Goals and methods A simulation study investigated how ceiling and floor effect (CFE) affect the performance of Welch’s t -test, F -test, Mann-Whitney test, Kruskal-Wallis test, Scheirer-Ray-Hare-test, trimmed t -test, Bayesian t -test, and the “two one-sided tests” equivalence testing procedure. The effect of CFE on the estimate of group difference and on its confidence interval, and on Cohen’s d and on its confidence interval was also evaluated. In addition, the parametric methods were applied to data transformed with log or logit function and the performance was evaluated. The notion of essential maximum from abstract measurement theory is used to formally define CFE and the principle of maximum entropy was used to derive probability distributions with essential maximum/minimum. These distributions allow the manipulation of the magnitude of CFE through a parameter. Beta, Gamma, Beta prime and Beta-binomial distributions were obtained in this way with the CFE parameter corresponding to the logarithm of the geometric mean. Wald distribution and ordered logistic regression were also included in the study due to their measure-theoretic connection to CFE, even though these models lack essential minimum/maximum. Performance in two-group, three-group and 2 × 2 factor design scenarios was investigated by fixing the group differences in terms of CFE parameter and by adjusting the base level of CFE. Results and conclusions In general, bias and uncertainty increased with CFE. Most problematic were occasional instances of biased inference which became more certain and more biased as the magnitude of CFE increased. The bias affected the estimate of group difference, the estimate of Cohen’s d and the decisions of the equivalence testing methods. Statistical methods worked best with transformed data, albeit this depended on the match between the choice of transformation and the type of CFE. Log transform worked well with Gamma and Beta prime distribution while logit transform worked well with Beta distribution. Rank-based tests showed best performance with discrete data, but it was demonstrated that even there a model derived with measurement-theoretic principles may show superior performance. Trimmed t -test showed poor performance. In the factor design, CFE prevented the detection of main effects as well as the detection of interaction. Irrespective of CFE, F -test misidentified main effects and interactions on multiple occasions. Five different constellations of main effect and interactions were investigated for each probability distribution, and weaknesses of each statistical method were identified and reported. As part of the discussion, the use of generalized linear models based on abstract measurement theory is recommended to counter CFE. Furthermore, the nec...

We explore the role of eye movements in a chase detection task. Unlike the previous studies, which focused on overall performance as indicated by response speed and chase detection accuracy, we decompose the search process into gaze events such as smooth eye movements and use a data-driven approach to separately describe these gaze events. We measured eye movements of four human subjects engaged in a chase detection task displayed on a computer screen. The subjects were asked to detect two chasing rings among twelve other randomly moving rings. Using principal component analysis and support vector machines, we looked at the template and classification images that describe various stages of the detection process. We showed that the subjects mostly search for pairs of rings that move one after another in the same direction with a distance of 3.5–3.8 degrees. To find such pairs, the subjects first looked for regions with a high ring density and then pursued the rings in this region. Most of these groups consisted of two rings. Three subjects preferred to pursue the pair as a single object, while the remaining subject pursued the group by alternating the gaze between the two individual rings. In the discussion, we argue that subjects do not compare the movement of the pursued pair to a singular preformed template that describes a chasing motion. Rather, subjects bring certain hypotheses about what motion may qualify as chase and then, through feedback, they learn to look for a motion pattern that maximizes their performance.

We investigate the influence of perceived displacement of moving agent-like stimuli on the performance in dynamic interactive tasks. In order to reliably measure perceived displacement we utilize multiple tasks with different task demands. The perceived center of an agent's body is displaced in the direction in which the agent is facing and this perceived displacement is larger than the theoretical position of the center of mass would predict. Furthermore, the displacement in the explicit judgment is dissociated from the displacement obtained by the implicit measures. By manipulating the location of the pivot point, we show that it is not necessary to postulate orientation as an additional cue utilized by perception, as has been suggested by earlier studies. These studies showed that the agent's orientation influences the detection of chasing motion and the detection-related performance in interactive tasks. This influence has been labeled wolfpack effect. In one of the demonstrations of the wolfpack effect participants control a green circle on a display with a computer mouse. It has been shown that participants avoid display areas with agents pointing toward the green circle. Participants do so in favor of areas where the agents point in the direction perpendicular to the circle. We show that this avoidance behavior arises because the agent's pivot point selected by the earlier studies is different from where people locate the center of agent's body. As a consequence, the nominal rotation confounds rotation and translation. We show that the avoidance behavior disappears once the pivot point is set to the center of agent's body.

Additive and multiplicative regression models of habituation were compared regarding the fit to looking times from a habituation experiment with infants aged between 3 and 11 months. In contrast to earlier studies, the current study considered multiple probability distributions, namely Weibull, gamma, lognormal and normal distribution. In the habituation experiment the type of contrast between the habituation and the test trial was varied (luminance, color or orientation contrast), crossed with the number of habituation trials (1, 3, 5, or 7 habituation trials) and crossed with three age cohorts (4, 7, 10 months). The initial mean LT to dark stimuli (around 3.7 s) was considerably shorter than the mean LT to green and gray stimuli (around 5 s). Infants showed the strongest dishabituation to changes from dark to bright (luminance contrast) and weak-to-no dishabituation to a 90-degrees rotation of the gray stimuli (orientation contrast). The dishabituation was stronger after five and seven habituation trials, but the result was not statistically robust. The gamma distribution showed the best fit in terms of log-likelihood and mean absolute error and the best predictive performance. Furthermore, the gamma distribution showed small correlations between parameters relative to other models. The normal additive model showed an inferior fit and medium correlations between the parameters. In particular, the positive correlation between the initial looking time (LT) and the habituation rate was likely responsible for a different interpretation relative to the multiplicative models of the main effect of age on the habituation rate. Otherwise, the additive and multiplicative models provided similar statistical conclusions. The performance of the model versions without pooling and with partial pooling across participants (also called random-effects, multi-level or hierarchical models) were compared. The latter type of models showed worse data fit but more precise predictions and reduced correlations between the parameters. The performance of model variants with auto-regressive time structures were explored but showed considerably worse fit. The performance of quadratic models that allowed non-monotonic changes in LTs were investigated as well. However, when fitted with LT data, these models did not produce non-monotonic change in LTs. The study underscores the utility of partial-pooling models in terms of providing more accurate predictions. Further, it agrees with previous research in that a multiplicative LT model is preferable. Nevertheless, the current results suggest that the impact of the choice of an additive model on the statistical inference is less dramatic then previously assumed.