Numerical test of the Cardy-Jacobsen conjecture in the site-diluted Potts model in three dimensions

We present a microcanonical Monte Carlo simulation of the site-diluted Potts model in three dimensions with eight internal states, partly carried out on the citizen supercomputer Ibercivis. Upon dilution, the pure model’s first-order transition becomes of the second order at a tricritical point. We compute accurately the critical exponents at the tricritical point. As expected from the Cardy-Jacobsen conjecture, they are compatible with their random field Ising model counterpart. The conclusion is further reinforced by comparison with older data for the Potts model with four states.

Descriptive analysis of the test of everyday attention for children in a Spanish normative sample

Introduction. Test of Everyday Attention for Children (TEA-Ch) has been validated in different countries demonstrating that it is an instrument with a correct balance between reliability and duration. Given the shortage of trustworthy instruments of evaluation in our language for infantile population we decide to explore the Spanish version of the TEA-Ch. Methods. We administered TEA-Ch (version A) to a sample control of 133 Spanish children from 6 to 11 years enrolled in school in the Community of Madrid. Four children were selected at random by course of Primary Education, distributing the sex of equivalent form. Descriptive analysis and comparison by ages and sex in each of the TEA-Ch's subtests were conducted to establish a profile of the sample. In order to analyze the effect of the age, subjects were grouped in six sub-samples: 6, 7, 8, 9, 10 and 11 years-old. Results. This first descriptive analysis demonstrates age exerted a significant effect on each measure, due to an important "jump" in children's performance between 6 and 7 years-old. The effect of sex was significant only in two visual attention measures (Sky Search & Map) and interaction age and sex exerted a significant effect only in the dual task (Score DT). Conclusions. The results suggest that the Spanish version of the TEA-Ch (A) might be a useful instrument to evaluate attentional processes in Spanish child population.

Analysis of residuals in contingency tables: another nail in the coffin of conditional approaches to significance testing.

Omnibus tests of significance in contingency tables use statistics of the chi-square type. When the null is rejected, residual analyses are conducted to identify cells in which observed frequencies differ significantly from expected frequencies. Residual analyses are thus conditioned on a significant omnibus test. Conditional approaches have been shown to substantially alter type I error rates in cases involving t tests conditional on the results of a test of equality of variances, or tests of regression coefficients conditional on the results of tests of heteroscedasticity. We show that residual analyses conditional on a significant omnibus test are also affected by this problem, yielding type I error rates that can be up to 6 times larger than nominal rates, depending on the size of the table and the form of the marginal distributions. We explored several unconditional approaches in search for a method that maintains the nominal type I error rate and found out that a bootstrap correction for multiple testing achieved this goal. The validity of this approach is documented for two-way contingency tables in the contexts of tests of independence, tests of homogeneity, and fitting psychometric functions. Computer code in MATLAB and R to conduct these analyses is provided as Supplementary Material.

The transducer model for contrast detection and discrimination: formal relations, implications, and an empirical test.

The transducer function mu for contrast perception describes the nonlinear mapping of stimulus contrast onto an internal response. Under a signal detection theory approach, the transducer model of contrast perception states that the internal response elicited by a stimulus of contrast c is a random variable with mean mu(c). Using this approach, we derive the formal relations between the transducer function, the threshold-versus-contrast (TvC) function, and the psychometric functions for contrast detection and discrimination in 2AFC tasks. We show that the mathematical form of the TvC function is determined only by mu, and that the psychometric functions for detection and discrimination have a common mathematical form with common parameters emanating from, and only from, the transducer function mu and the form of the distribution of the internal responses. We discuss the theoretical and practical implications of these relations, which have bearings on the tenability of certain mathematical forms for the psychometric function and on the suitability of empirical approaches to model validation. We also present the results of a comprehensive test of these relations using two alternative forms of the transducer model: a three-parameter version that renders logistic psychometric functions and a five-parameter version using Foley's variant of the Naka-Rushton equation as transducer function. Our results support the validity of the formal relations implied by the general transducer model, and the two versions that were contrasted account for our data equally well.