Variable Autoconcepto En lo que concierne a la percepción que tiene el sujeto de sí mismo con respecto a los demás (auto concepto), este ha sido analizado en sus

Contrary to this commonly accepted notion of conservativeness, Kiesel, Miller and Ulrich (2007) have presented simulation data which suggests, that the RMI test is prone to false alarms, that is the inadequate rejection of race models based on flaws and biases in the tests’ procedure. The authors identified two weighty sources for such erroneous test

outcomes – an estimation bias working against race models and an accumulation of type I errors, when testing the RMI at multiple time points.

In the estimation literature (e.g. Gilchrist, 2000) it is a general finding that quantile estimators tend to overestimate the lowest percentiles and underestimate the highest percentiles. In the standard RMI test proposed by Ulrich et al. (2007) the estimation of the cumulative distribution functions for all experimental conditions plays a central role for computing the RMI bound and testing potential violations thereof (see algorithm step 1). Kiesel et al. (2007) defined a bias measure that quantifies the amount of deviation from the true cumulative distribution functions per probability point. Whenever this bias is negative, the RMI test is biased towards violations and thus incorrectly rejecting race models. When it is positive, it further pushes the test towards conservatism as violations are hindered. The authors used synthesized reaction times (using the ex-Wald distribution, Schwarz, 2001) to emulate racers with samples sizes of 10, 20 or 40 per condition. The results show that (depending on the sample sizes of the three conditions) substantial systematic bias pattern

can emerge. These are mostly negative in value and thus tend to produce violations of the RMI. Unfortunately these biases were not restricted to lower sample sizes but would also emerge for the largest sample size in their study (i.e. 40 samples per condition). The authors advise researchers to remain cautious, when they find violations of the RMI for studies with sample sizes lower than 20.

Another aspect this study addressed was the amount of type I error or α accumulation of the test. In the last step of the algorithm the empirical CDF of the redundant condition is compared to the estimated RMI bound. This comparison is realized by applying t-tests at typically multiple probability points. As the RMI test is generally considered to be

conservative, this multiple testing should increase the power of the test, as it is given more data points to become significant. Each t-test is set up with a significance level α to control for the amount of false alarms. Usually α is set to be 0.05, meaning that 1 out of 20 tests is prone to falsely find a statistically significant violation of the RMI bound. When conducting more than one t-test, this error probability inflates with each additional t-test. A numeric example shall illustrate this fact: Let α = P(“rejecting H0” | “H0 is true”) = 0.05, where H0 is “the

data was generated by a race model”. Then P(“retaining H0” | “H0 is true”) = 1 – α for one

testing the RMI at one probability point of the quantile function. When doing this k times on the same data however, the probability then is P*(k) = P(“retaining H0 for k probabilities” | “H0

is true”) = P(“retaining H0” | “H0 is true”)k = (1 – α)k, for k = 5 this yields P*(k = 5) = 0.774, and

the complementary event of P*(k = 5), that is, at least on t-test is committing a false alarm is 1 - P*(5) = 0.226. This effective α error of 22.6% is then more than four times higher than the inner significance level, originally set to control the false alarm rate. Kiesel et al. (2007) simulated race models where the number of participants (20 or 40), RMI test points (5 or 10) and the inner significance level (α = 0.01 and 0.05) were varied systematically. The

simulations revealed that type I errors (i.e. false alarms) are accumulated to a remarkable degree. And that despite the fact that the t-tests are highly correlated across percentiles). The authors provide practical advice how to combat α accumulation, e.g. by applying a stricter significance level (cf. Bonferroni correction, see Holm, 1979), restricting the range of the t-test to only early (and theoretically more violation prone) percentile points or replication via independent experiments.

The investigations by both Townsend and Honey (2007), and Kiesel et al. (2007) have increased the knowledge about the RMI test. However, their results simultaneously also increase the uncertainty of what to conclude from applying the RMI test. In cases where violations are missing, a potentially high base time variance might have filtered them out of the race model test function. And in cases where violations are found, this might be due to an estimation artifact of the test algorithm. Furthermore, both simulation studies have several

shortcomings that prevent a direct generalization of their results to other experimental settings or conditions. The most severe deficiency is the lack of a plausible model for the generation of reaction times in their simulations.

In the next chapter, state-of-the-art models of decision making (and in consequence, models of reaction times) will be presented in the form of sequential sampling models. The Ratcliff diffusion model will be detailed, as it forms the theoretical and computational basis for the implementation of both race and coactivation models in the present studies’ simulations. The chapter will be concluded by an application of Ratcliff diffusion models to the redundant signals paradigm and the RMI testing. Both known and novel issues of RMI testing will be presented that motivate the simulation and empirical work of the present study.