Exogenous attention can be counter-selective: onset cues disrupt sensitivity to color changes

Abstract

In peripheral spatial cueing paradigms, exogenous attentional capture is commonly observed after salient onset cues or with cues contingent on target characteristics. We proposed that exogenously captured attention disrupts the selectivity to target features. We tested this by experimentally emulating the everyday observation that in a viewing situation in which the observer is monitoring a stationary display fort change to occur, the onset of a salient stimulus (onset cue) or a change in a stationary stimulus similar to the expected one (contingent cue) has a distracting effect. As predicted, we found that both types of cues reduced the target detection sensitivity but enhanced the bias to respond in a go-nogo-paradigm. With the onset cue, the sensitivity loss was more pronounced at the side of the cue, whereas the contingent cue affected both sides likewise. Moreover, the effects of the onset cue interacted with the task difficulty: the more selectivity a task required the more immune it was against disruption, but the more likely was a response. We concluded that onset capture disrupts selective attention by adding noise to the processing of the target location. The effects of contingent capture could be explained with cue-target confounding. Finally, we suggest a new model of attentional capture in which exogenous and endogenous components interact in a dynamic way.

Appendices

Appendix 1

Behavioral measures of accuracy and bias

Let us start from an experimental 3 × 2-design for one subject with the factors ‘cue’ C with the three levels C _n , C _v , C _i (no, valid, or invalid cue) and ‘target’ S with the two levels S ₀, S ₁ (target absent or present). The dependent measure is the binary ‘response’ R with the values R ₀, R ₁ (no, yes). If each of the six conditions is presented n times to a subject, a joint frequency distribution as displayed in Table 11 is the result. Since a cue is neither valid nor invalid when there is no target, the conditions C _v S ₀ and C _i S ₀ are phenomenologically identical and the respective frequencies are summed.

Table 11 Joint frequency distribution of the variables target S, cue C, and response R in one subject, with each stimulus configuration presented n times

Accordingly, when computing hit and false alarm rates, the latter were pooled across all cued trials. Equation 1 shows the resulting three hit rates pH _n , pH _v , pH _i and two false alarm rates pF _n , pF _vi for this situation.

$$\begin{aligned} pH_{n}&= \frac{d_n}{c_n+d_n};\; pH_{\rm v}= \frac{d_{\rm v}}{c_{\rm v}+d_{\rm v}};\; pH_{{\rm i}}= \frac{d_{\rm i}}{c_{\rm i}+d_{\rm i}};\\ pF_{n}&= \frac{b_n}{a_n+b_n};\; pF_{\rm vi} = \frac{b_{\rm vi}}{a_{\rm vi}+b_{\rm vi}}, \end{aligned}$$

(1)

Target detection accuracy pC and response bias pR with pooled false alarms

For assessing target detection accuracy and response bias, the rate of correct responses pC and the rate of yes-responses pR were analyzed for each of the three cueing conditions. For the no-cue condition, they are defined from Table 11 as

$$pC_n = \frac{a_{n}+d_{n}}{a_{n}+b_{n}+c_{n}+d_{n}}= .5\,(1+pH_{n}-pF_{n})$$

(2)

and

$$pR_n = \frac{b_{n}+d_{n}}{a_{n}+b_{n}+c_{n}+d_{n}}= .5\,(pH_{n}+pF_{n}).$$

(3)

However, when proceeding in this manner for validly and invalidly cued trials, the six variables pC _j and pR _j for j = n, v, i would be multicollinear because they were linearly combined from the five variables pH _n , pH _v , pH _i , pF _n , pF _vi . (For example, the differences pC _v  − pC _i and pR _v  − pR _i were identical then.)

