The effects of a high-probability instruction sequence and response-independent reinforcer delivery on child compliance

We compared the effects of a high-probability (high-p) instruction sequence and a fixed-time (FT) schedule of reinforcement on the compliance of 2 typically developing children. A multielement experimental design with a reversal component was implemented according to a multiple baseline across participants arrangement. Both the high-p and FT conditions resulted in increased compliance for both participants during the multielement sessions. These results suggest that it may be possible to increase compliance without a response requirement of the type arranged in the high-p instruction sequence.     

Notes on discounting

In general, if a variable can be expressed as a function of its own maximum value, that function may be called a discount function. Delay discounting and probability discounting are commonly studied in psychology, but memory, matching, and economic utility also may be viewed as discounting processes. When they are so viewed, the discount function obtained is hyperbolic in form. In some cases the effective discounting variable is proportional to the physical variable on which it is based. For example, in delay discounting, the physical variable, delay (D), may enter into the hyperbolic equation as kD. In many cases, however, the discounting data are not well described with a single-parameter discount function. A much better fit is obtained when the effective variable is a power function of the physical variable (kDS in the case of delay discounting). This power-function form fits the data of delay, probability, and memory discounting as well as other two-parameter discount functions and is consistent with both the generalized matching law and maximization of a constant-elasticity-of-substitution utility     

Estimation and visualization of confusability matrices from adaptive measurement data

We present a simple but effective method based on Luce’s choice axiom [Luce, R.D. (1959). Individual choice behavior: A theoretical analysis. New York: John Wiley & Sons] for consistent estimation of the pairwise confusabilities of items in a multiple-choice recognition task with arbitrarily chosen choice-sets. The method combines the exact (non-asymptotic) Bayesian way of assessing uncertainty with the unbiasedness emphasized in the classical frequentist approach.We apply the method to data collected using an adaptive computer game designed for prevention of reading disability. A player’s estimated confusability of phonemes (or more accurately, phoneme-grapheme connections) and larger units of language is visualized in an easily understood way with color cues and explicit indication of the accuracy of the estimates. Visualization of learning-related changes in the player’s performance is considered.The empirical validity of the choice axiom is evaluated using the game data itself. The axiom appears to hold reasonably well although a small systematic violation is observable for the smallest choice-set sizes.     

A Bayesian-optimal principle for learner-friendly adaptation in learning games

Adaptive learning games should provide opportunities for the student to learn as well as motivate playing until goals have been reached. In this paper, we give a mathematically rigorous treatment of the problem in the framework of Bayesian decision theory. To quantify the opportunities for learning, we assume that the learning tasks that yield the most information about the current skills of the student, while being desirable for measurement in their own right, would also be among those that are efficient for learning. Indeed, optimization of the expected information gain appears to naturally avoid tasks that are exceedingly demanding or exceedingly easy as their results are predictable and thus uninformative. Still, tasks that are efficient for learning may be experienced as too challenging, and the resulting failures can lower motivation. Therefore, in addition to quantifying the expected informational benefit for learning of any prospective task to be presented next, we also model the expected motivational cost of its presentation, measured simply as the estimated probability of failure in our example model. We propose a “learner-friendly” adaptation algorithm that chooses the learning tasks by optimizing the expected benefit divided by the expected cost. We apply this algorithm to a Rasch-like student model implemented within a real-world application and present initial results of a pilot experiment.     

Rate, Probability and Matching: Comments on ��The Identities Hidden in the Matching Laws, and Their Uses�� by David Thorne

David Thorne's (2010) article, “The Identities Hidden In The Matching Laws, And Their Uses” performs a valuable service in pointing out alternative expressions of matching. However, some identities tend to obscure rather than illuminate empirical relationships. Three such problematic instances are discussed: interresponse time as a function of interval and ratio schedule parameters; probability equality as implying rate matching; the apparent simplicity of probabilistic functions, as opposed to response rate functions, of reinforcement rate.     

