Results

Behavioral data. The behavioral data are depicted in Table 1. As expected, error rates did not differ significantly between the three tasks, F < 1. In contrast, response times of correct responses, F(2,39) = 51.8, p < 0.001, as well as response times of error

responses, F(2,39) = 47.9, p < 0.001, revealed a strong effect of response set size. An ANOVA comparing correct and error response times revealed an interaction of response set size and type of response (correct, error), F(2,39) = 12.7, p < 0.001, indicating that the effect of response set size was stronger for error responses. The signaling latencies also showed an effect of response set size which failed to reach significance, F(2,39) = 2.70, p = 0.08. However, an additional analysis involving only the two-choice task and the eight-choice task revealed a significant difference, F(1,39) = 4.96, p < 0.05. Neither the frequencies of signaling responses nor the frequencies of false alarms differed for any of the experimental conditions, all Fs < 1. Finally, there was a reliable effect of response set size on proportional post-error slowing, F(1,39) = 6.01, p < 0.01. Taken together, the analyses of behavioral data show that an increasing response set size not only impairs response times of the initial response, as predicted by Hick’s Law, it also impairs action monitoring as indicated by longer signaling latencies and reduced post-error slowing.

ERP data: Peak-to-peak analysis. In contrast to the behavioral data, the results of ERP data (Fig. 1) revealed no clear picture. Regarding the Ne/ERN on error trials, there was no significant effect of response set size on the peak-to-peak amplitudes despite of a clear trend toward reduced Ne/ERNs for larger set sizes (two-choice task: 8.76 µV, four-choice task: 6.78 µV, eight-choice task: 6.03 µV), F(2,39) = 1.48, p = 0.24.

Moreover, a peak-to-peak analysis of the CRN on correct responses was not possible because the majority of participants showed no clear CRN peaks.

Two choice correct

Figure 1. Panels A – C: Response-locked grand average waveforms for correct trials (thin lines) and for error trials (thick lines) in the two-choice task (black lines), in the four-choice task (grey lines), and in the eight-choice task (light grey lines) , ms = milleseconds, µV = microvolt.

Nevertheless, Figure 1 shows that the waveform on correct responses is more positive for the eight-choice task than for the four-choice task or the two-choice task. On the one hand, this effect could reflect a blurred CRN. On the other hand, it could be due to stimulus-locked components contaminating the response-locked waveforms

differentially in our three conditions, a possibility which has been discussed by Coles et al. (2001) to account for the CRN. Because response times vary considerably across the three conditions, response-related components and stimulus-related components overlap differentially in the post-response period. For instance, the stimulus-locked P300

typically causes a positivity at latencies of 400 ms to 600 ms after stimulus presentation.

This positivity should affect the post-response period of the two-choice task more strongly than that of the eight-choice task because mean response time of the former is 480 ms whereas that of the latter is 634 ms. This could explain why an increasing response set size leads to an increasing negativity (or reduced positivity) in the post-response period of correct trials. Moreover, the same effect should also influence the waveforms of error trials leading to an increasing overestimation of the Ne/ERN with an increasing response set size. As a consequence, to obtain a measure for the real effect of

response set size on the Ne/ERN, the contribution of stimulus-locked components to our effects need to be isolated.

ERP data: Distributional analysis. To explore whether our results are influenced by the overlap of stimulus-locked and response-locked potentials, we examined ERPs as a function of response time. To achieve this, a running averages procedure was applied as suggested by Coles et al. (2001). First, trials were sorted by response time for each condition and participant separately. Next, overlapping trial bins of 20 ms width were created, which were staggered by 5 ms (e.g., 300-320, 305-325, 310-330 etc.), and each trial was assigned to the respective bins. Then, average ERPs were calculated for each bin containing more than two trials. Finally, grand averages were computed across participants for those bins for which data were available for all participants. Figure 2 plots the results for correct trials and error trials of each condition at electrode site FCz.

In the figure, only trials with neutral stimuli were considered (Footnote 2). Note that in this figure, stimulus-related activity appears as vertical bands of voltage changes, and response-related activity appears as diagonal bands of voltage changes along the line representing the average response time in each bin.

