Solidaridad

A general recommendation to be inferred from the simulation is to perform an a priori simulation of the RMI test before “jumping to conclusions”. By that, parameters like the subject and sample size, probability test points and violation criterion can be set, so that

overall type I errors and (potential) estimation biases are minimized while power is maximized. An increase of the significance level is strongly disadvised, as it has a

disproportional effect on power and overall type I errors in the simulation. The most satisfying results are achieved for high sample and subject sizes, when high base time variance and negative correlation can be excluded.

Furthermore a power analysis provides the community (and the respective journal) with quantitative estimates of the overall type I errors and power rates and thus helps to solidify results (or null results). This is also in line with the new statistical guidelines

(concerning the problem area of publication bias and reporting power analyses) publishers and journals are currently implementing (for example, Open Science Collaboration, 2012). Another more diagnostic use of the simulation framework can be to re-analyze “failed

attempts” to detect violations and check, whether this was due to an underpowered design or potential estimation biases.

On a practical level, the question arises how to find the right coactivation strength for specific data sets. One pragmatic approach is to use programs that allow for estimation of the RDM parameters. One, the EZ diffusion model (Wagenmakers et al., 2007) uses a simplified version of diffusion models and provides an interactive homepage, where researchers can do a fast parameter fitting (http://www.ejwagenmakers.com/EZ.html). An alternative is the fastdiffusion model analysis program (Voss & Voss, 2007). With both, one can estimate the RDM parameters of the single channels and then simulate different λ’s to see which can produce the observed empirical RSE. More computationally intensive methods involve numerical fitting of the CDFs X, Y and XYC to a drift rate constrained

coactivation model and find the parameters rendering the best goodness-of-fit (for concrete fitting steps see chapter 3.2 or Ratcliff, 2002 or Gomez et al., 2007).

4.5.8 Conclusion

Summing up, the simulation study gives the following answers to the explicated research questions. The RMI test indeed is a very conservative test, as it misses out on (latent) coactivation in most empirically plausible cases. When coactivation models are used that produce a comparable RSE, violations can only be achieved for high sample and subject sizes and under the assumption that the base time variance is low. When the data is afflicted with a high base time variance, the chances of detecting violations of the RMI are yet worse.

The amount of estimation bias is negligible for both race and coactivation models as it is confined to a narrow -0.5 to 0.5 ms band for plausible probability ranges and experimental conditions (i.e. high enough sample sizes per experimental condition).

Concerning the effect of a highly varying base time component on the power, the simulations reaffirmed the results by Townsend and Honey (2007). A high base time variance decreases both the power and the type I errors of the RMI test. An extension of their results is the phenomenon that low base time variances produce large type I errors if the channel correlation is maximally negative. Thus, empirically it is important to find a means to estimate the channel correlation and at best, exclude the maximum negative case.

A novel finding is that the distribution relation affects the detectability of RMI violations: the more pronounced the difference in distributions, the higher the chances to detect coactivation, if it is the source of the RSE.

Overall, this study integrates and extends the studies of Towsend and Honey (2007) and Kiesel et al. (2007) in form of the simulation framework. Using state-of-the art models of decision making, it enables researchers now to further investigate and assess the RMI test for various experimental tasks, conditions and test related parameters. Also it provides a tool to optimally set up the RMI test, depending on the intention of the researcher (be it minimize α accumulation or maximize power of the test). Albeit, the RMI test alone is not able to settle the question of cognitive architecture in the redundant signals paradigm, it is the critical first step to rule out a large class of otherwise self-evident models.

5

GENERAL DISCUSSION

The application of formal mathematical models to empirical cognitive and

Experimental psychology has paved the way for numerous revelations on the inner workings of the mind (e.g. the serial-parallel dilemma Townsend & Wenger, 2004). One prevalent enigma is the question about cognitive architecture in contexts where an integration of signals is necessary to carry out perceptual-motor tasks (e.g. the redundant signals

paradigm). A prime example of how mental chronometry can help answer this question is the distributional bound on reaction times for the redundant signals effect, presented by Miller (1982). It established a pivotal non-parametrical test to exclude one class of explanatory model – race models. Furthermore it minimizes the risk of model mimicry as it is formulated on a distributional level and thus accounts for a larger proportion of the data.

The present study makes a vital contribution to this endeavor as it combines state-of- the-art models of decision making to the rigor of distributional testing. This combination enables researchers to analyze and evaluate the performance of the RMI test by means of computer intensive methods, such as Monte Carlo simulations and numerical fittings. The present study pursued objectives on a theoretical and methodological level. On a theoretical level it investigated the locus of coactivation for two bimodal detection tasks (with focused and divided attention). There, the quantile proportion fitting revealed that a combined decisional and nondecisional coactivation model was in best agreement to the data of

Experiment 1 and 2. Interestingly, for the divided attention detection task in Experiment 2, the motor coactivation contributed more strongly to the redundant signals effect, than the

decisional component.

On a methodological level, the study improved the understanding and value of the RMI test as a statistical tool, as the interplay of various psychological and experimental parameters on type I errors and power rates was explicated. Novel findings are the strong vulnerability of the test in terms of type I error accumulation when the data is maximally negatively correlated, and the pronounced distribution relation effect, which can impact the power of the test substantially. The present study is also the first to implement and test a mechanistic model of coactivation that allows for controlling the strength of integration. The study could show that such coactivation models frequently fail to produce RMI violations and healthy power rates are only attainable, if high base time variance can be excluded and both sample and subject sizes are maximized. The here developed simulation framework

furthermore provides a well-grounded diagnostic tool for the RMI test, as it enables

to its modular design, it can be adapted to different RMI tests, decision models and experimental and statistical parameters.

In this last chapter, limitations and theoretical and methodological implications of the present study are discussed.

5.1 Limitations of the present Study