Therefore, the following variables were computed instead:

$$pC_{{\rm v}} = .5\,(1+pH_{{\rm v}}-pF_{\rm vi})$$

(4)

$$pC_{{\rm i}} = .5\,(1+pH_{{\rm i}}-pF_{{\rm vi}})$$

(5)

$$pR_{{\rm vi}} = .5\,(pH_{{\rm vi}}+pF_{{\rm vi}})$$

(6)

with the pooled hit rate pH _vi  = .5 (pH _v  + pH _i ).

Defining pC and pR as linear combinations of pH and pF is statistically useful for the following reasons:

• 1. At the descriptive level, i.e., in a sample of N subjects, each of the above measures can be regarded as a vector of length N. In terms of the linear model, the five primary measures build up a (N × 5) design matrix

  $${\mathbf{X}}\,=\,(\,\overrightarrow{pH}_{n}, \overrightarrow{pH}_{\rm v}, \overrightarrow{pH}_{{\rm i}}, \overrightarrow{pF}_{n}, \overrightarrow{pF}_{{\rm vi}}),$$

  as well as the five secondary measures

  $${\mathbf{Y}}\,=\,(\,\overrightarrow{pC}_n, \overrightarrow{pC}_{\rm v}, \overrightarrow{pC}_{\rm i}, \overrightarrow{pR}_n, \overrightarrow{pR}_{{\rm vi}}\,).$$

  It is easily shown with the help of basic matrix algebra that the columns of Y are linearly independent if and only if the columns of X are linearly independent.

Proof

Consider the (5 × 5) transformation matrix

$${\mathbf{A}}\,=\, \left( \begin{array}{lllll} .5 & 0 & 0 & .5 & 0\\ 0 & .5 & 0 & 0 & .25\\ 0 & 0 & .5 & 0 & .25\\ -.5 & 0 & 0 & 0 & 0\\ 0 & -.5 & -.5 & .5 & .5 \end{array} \right)$$

and the (N × 5) translation matrix

$${\mathbf{B}}\,=\, \left( \begin{array}{lllll} .5 & .5 & .5& 0 & 0\\ .5 & .5 & .5& 0 & 0\\ \vdots & & & &\\ .5 & .5 & .5& 0 & 0 \end{array}. \right)$$

Then, the design matrix Y results from the design matrix X by the affine linear transformation

$${\mathbf{Y}}\,=\,{\mathbf{X}}\, {\mathbf{A}} + {\mathbf{B}}.$$

The proposition follows from A having full rank (det   A = .0625).

• 2. At the theoretical level, let

  $${\mathbf{x}}\,=\,(\,\pi(H)_n, \pi(H)_{\rm v}, \pi(H)_{\rm i}, \pi(F)_n, \pi(F)_{{\rm vi}}\,)^{\prime}$$

  and

  $${\mathbf{y}}\,=\,(\,\pi(C)_n, \pi(C)_{\rm v}, \pi(C)_{\rm i}, \pi(R)_n, \pi(R)_{{\rm vi}}\,)^{\prime}$$

  denote the two 5-dimensional random vectors that produce design matrices as the above X and Y when realized N times independently. With the above (5 × 5)-matrix A and the vector

  $${\mathbf{b}}\,=\, (.5 , .5, .5, 0, 0)^{\prime}\,,$$

  the random vector y results from the random vector x by the linear transformation

  $${\mathbf{y}}\,=\,{\mathbf{A}}\, {\mathbf{x}} + {\mathbf{b}},$$

  and for their means and covariance matrices the relations

  $$\begin{aligned} E({\mathbf{y}})&= {\mathbf{A}}\, E({\mathbf{x}}) + {\mathbf{b}},\\ V({\mathbf{y}})&= {\mathbf{A}}\, V({\mathbf{x}})\, {\mathbf{A}}^{\prime} \end{aligned}$$

  hold. Furthermore, since A is symmetric with full rank, x is multivariately normally distributed if and only if y is is multivariately normally distributed. Therefore, it makes no difference for any common inference statistic whether it is carried out on the set of primary measures as defined in Eq. (1) or the set of secondary measures as defined in Eqs. (2)–(6).

