Data analysis

Out of the methods available to address the AB effect, the Condition×Lags analysis of variance (ANOVA) is the solution preferred by most researchers to compare T2 conditions in dual–task experiments. Unfortunately, Cousineau et al. (2006) showed that this procedure neglects important aspects of the data and, more importantly, that the necessary assumptions for such tests (i.e., sphericity of the variance-covariance matrix, identity of the variance-covariance matrix across conditions, and normality of the distributions) are often not met. The authors addressed this latter issue in a series of simple experiments, and through Monte Carlo simulations of large datasets.

Results showed that both the intrinsic setting of AB experiments (e.g., performance at lag n and lag n+1 being strongly correlated), as well as the between- and within-subject variability, often yield the rejection of most assumptions. Consequently, significance tests can be misinterpreted in many ways.

To overcome these shortcomings, Cousineau et al. (2006) proposed a parametric solution to focus the analysis on particular aspects of the AB curve, which are likely to be of theoretical importance.

The method they propose uses curve-fitting techniques to quantify four aspects of the data: the duration of the effect, the amplitude between the minimum and the asymptotic performance, the minimum performance, and the amount of Lag-1 sparing. This approach is a-theoretical in essence, as it does not rely on a particular interpretative theory of the AB, but provides an objective way to characterize the resulting curve. To validate their method, the authors applied this technique to data gathered in experimental settings, and to simulated datasets. Results showed that, in addition to easing the comparison of results between experiments, this method is valid, and allows

the testing of particular aspects of the data to be tested at a time. More importantly, results showed that this method yields to more powerful statistical tests than conventional methods.

Simply put, Cousineau et al. (2006) defined an equation with four parameters, which scale different parts of an AB curve (figure 5.2). They then performed a constrained fit of the equation over the data, and used the value of the four fitted parameters to test specific hypothesis. Fitting can be achieved through the minimization of the root mean square deviation, the sum of squared error, or the chi-square index of fit (Van Zandt, 2000; Cousineau et al., 2004; Heathcote, 2004; Cousineau et al., 2006).

The particularity of this method resides in the informational value of the four parameters. Re-searchers are provided with objective measures of particular aspects of the AB curve, which they can then use to render hypotheses as to the cognitive processes underlying the AB effect. Of interest for cognitive theorists is the fact that these parameters refer to different periods of the unfolding of the AB (Figure 5.2, panel a), which we will discuss later. Let us now provide a description of each parameter.

Beta (β) – Duration of the AB phenomenon

Beta measures the width of the curve, reflecting the duration of the effect (Figure 5.2, panel b).

It corresponds to the amount of time needed for P(T2|T1) (i.e., the probability of success to the task on T2 given a correct response to the task on T1) to come back to baseline, after the blink has occurred. The bigger theβ, the longer the duration of the blink. It is interesting to note that βrefers to a period of time starting at about 200 msec to 500 msec after the onset of T1, a rather late stage of the processing of T1. We can refine our hypotheses: A modulation of the AB will yield smallerβ (H1β, and H2β).

Delta (δ) – Relative blink

Delta measures the amplitude between the minimum and the asymptotic performance described by the curve (Figure 5.2, panel c). It refers to what researchers commonly call the ”blink”, describing the temporary dysfunction in the processing of T2, compared to baseline, which occurs after the perception, and correct identification of T1. The smaller theδ, the less AB effect (i.e., the flatter the curve) ; refining our hypotheses: A modulation of the AB will yield smallerδ(H1δ, andH2δ).

Figure 5.2: Panel a. Typical AB curve displaying the four parameters manipulated by Cousineau et al. (2006). In our work, we distinguish three main periods of the processing, noted A, B, and C. Periods A and C refer to the unfolding of the processing stream, whereas period B refers to the apex of the interference mechanism occurring in response to the perception of T1. Panel b, c, d, e. Possible results of an AB experiment manipulating a factor of interest Condition (dotted and dashed lines) and Lags (1 through 8). Manipulation of parametersβ,δandλgenerate a Condition×Lags interaction in an ANOVA. Only the manipulation ofγgenerates a main effect of Condition in an ANOVA. Copyright, Canadian Psychology Association, 2008.

Gamma (γ) – Performance level of the minimum

Gamma represents the vertical aspect of the curve. It measures the objective minimum of the blink, regardless of the shape of the curve (Figure 5.2, panel d). The bigger theγ, the better the minimum performance. We can refine our hypotheses: A modulation of the AB will yield greater γ(H1γ, andH2γ).

Lambda (λ) – Amount of Lag-1 sparing

Lambda measures what is commonly called the Lag-1 sparing, that is the amount of time after the perception of T1 until the peak of the interference over T2. During this short period of time, P(T2|T1) decreases to reach a minimum at about 300 msec after the onset of T1. The bigger the λ, the less Lag-1 sparing (i.e., the earlier the ”closure of the attentional gate”). It is interesting to note that, during this short period of time, performance on T2 stimuli can be very high, showing that both T1 and T2can be processed somehow simultaneously (Visser et al., 1999; Kessler et al., 2006). However, the processing of T2 seems to interfere with the performance on T1 stimuli, as the performance on T1 stimuli often starts low, increasing across later lags (Shapiro, Raymond,

& Arnell, 1997; Cousineau et al., 2006; Nieuwenhuis, Gilzenrat, et al., 2005; Nieuwenhuis et al., 2007). This latter phenomena confirms the hypothesis that the goal of the blink may be to prevent T2 stimuli from interfering with the processing of T1 stimuli (Raymond et al., 1992; Sergent et al., 2005; Hommel & Akyurek, 2005). The stronger the interference of T2 stimuli, the greater the λ(H1λ, andH2λ).