Relating tests given to different samples

Suppose a collection of standard tests is given to all subjects in a random sample, but a different new test is given to each group of subjects in nonoverlapping subsamples. A simple method is developed for displaying the information that the data set contains about the correlational structure of the new tests. This is possible to some extent, even though each subject takes only one new test. The method uses plausible values of the partial correlations among the new tests given the standard tests in order to generate plausible simple correlations among the new tests and plausible multiple correlations between composites of the new tests and the standard tests. The real data example included suggests that the method can be useful in practical problems.     

Estimation in the power law

Most psychophysicists neglect to consider how error should be characterized in applications of the power law. Failures of the power law to agree with certain theoretical predictions may be due to bias of parameter estimates. A power law with lognormal product structure is proposed and approximately unbiased parameter estimates are given for several common estimation situations.     

Grading distractor-identification tests

On distractor-identification tests students mark as many distractors as possible on each test item. A grading scale is developed for this type testing. The scale is optimal in that it is the unique scale giving an unbiased estimate of the student's true score, i.e., the score that would result if no guessing occurred. If the test is administered as a usual multiple choice test and graded using the usual correction for guessing scale, the expected item score is the same as for the distractor-identification testing using the optimal grading scale. However, the variance of the item score is shown to be less for distractor-identification testing than for usual multiple choice testing under certain conditions.     

The bias function of the maximum likelihood estimate of ability for the dichotomous response level

Samejima has recently given an approximation for the bias function for the maximum likelihood estimate of the latent trait in the general case where item responses are discrete, generalizing Lord's bias function in the three-parameter logistic model for the dichotomous response level. In the present paper, observations are made about the behavior of this bias function for the dichotomous response level in general, and also with respect to several widely used mathematical models. Some empirical examples are given.     

An approximation for the bias function of the maximum likelihood estimate of a latent variable for the general case where the item responses are discrete

Lord developed an approximation for the bias function for the maximum likelihood estimate in the context of the three-parameter logistic model. Using Taylor's expansion of the likelihood equation, he obtained an equation that includes the conditional expectation, given true ability, of the discrepancy between the maximum likelihood estimate and true ability. All terms of orders higher thann ^?1 are ignored wheren indicates the number of items. Lord assumed that all item and individual parameters are bounded, all item parameters are known or well-estimated, and the number of items is reasonably large. In the present paper, an approximation for the bias function of the maximum likelihood estimate of the latent trait, or ability, will be developed using the same assumptions for the more general case where item responses are discrete. This will include the dichotomous response level, for which the three-parameter logistic model has been discussed, the graded response level and the nominal response level. Some observations will be made for both dichotomous and graded response levels.     

The relationship between feeding rate and patch choice.

Rats in a laboratory foraging simulation searched for sequential opportunities to feed in two patches that differed in the rate at which food pellets were delivered (controlled by fixed-interval schedules) and in the size of the pellets. The profitability of feeding in each patch was calculated in terms of time (grams per minute) and in terms of effort (grams per bar press). These values were the result of the imposed fixed interval, the size of the pellets, and the rate at which the rats pressed the bar in each condition. The rats ate more food and larger meals, but not more frequent meals, at the patch offering the higher rate of food consumption, calculated as grams per minute. The relative intake at any patch was a function of the relative rate of intake during meals at that patch compared to the other patch. Rats respond to explicit manipulations of feeding time in the same manner as they respond to manipulations of feeding effort.     

A numerical approach to the approximate and the exact minimum rank of a covariance matrix

A concept of approximate minimum rank for a covariance matrix is defined, which contains the (exact) minimum rank as a special case. A computational procedure to evaluate the approximate minimum rank is offered. The procedure yields those proper communalities for which the unexplained common variance, ignored in low-rank factor analysis, is minimized. The procedure also permits a numerical determination of the exact minimum rank of a covariance matrix, within limits of computational accuracy. A set of 180 covariance matrices with known or bounded minimum rank was analyzed. The procedure was successful throughout in recovering the desired rank.The authors are obliged to Paul Bekker for stimulating and helpful comments.     

Temporal perception in closed-skill sports: An experimental study on expert swimmers and runners

The cognitive benefits of closed-skill sports practice have so far been scantily investigated. Here, we thus focused on the potential impact of swimming and running - two sports that highly rely on a precise control of timing - on time processing. To investigate the impact of these closed-skill sports on time perception and estimation, three groups of participants (for a total of eighty-four young adults) took part in the present study: expert swimmers, expert runners, and non-athletes. The ability to process temporal information in the milliseconds and seconds range was assessed through a time reproduction and a finger-tapping tasks, while a motor imagery paradigm was adopted to assess temporal estimation of sport performance in a wider interval range. We also employed the Vividness of Movement Imagery Questionnaire to assess the individual's ability of motor imagery. Results showed that closed-skill sports, specifically time-related disciplines, enhance motor imagery and time perception abilities. Swimmers were more accurate and consistent in perceiving time when compared to runners, probably thanks to the sensory muffled environment that leads these athletes to be more focused on the perception of their internal rhythm.     

Effect sizes in ANCOVA and difference-in-differences designs

It is common practice in both randomized and quasi-experiments to adjust for baseline characteristics when estimating the average effect of an intervention. The inclusion of a pre-test, for example, can reduce both the standard error of this estimate and—in non-randomized designs—its bias. At the same time, it is also standard to report the effect of an intervention in standardized effect size units, thereby making it comparable to other interventions and studies. Curiously, the estimation of this effect size, including covariate adjustment, has received little attention. In this article, we provide a framework for defining effect sizes in designs with a pre-test (e.g., difference-in-differences and analysis of covariance) and propose estimators of those effect sizes. The estimators and approximations to their sampling distributions are evaluated using a simulation study and then demonstrated using an example from published data.     

Mixture-modelling-based Bayesian MH-RM algorithm for the multidimensional 4PLM

Several recent works have tackled the estimation issue for the unidimensional four-parameter logistic model (4PLM). Despite these efforts, the issue remains a challenge for the multidimensional 4PLM (M4PLM). Fu et al. (2021) proposed a Gibbs sampler for the M4PLM, but it is time-consuming. In this paper, a mixture-modelling-based Bayesian MH-RM (MM-MH-RM) algorithm is proposed for the M4PLM to obtain the maximum a posteriori (MAP) estimates. In a comparison of the MM-MH-RM algorithm to the original MH-RM algorithm, two simulation studies and an empirical example demonstrated that the MM-MH-RM algorithm possessed the benefits of the mixture-modelling approach and could produce more robust estimates with guaranteed convergence rates and fast computation. The MATLAB codes for the MM-MH-RM algorithm are available in the online appendix.