To summarize, it is statistically equivalent whether the hits and false alarms pH and pF are analyzed or the target detection accuracy and response bias pC and pR. However, the latter is more convenient for interpretation.

Appendix 2

Variants of signal detection theory (SDT)

The following theoretical section is divided into three subsections: First, we will briefly recapitulate the standard SDT model and its parameters. Then, we will discuss how it can be extended to our five stimulus classes. Third, we will generalize the model by weakening some assumptions. The parameter estimations from the best fitting model variant were used for drawing conclusions on mechanisms involved in the cueing effects.

Although most readers will be familiar with the standard model, we will recapitulate it briefly as a starting point for the modifications introduced below. In standard SDT (Marcum, 1947; psychophysical adaptation by Green & Swets, 1966), the sensory representations evoked by targets (S ₁) and non-targets (S ₀) are assumed to range along a one-dimensional random variable which is normally distributed for targets and nontargets with equal variances but different means (see Fig. 6). The sensitivity d′ is conceptualized as the difference between the target and nontarget mean in units of standard deviation. An alternative sensitivity measure is A _z , the area under the ROC curve (isosensitivity curve for a given d′ value), which can be interpreted as the probability that the sensory representation of the target exceeds that of the non-target when both are independently sampled from the two conditional distributions. A _z is identical to $F(d^{\prime}/\sqrt{2})$, with F denoting the cumulative distribution function of the standard normal. The raw criterion measure λ is a fixed variable value above which the observer responds “yes”. For interpreting it as bias, the criterion measure is usually centered at the point of equal hit and miss rate ζ (which can sensibly be interpreted as point of zero bias and which equals d′/2 when the variances are equal). The bias is thus defined as c = λ − d′/2 (Macmillan & Creelman, 1991; also termed λ_center in Wickens, 2002). An alternative measure of bias is the so-called β (with or without logarithm), the ratio of the two conditional probability densities at the criterion value c. Note that log(β) is identical to c·d′ (Wickens, p. 30).

Fig. 6

Standard SDT model (left) and ROC for a given d′ value (right). The relevant parameters are depicted in blue. The green area in the left diagram shows the probability of a hit π(H), the red area that of a false alarm π(F)

SDT for five stimulus classes

There exist several attempts to apply SDT to spatial cueing experiments (e.g., Bashinsky & Bacharach, 1980; Müller & Findley, 1987; Prinzmetal et al., 2008). Mostly, the three trial types (no cue, valid cue, invalid cue) were treated as three different pairs of nontarget and target distributions, yielding three independent estimations of the sensitivity and the criterion/bias measure.

In the present experiments, however, there were five stimulus classes (nontarget trials without and with cue, and target trials without, with valid, or with invalid cue). SDT can thus be applied as usual to the uncued trials, assuming a pair of nontarget and target distribution and estimating the sensitivity d ^′ _n , and the criterion/bias λ _n /c _n . However, since the criterion is estimated solely from the false alarm rate of which there is only one in the sample of all cued trials, the remaining three stimulus classes (target with valid cue, target with invalid cue, nontarget with cue) have to be treated together in one model.

How many parameters does this latter situation—the SDT with three stimulus classes—contain? First, the two target distributions (validly cued and invalidly cued targets) with their two means μ _v and μ _i constitute two sensitivies d′(v) and d′(i). Second, and now the situation requires second thought, the nontarget distribution with its false alarm rate constitutes one criterion, which will be indexed λ(vi) in the following. The bias c is the difference between the criterion value, of which there is one, and the point of equal false alarm and miss rate (‘zero bias’), of which there are two. Obviously, it does not make much sense to compute two different biases from only one criterion. (Moreover, the difference between these two biases would directly reflect the difference between the two sensitivities.) It seems more sensible to redefine the point of ‘zero bias’ instead: If there are two target types, validly and invalidly cued ones, we defined an observer to have ‘zero bias’ if his/her criterion met the point at which the false alarm rate matches the pooled miss rate across the two target types. Consequently, we defined the bias as the difference between the actual criterion and the point of zero bias. To estimate its value, we proceeded from the already estimated parameters λ(vi), d′(v), and d′(v), pooled the estimated miss rates, identified the point ζ at which the pooled miss rate equaled the estimated false alarm rate, and then computed the bias as c(vi): = λ(vi) − ζ.

