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.     

The effect of facial attractiveness on temporal perception

Previous research suggests that feelings of fear, dislike, shame and sadness affect our perception of duration (Droit-Volet et al., 2004; Gil et al., 2009). The current study sought to expand our understanding of the variables which moderate temporal perception by examining whether the attractiveness of a face influenced its perceived duration. Participants completed a verbal estimation task in which they judged the duration of attractive, unattractive and neutral faces. The results showed that participants underestimated the duration of unattractive faces relative to attractive and neutral faces. Estimates of unattractive faces were also less accurate than those of the attractive and neutral faces. The results are consistent with Gil et al.'s (2009) suggestion that the duration of disliked stimuli are underestimated relative to liked and neutral stimuli because they detract attention from temporal perception. Analysis of the slope and intercept of the estimation gradients supports Zakay and Block's (1997) suggestion that reduced attention to time results in a multiplicative underestimation of duration.     

Imprecise Epistemic Values and Imprecise Credences

A number of recent arguments purport to show that imprecise credences are incompatible with accuracy-first epistemology. If correct, this conclusion suggests a conflict between evidential and alethic epistemic norms. In the first part of the paper, I claim that these arguments fail if we understand imprecise credences as indeterminate credences. In the second part, I explore why agents with entirely alethic epistemic values can end up in an indeterminate credal state. Following William James, I argue that there are many distinct alethic values that a rational agent can have. Furthermore, such an agent is rationally permitted not to have settled on one fully precise value function. This indeterminacy in value will sometimes result in indeterminacy in epistemic behaviour—that is, because the agent’s values aren’t settled, what she believes might not be.     

Can membership-functions capture the directionality of verbal probabilities?

Verbal probabilities are a common mean for communicating risk and uncertainties in many decision-making settings (e.g., finance, medicine, military). They are considered directional because they elicit a focus on either the outcome occurrence (e.g., there is a chance) or on its non-occurrence (e.g., it is unlikely). According to a quantitative perspective, directionality is dependent on the vague probabilistic meaning conveyed by verbal probabilities—e.g., p(outcome) > .50 = > focus on outcome occurrence. In contrast a more qualitative perspective suggests that directionality depends on contextual factors. The present study tested whether the directionality of verbal probabilities was determined by their vague probabilistic meaning, by contextually manipulated variables (i.e., representativeness and base rate), or by a combination of both. Participants provided their own expressions to describe the guilt of a suspect and then assessed the vague probabilistic meaning and directionality associated with those expressions. Results showed that directionality was mainly determined by the vague probabilistic meaning but also by the base rate of guilt. Although attention focus on the occurrence or the non-occurrence of the target outcome is dependent on vague probabilistic meaning, it cannot be fully accounted for by it.