B.3.6.2.5. Data analyses

For all ANOVAS, RTs faster than 200 ms and longer than 2000 ms were discarded, as representing anticipation and inattention, respectively. The integration between two processes were also tested by a dedicated method. Miller (1982) proposed a test that allowed rejecting the hypothesis of a "Horse-Race" between two independent processes. He cited Raab (1962) who showed that two redundant independent signals could induce a mean RT acceleration because of a mere statistical facilitation, even if there was no true integration or coactivation between these two signals. The falsification of the Miller's inequality allows to discard this kind of horse "Horse-Race" hypothesis, and to prove that both signals are genuinely integrated at some locus.

The statistical facilitation hypotheses was tested using a MATLAB implementation of the algorithm proposed by Ulrich, Miller, and Schröter (2007). This algorithm allowed to analyse the violations of the race model inequality (Miller, 1982). The cumulative distribution functions (CDF) of correct RTs were estimated independently for each of the three conditions of interest: a) merely salient target, b) merely relevant target, c) salient and relevant target (redundant). This was done independently for each salience-relevance similarity condition. Then, the CDF of the redundant condition was compared to the computed sum of single CDFs (i.e. a and b), predicted by the Race Model.

These CDFs were compared according to two methods: on the basis of raw data and on vincentized distributions (Vincent, 1912). Both methods produced very similar results.

For raw data, t-tests were computed at each time-point. We only reported as significant the time points where ten successive t-tests were below a threshold probability of p = .05. Actually, in the series reported, all the 37 successive t-tests were significant.

According to the second method, individual vincentized distributions were computed for each condition (including the theoretical sum). Then percentile distribution of the theoretical sum was compared to the distribution of the observed redundant condition. Successive t-tests were computed for percentiles 10 %, 15 %, 20 % and 25 %, according to Kiesel et al.'s (2007) recommendations.