Categoricity Theorems and Conceptions of Set

Two models of second-order ZFC need not be isomorphic to each other, but at least one is isomorphic to an initial segment of the other. The situation is subtler for impure set theory, but Vann McGee has recently proved a categoricity result for second-order ZFCU plus the axiom that the urelements form a set. Two models of this theory with the same universe of discourse need not be isomorphic to each other, but the pure sets of one are isomorphic to the pure sets of the other.This paper argues that similar results obtain for considerably weaker second-order axiomatizations of impure set theory that are in line with two different conceptions of set, the iterative conception and the limitation of size doctrine.     

低色温低强度背景光照射下液晶显示颜色编码的实验研究

采用一台有源矩阵彩色液晶显示器作为主要实验装置,对低色温、低强度背景光照射下液晶显示颜色编码范围及其与色标大小的关系进行了研究。实验结果表明:(1)液晶显示器上色标大小对绝对辨认效果有显著影响,随着色标的增大,辨认错误率随之下降,但下降率则随色标的增大而递减。(2)在色温为3100K的低强度背景光照射下,液晶显示的颜色编码范围因色标大小不同而存在显著差异,当色标面积减小到1×1mm2至2×2mm2时,编码色数目仅限于3-4种。     

A Test by Any Other Name: P Values,Bayes Factors,and Statistical Inference

Procedures used for statistical inference are receiving increased scrutiny as the scientific community studies the factors associated with insuring reproducible research. This note addresses recent negative attention directed at p values, the relationship of confidence intervals and tests, and the role of Bayesian inference and Bayes factors, with an eye toward better understanding these different strategies for statistical inference. We argue that researchers and data analysts too often resort to binary decisions (e.g., whether to reject or accept the null hypothesis) in settings where this may not be required.     

A Comparative Investigation of Confidence Intervals for IndependentVariables in Linear Regression

In linear regression, the most appropriate standardized effect size for individual independent variables having an arbitrary metric remains open to debate, despite researchers typically reporting a standardized regression coefficient. Alternative standardized measures include the semipartial correlation, the improvement in the squared multiple correlation, and the squared partial correlation. No arguments based on either theoretical or statistical grounds for preferring one of these standardized measures have been mounted in the literature. Using a Monte Carlo simulation, the performance of interval estimators for these effect-size measures was compared in a 5-way factorial design. Formal statistical design methods assessed both the accuracy and robustness of the four interval estimators. The coverage probability of a large-sample confidence interval for the semipartial correlation coefficient derived from Aloe and Becker was highly accurate and robust in 98% of instances. It was better in small samples than the Yuan-Chan large-sample confidence interval for a standardized regression coefficient. It was also consistently better than both a bootstrap confidence interval for the improvement in the squared multiple correlation and a noncentral interval for the squared partial correlation.     

Estimation of the Coefficient of Variation with Minimum Risk: A Sequential Method for Minimizing Sampling Error and Study Cost

The coefficient of variation is an effect size measure with many potential uses in psychology and related disciplines. We propose a general theory for a sequential estimation of the population coefficient of variation that considers both the sampling error and the study cost, importantly without specific distributional assumptions. Fixed sample size planning methods, commonly used in psychology and related fields, cannot simultaneously minimize both the sampling error and the study cost. The sequential procedure we develop is the first sequential sampling procedure developed for estimating the coefficient of variation. We first present a method of planning a pilot sample size after the research goals are specified by the researcher. Then, after collecting a sample size as large as the estimated pilot sample size, a check is performed to assess whether the conditions necessary to stop the data collection have been satisfied. If not an additional observation is collected and the check is performed again. This process continues, sequentially, until a stopping rule involving a risk function is satisfied. Our method ensures that the sampling error and the study costs are considered simultaneously so that the cost is not higher than necessary for the tolerable sampling error. We also demonstrate a variety of properties of the distribution of the final sample size for five different distributions under a variety of conditions with a Monte Carlo simulation study. In addition, we provide freely available functions via the MBESS package in R to implement the methods discussed.     

Stimulus–response correspondence effect as a function of temporal overlap between relevant and irrelevant information processing

The stimulus–response correspondence (SRC) effect refers to advantages in performance when stimulus and response correspond in dimensions or features, even if the common features are irrelevant to the task. Previous research indicated that the SRC effect depends on the temporal course of stimulus information processing. The current study investigated how the temporal overlap between relevant and irrelevant stimulus processing influences the SRC effect. In this experiment, the irrelevant stimulus (a previously associated tone) preceded the relevant stimulus (a coloured rectangle). The irrelevant and relevant stimuli onset asynchrony was varied to manipulate the temporal overlap between the irrelevant and relevant stimuli processing. Results indicated that the SRC effect size varied as a quadratic function of the temporal overlap between the relevant stimulus and irrelevant stimulus. This finding extends previous experimental observations that the SRC effect size varies in an increasing or decreasing function with reaction time. The current study demonstrated a quadratic function between effect size and the temporal overlap.     

Linked proximal and distal changes in the reaching behavior of 5- to 12-month-old human infants grasping objects of different sizes

This study evaluates age-related proximal and distal changes in reaching organization for objects of different sizes. To this end, eight objects ranging from 2 to 9 cm diam. were presented to 23 infants ages 5 to 12 months. Proximal control was determined by the relative frequencies of bimanual reaching for large and small objects. Distal control was assessed by hand opening and orientation with respect to an object, and by the proportion of the object being included within hand opening at touch. Five-month-old infants tended to reach bimanually regardless of object size. Starting at 7 to 8 months, infants tended to reach for large objects bimanually more often than for small ones. Only at 11 to 12 months did reaching closely reflect the object’s diameter. The frequency of thumb-index finger angle opening during the approach phase also increased after 7 to 8 months of age, as well as the adjustment of the angle to the object diameter and the proportion of the object within hand opening at touch. Proximal and distal changes appeared coupled at 5 to 6 months, when the few subjects showing evidence of some proximal adjustments to object size were also those who exhibited some distal adjustments. After they started to appear, however, proximal and distal adjustments seemed to be independent, as revealed by the lack of correlation of proximal and distal changes between 7 and 12 months.     

Relationships between factors of intelligence and brain volume

The recent explosion of studies aimed at determining the biological basis of intelligence has revealed that cognitive ability has a strong biological substrate. This study expands on this literature by examining the relation between cognitive ability and MRI-measured brain volume and head size in a sample of adult male siblings recruited from the London, Ontario community in Canada. It was found that brain volume correlated with IQ at 0.35 (P<0.01), thus replicating the results of past studies. Corrections for restriction of range and attenuation in both this and past studies suggest that the population value of the brain volume-IQ correlation is closer to 0.50. Head size variables, with one exception, also showed the expected positive correlations with IQ. The results of a vector analysis on factor scores indicated that the more highly g-loaded a test was the more highly it correlated with brain volume (r=0.59, P<0.01). The sum of the data suggested that although brain volume (and to a lesser extent, head size) is predictive of g, fluid ability, and memory, it does not predict crystallized ability. Unexpectedly, the higher the spatial imaging loading of a test, the less its correlation with brain volume (vector correlation=−0.84, P<0.001).