《心理统计学》教学内容的新探索

本文在对当前国内外主要心理统计学教材进行比较的基础上,指出与上个世纪八十年代的心理统计学教材内容相比较,在内容上的新探索主要体现在（1）由“假设检验”的内容中发展出“统计检验力”和“效果大小”的统计指标和估计方法;（2）引进一般线性模型来统合方差分析和回归分析这两种统计方法;（3）适度增加一些“多元统计分析”的内容等三个方面.本文对前两个方面的新内容作了简要评述,并对教材内容的编排方面提出了新的思路.     

How do we convert a number into a finger trajectory?

How do we understand two-digit numbers such as 42? Models of multi-digit number comprehension differ widely. Some postulate that the decades and units digits are processed separately and possibly serially. Others hypothesize a holistic process which maps the entire 2-digit string onto a magnitude, represented as a position on a number line. In educated adults, the number line is thought to be linear, but the “number sense” hypothesis proposes that a logarithmic scale underlies our intuitions of number size, and that this compressive representation may still be dormant in the adult brain. We investigated these issues by asking adults to point to the location of two-digit numbers on a number line while their finger location was continuously monitored. Finger trajectories revealed a linear scale, yet with a transient logarithmic effect suggesting the activation of a compressive and holistic quantity representation. Units and decades digits were processed in parallel, without any difference in left-to-right vs. right-to-left readers. The late part of the trajectory was influenced by spatial reference points placed at the left end, middle, and right end of the line. Altogether, finger trajectory analysis provides a precise cognitive decomposition of the sequence of stages used in converting a number to a quantity and then a position.     

Monaural Loudness Adaptation for Middle-Intensity Middle-Frequency Signals: The Importance of Measurement Technique

Using the Simple Adaptation technique (SA) and the Ipsilateral Comparison Paradigm (ICP), the authors studied monaural loudness adaptation to a middle-intensity [60 dB(A)] tone at signal frequencies of 250, 1000, and 4000 Hz in the left and right ears. Adaptation effects were absent when the SA procedure was used. However, they were observed uniformly across all frequency values with the ICP, a result that challenges the assertion in the literature, on the basis of SA measures, that loudness adaptation for middle-intensity signals occurs only at frequencies above 4000 Hz. The ICP features periodic intensity modulations (±10 dB relative to the base signal) to accommodate listeners' needs for referents by which they can gauge subtle changes in the loudness of the adapting tone, a key component that is missing in the SA method. Adaptation effects in this investigation were similar in both ears, supporting the equal susceptibility assumption common in loudness adaptation studies.     

Do Children Perceive Postural Constraints When Estimating Reach or Action Planning?

Estimation of whether an object is reachable from a specific body position constitutes an important aspect in effective motor planning. Researchers who estimate reachability by way of motor imagery with adults consistently report the tendency to overestimate, with some evidence of a postural effect (postural stability hypothesis). This idea suggests that perceived reaching limits depend on an individual's perceived postural constraints. Based on previous work with adults, the authors expected a significant postural effect with the Reach 2 condition, as evidenced by reduced overestimation. Furthermore, the authors hypothesized that the postural effect would be greater in younger children. They then tested these propositions among children aged 7, 9, and 11 years by asking them to estimate reach while seated (Reach 1) and in the more demanding posture of standing on 1 foot and leaning forward (Reach 2). Results indicated no age or condition difference, therefore providing no support for a postural effect. When the authors compared these data to a published report of adults, a developmental difference emerged. That is, adults recognize the perceived postural constraint of the standing position resulting in under- rather than overestimation, as displayed in the seated condition. Although preliminary, these observations suggest that estimates of reach (action planning) continue to be refined between late childhood and young adulthood.     

Communal Versus Individual Learning of a Math-Estimation Task: African American Children and the Culture of Learning Contexts

The authors compared the performance of 78 African American 5th-grade students who studied a math-estimation task in one of two learning contexts. Learning contexts differed in the degree to which they afforded the expression of communalism. ANCOVA confirmed that posttest performance was best for students who studied in the high communal-learning context. The findings support A. W. Boykin's (1994) contention that the cultural context of learning can be a critical mediator of children's performance.