic facilitation was more pronounced for incompatible responses than for compatible responses. Both experiments showed the anticipated decrease in automatic facilitation with advancing age. Finally, the first-order alternation effect showed the predicted age-related increase, but the cost-benefit pattern revealed an opposite trend, suggesting that the first-order and higher order indexes of subjective expectancy may relate to dissociable mechanisms.     

Critical levels and magnitude of effects

Researchers sometimes report an effect of an experimental manipulation on a dependent variable in terms of the difference between levels of a certain nuisance variable required in the different experimental conditions to reach a given criterion of behavior. This method, however, may yield illusory impressions about magnitude of effects.