550

Figure 2. Stimulus-locked voltage changes as a function of response time. ERPs were sorted by response time and assigned to overlapping response time bins of 20 milliseconds width

staggered by 5 milliseconds. Averages for bins containing more than two trials were computed, and plotted in a raster such that response time in milliseconds is represented on the ordinate, and trial time in milliseconds is represented on the abscissa. Positive voltages are depicted in red, and negative voltages are depicted in blue. Panels A, B, and C: Correct trials in the two-choice task, the four-choice task, and the eight-choice task, respectively. Panels D, E and F: Error trials in the two-choice task, the four-choice task, and the eight-choice task, respectively. The

diagonal black line from the bottom to the top of each plot marks the average response time in each bin, ms = milleseconds, µV = microvolt. See text for further details.

Inspection of Figure 2 reveals a strong positivity in the post-response period of correct trials with response times between 400 ms and 600 ms. This positive maximum

presumably resulted because, in this time window, the overlap of a response-related positivity with the stimulus-related P300 was maximal which implies very high voltages according to the law of superposition. Indeed, as response time increased above 600 ms (which occurred mainly in the four-choice task and the eight-choice task), diagonal response-related positivities and vertical stimulus-related positivities (P300) split up. As a consequence, response-locked averages were more positive in the post-response period for trials with response times between 400 ms and 600 ms than in trials with slower response times. This could explain why increasing response set size implies decreasing voltages in the post-response period of correct trials.

The effect of overlapping stimulus-locked and response-locked components is mainly observable in the distributions of correct responses which provide sufficient data to consider a large range of response times. However, the same effect should influence the waveforms of error responses. On these trials, the overlap of stimulus-locked and response-locked components should imply an underestimation of the Ne/ERN for trials with response times around 400 ms to 600 ms. Because these trials are most frequent in the two-choice task but infrequent in the eight-choice task, this effect should counteract the hypothesized reduction of the Ne/ERN amplitude with increasing response set size.

The question emerges how an unbiased measure of the Ne/ERN could be obtained. An ideal solution would be to compare only error trials with similar response times.

Unfortunately, this is not possible because there is little overlap in response time distributions between error trials of different response set sizes. Therefore, we chose an alternative procedure. Instead of analyzing peak-to-peak measures, we used a difference amplitude measure frequently used in studies on the Ne/ERN (Yeung et al., 2004). The Ne/ERN was now defined as the amplitude difference between correct and error trials in a time window ranging from 25 ms before the response until 100 ms after the response at electrode FCz.

One problem of this procedure is that it cannot distinguish between Ne/ERN and CRN.

However, since most participants showed no robust negative peak following correct responses, we concluded that CRNs are negligible in the present data. Moreover, within each condition, we matched correct and error trials for response time. This ensures that

the two trial types are similar with respect to the overlap of response-locked and stimulus-locked components. As a consequence, by subtracting the waveforms of both trial types, the influence of stimulus-locked components should be eliminated. To achieve this, correct and error trials were used that fell in the interval [410 ms, 480 ms]

for the two-choice task, [440 ms, 590 ms] for the four-choice task, and [510 ms, 690 ms]

for the eight-choice task. These are the same intervals that were used for distributional analysis of the error data.

ERP data: Mean difference amplitude analysis. The resulting waveforms for correct and error trials are depicted in Figure 3 (panels A-C). The analysis of amplitude differences now revealed a significant effect of response set size, F(2,39) = 7.07, p > 0.01. Mean difference Ne/ERN amplitudes were largest in the two-choice task (7.63 µV),

intermediate in the four-choice task (5.97 µV), and smallest in the eight-choice task (4.12 µV) (see, Figure 3, panel D).

Two choice correct

Figure 3. Panels A – C: Response-locked grand average waveforms for correct trials (thin lines) and for error trials (thick lines) in the two-choice task (black lines), in the four-choice task (grey lines), and in the eight-choice task (light grey lines). Panel D: Response-locked grand average difference waveforms (correct – error) in the two-choice task (black lines), in the four-choice task (grey lines), and in the eight-choice task (light grey lines). Within each task, a subset of correct and error trials matched for response times was used to control for differential overlap of response-locked components by stimulus-related activity, ms = milleseconds, µV = microvolt.

See text for further details.