3. Marco Metodológico
3.2 La sistematización de experiencias educativas
We first report the results of our bias function analysis, which is depicted in Figures 3.3-5. The bias functions for each of the four target display patterns, averaged across all salience groups, are depicted in Figure 3.3 A. The three salience-based functions (i.e., SAL-NUM, SAL, and SAL+NUM) are almost
indistinguishable up to 300-350 ms, at which point they begin to diverge from one another. This divergence is perhaps best conceived as a deviation from the SAL function in two different directions, due to either subtracting (i.e., SAL-NUM) or adding (i.e., SAL+NUM) the influence of numerosity.
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Figure 3.3 The interaction of salience and numerosity over time. These plots show average bias functions for the four target conditions of interest. Red traces show the bias transition function, which is the response to displays where luminance contrast and numerosity bias the reach in different directions (i.e., SAL-NUM). Green traces show the response to displays that differed only in luminance contrast (i.e.,SAL). Magenta traces show the response to displays that differed only in numerosity (i.e., NUM). Blue traces show the response to displays where luminance contrast and numerosity bias the reach in the same direction (i.e., SAL+NUM). A, Bias functions averaged over all salience groups. B, Bias functions averaged within salience groups. Shaded regions indicate bootstrapped 95% confidence intervals.
One target pattern that was of special interest is the SAL-NUM pattern, in which there were two high-salience targets on one side of space and four low-salience
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targets on the other side. This put the biases of target salience and numerosity into direct opposition, allowing us to observe their interaction over time. As
expected, the influence of salience overpowered that of numerosity at the earliest time points (small Delay + RT). This was true even in the LOW salience group, in which the confidence interval briefly dipped below 0 at around 325 ms. Based on past work that showed a small but significant bias toward numerosity in response to a SAL-NUM display after a 500 ms delay (Wood et al., 2011), we had
expected to see a transition to a numerosity bias by the end of the tested time range in the present study. Instead, we observed a stabilization of the bias transition function at equilibrium between salience and numerosity (Figure 3.3 A
and B). This finding is even more striking when one considers the magnitude of the NUM bias function (plotted in magenta for Figures 3.3 and 3.4).
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Figure 3.4 Pure salience (SAL) and pure numerosity (NUM) bias functions over time. A, Salience and numerosity bias strength averaged over all salience groups. B, Salience and numerosity bias functions averaged within salience groups. Note that the trace for the SAL condition is inverted for display purposes. Shaded regions indicate
bootstrapped 95% confidence intervals.
Considered together, the SAL and NUM bias functions help explain the shape of the bias transition function, in particular its stabilization at equilibrium. Figure 3.4 isolates the SAL and NUM bias functions, and compares their magnitudes over time. At the earliest time points, there was no bias whatsoever in response to the NUM target display (see Figure 3.4A). In other words, reaches were going
directly up the middle, presumably because these reaches were being initiated prior to any numerosity information arriving to the relevant neural pathways. After
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150 ms of exposure to the targets, the numerosity bias came online and grew until it peaked at around 350 ms and then stayed constant across the remainder of the sampled time range (Figure 3.4A). This is in contrast to the SAL bias function, which peaked considerably higher and slightly earlier (i.e., by roughly 50-100 ms) than the NUM bias function, after which it logarithmically decayed until it reached what appeared to be a steady state of continued salience bias near the end of the sampled time range (Figure 3.4A). Notably, these two
independent bias functions intersect at roughly 450 ms, which is exactly the time when the SAL-NUM bias transition function stabilized (compare intersection of pink and green curves in Figure 3.4A with the red curve in Figure 3.3A). The persistent effects of the pure NUM and SAL biases neatly accounts for the observation that the SAL-NUM bias transition function never completed a full transition to a numerosity bias. The fact that the salience bias exerted a persistent influence on visuomotor competition after at least 700 ms of visual exposure to the targets is one of the more surprising findings of this study, given the empirical precedent of a 250 ms window for the effect of salience.
Figure 3.5 Between-group differences in salience-based bias function overlap. A, The degree of spread between the three salience-based bias functions (i.e., SAL-NUM, SAL,
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and SAL+NUM), compared across salience groups. The magnitude of salience bias spread is inversely proportional to the influence of numerosity within a given target salience group. Error bars indicate SEM. * p < 0.05. B, Target contrast values of the three salience groups, mapped onto the logarithmic contrast response function. This figure illustrates the proposed mechanism underlying the results depicted in A.
We noted that the salience-based bias functions (i.e., SAL-NUM, SAL, and SAL+NUM) showed differing degrees of overlap between the three different salience groups (Figure 3.3 B). We quantified salience bias spread as follows: for each participant, we first averaged each of the three salience-based bias
functions over the entire temporal range. We then assigned each of these values a difference score by subtracting the grand mean of all three from each individual bias function mean. Next, we took the slopes of a linear regression over the three resulting difference scores for each participant. In essence, the steepness of the slope is a measure of the degree of spread between the three salience-based bias functions. In turn, the degree of spread is indicative of the magnitude of the numerosity effect in the SAL-NUM and SAL+NUM bias functions. In other words, a smaller salience bias spread indicates a weaker influence of numerosity. Figure 3.5 A depicts the average regression slopes for the three target salience groups. Only the difference between the LOW and HIGH salience groups came out as significant (p = 0.015). Given the general direction of the effect and the significant difference between the LOW and HIGH groups, we take this as evidence that increasing the contrast difference between targets (and, by extension, the magnitude of salience) diminishes the effect of numerosity in visuomotor competition.
Figure 3.5 B depicts a possible mechanism to explain the groupwise differences in salience spread; it shows the target contrast values of the salience groups mapped onto the logarithmic contrast response function. The function is
expansive at low contrasts and compressive at high contrasts (Boynton, Demb, Glover, & Heeger, 1999). In other words, a given span of contrast values at a
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high range evokes a thinner band of neural responses than the same span of contrast values at a lower range.