The resulting graphics in the upper panels of Fig. 4 may illustrate the procedure. (The reader should not be confused by the three criteria λ_C, λ_U, λ_L and accordingly three zero bias and three bias values, which correspond to the three payoff conditions that were realized in the experiments but disregarded in the above explanation for didactic reasons. The subscript c _a instead of c refers to the unequal variance model, which will be explained in the next subsection.)

Generalizations of model assumptions

To judge whether the distributional assumptions of the model were appropriate for the data, three payoff conditions had been realized in experiment 1 and 2, and two in experiment 3 (see “Methods” sections of the experiments). From the data of every subject, we obtained maximum-likelihood estimations of the mean of the target distribution in the uncued case and of the two means of the two target distributions in the cued case, with three instead of one criterion λ each in experiment 1 and 2, and two times two criteria in experiment 3. The nontarget distributions were always standardized to a mean of 0 and a variance of 1. This was done with and without the constraint of equal variances. Then, for every experiment and every subject, a goodness-of-fit test was computed with the help of the χ² statistic. At a significance level of α = .05, the Gaussian model with equal variances was rejected for five of the six subjects in experiment 1, three of the six subjects in experiment 2, and five of the six subjects in experiment 3. However, when allowing for heterogenous variances across all target distributions, the Gaussian model remained statistically unrefuted at α = 0.05 for every subject in every experiment. Further, generalizations like giving up the normal distribution (Green & Swets, 1966) or introducing decision noise see, e.g.,(see, e.g., Bonnel & Miller, 1994; Mueller & Weidemann, 2008; Benjamin, Diaz, & Wee, 2009) did not further improve the fit. We thus interpreted the parameters from the unequal variance Gaussian SDT model.

Several ideas exist on how to generalize d′ when allowing for unequal variances (Wickens, 2002). We used d _a , the difference between the mean of the target and the nontarget distribution in units of pooled standard deviation (which reduces to d′ if variances are equal). Since d _a estimations depend critically on the variances being accurately estimated, we also analyzed A _z , the area under the ROC curve, the estimation of which is more robust against changes in the underlying distributions or parameters and even nonnormality.

For investigating bias shifts in the heterogeneous variance model, we first looked at the raw criterion values λ_con, λ_bal, λ_lib for the three payoff conditions. Then, in loose analogy to the centered criterion c in standard SDT, we standardized the raw criteria in each pair of target-nontarget distributions by subtracting the point of zero bias $\zeta$ and dividing by the pooled standard deviation, resulting in so-called c _a -values (Wickens, 2002). (We refrained from using the bias measures β or log(β) for assessing criterion shifts because the maximum of a probability density function varies with its width, and consequently the ratios of density values are not comparable between pairs of distributions with different variance ratios, e.g., different subjects or cueing conditions.)

Note that the here described standardization of d′ and c into d _a and c _a , accounting for the unequal variance situation, does not interfere with the above considerations on how many sensitivities and biases can sensibly be estimated for the cued and the uncued case, accounting for the five stimulus classes.

In total, each subject came with three sensitivity estimates d _a (n), d _a (v), and d _a (i) (for uncued, validly cued and invalidly cued targets), and two bias estimates c _a (n) and c _a (vi) (for uncued and cued nontargets). The situation thereby mirrored the empirical situation in which three target detection accuracies pC and two response biases pR were computed. A difference existed only with regard to the three payoff conditions, which in the empirical situation triplicated both the number of accuracy measures pC and bias measures pR but in the SDT situation only the bias estimates.