Run Length
Figure 2(a) presents the average normalized run length (and
Figure 2(b) the average raw run length) for individual observers in the finger foraging condition. The results are ordered by performance difference between feature and conjunction foraging by observer. As in our previous study, there was a reliable difference in run length between feature and conjunction foraging. Specifically, the average run length was significantly shorter (paired
t(15) = 6.19,
p < .001, Cohen’s
d = 1.75) during feature (
M = 3.2 run, SD = 2.4 run) than conjunction (
M = 12.7 run,
SD = 7.3 run) foraging. Within this overall pattern, however, there are clear individual differences. Classifying observers in terms of the distance between their standardized scores in the two conditions, as described earlier, revealed that 11 participants showed consistent differences between feature and conjunction foraging, while 5 did not (see
Figure 2(a) and (
b)).
Similarly,
Figure 2(c) shows normalized run length data (and
Figure 2(d) the raw run length) for gaze foraging. As for finger foraging, there was a significant difference in run length between the two conditions. Again, the average run length was significantly shorter (paired
t(15) = 3.67,
p = .002, Cohen’s
d = 0.74) for feature (
M = 2.3 run,
SD = 0.9 run) than conjunction foraging (
M = 3.4 run,
SD = 1.9 run). However, as can be seen by comparing
Figure 2(a) and (
c), the separation between the two conditions appears much less marked for gaze foraging. This impression was confirmed when classifying individual observers, as with gaze foraging only 5 participants had consistent differences between feature and conjunction conditions, while the remaining 11 did not.
Figure 3 shows example foraging paths for finger and gaze foraging.
Below, we more directly compare performance in finger and gaze foraging. As already noted, such comparisons need to be interpreted with caution, given the methodological differences between the tasks, but are nonetheless useful as exploratory steps. First, we made a direct quantitative comparison on the normalized run length data. A 2 × 2 repeated measures ANOVA on run length revealed a significant main effect of condition (feature versus conjunction; F(1, 15) = 48.8, p < .001; ηpartial_squared = 0.76) and of foraging measure (finger versus eye gaze; F(1, 15) = 21.0, p < .001; ηpartial_squared = 0.58) but also a highly significant interaction (F(1, 15) = 23.6; p < .001; ηpartial_squared = 0.61). This is highlighted by comparing the number of participants classified as having the same or different patterns of foraging across feature and conjunction conditions. This difference in proportions between finger (5/16; 31.25%) and gaze (11/16; 68.75%) foraging clearly indicates that a larger number of participants continued to use random category selection when using their eyes.
Second, we computed the number of trials classified as nonrandom for each observer and compared these with a 2 × 2 ANOVA. To classify a trial as nonrandom, we used One-Sample Runs Tests with a Bonferroni correction to adjust the level of alpha for multiple tests (see
Kristjánsson et al., 2014 for details).
Table 1 provides a summary of this classification. We found a main effect of condition (
F(1, 15) = 63.8;
p < .001;
ηpartial_squared = 0.81) of foraging measure (
F(1, 15) = 115.7;
p < .001;
ηpartial_squared = 0.89) and a significant interaction between the two factors (
F(1, 15) = 42;
p < .001;
ηpartial_squared = 0.74). Most importantly, these results show that there is very little nonrandom foraging with gaze while for conjunction foraging with fingers the majority of trials are nonrandom consistent with the fact that we see very long runs in that condition.
Finally, we explored whether individual participants had similar run length behavior in the finger and gaze foraging conditions. Correlations on the difference scores (conjunction—feature) suggest that participants with similar feature and conjunction performance in the finger foraging task also have a tendency towards similar differences for gaze foraging (
r = .47;
p = .032; see
Figure 4). This correlation is far from perfect, however.
In summary, across a number of comparisons, we observe smaller differences between feature and conjunction foraging for gaze foraging than finger foraging. Gaze foraging therefore appears not to be under such strong constraints as finger foraging when the same attentional load is applied, at least for the displays tested here.
Switch Costs
Figure 5 presents switch costs within trials that measure whether there is a difference in movement time from the last target to the next as a function of whether observers switch between target types or continue choosing the same target.
Figure 6 shows switch costs in distance between consecutive taps (as in
Figure 5). Switch costs are overall higher in the conjunction condition, but consistent with the results on run length, switch costs during conjunction foraging are much larger for finger than gaze foraging. Again there is a large difference between finger and gaze foraging, perhaps reflecting differences between the mechanisms involved in the two foraging types.
A three-way repeated measures ANOVA on response time switch costs (
Figure 5) revealed significant main effects of condition (conjunction vs. feature;
F(1, 15) = 100,
p < .001;
ηpartial_squared = 0.87) and switching (
F(1, 15) = 52.4,
p < .001;
ηpartial_squared = 0.78) but not of foraging method (
F(1, 15) = 2.05,
p = .17;
ηpartial_squared = 0.12). The two-way interactions between condition and switch (
F(1, 15) = 45.2,
p < .001;
ηpartial_squared = 0.75), condition and foraging method (finger vs. gaze;
F(1, 15) = 8.45,
p = .011;
ηpartial_squared = 0.36) and switch and foraging method (
F(1, 15) = 23.4,
p < .001;
ηpartial_squared = 0.61) were all significant. Finally, the three-way interaction was significant (
F(1, 15) = 17.8,
p < .001;
ηpartial_squared = 0.54), confirming that switch costs as a function of feature versus conjunction foraging differ between the two foraging methods.
A three-way repeated measures ANOVA on switch costs in distance between consecutive taps (
Figure 6; note difference in scales between conditions) showed significant main effects of condition (
F(1, 15) = 77.5,
p < .001;
ηpartial_squared = 0.838), of switching (
F(1, 15) = 24.7,
p < .001;
ηpartial_squared = 0.623), and of foraging method (
F(1, 15) = 41.1,
p < .001;
ηpartial_squared = 0.733). The two-way interactions between condition and foraging method, between condition and switch, and between foraging method and switch were all significant (
F(1, 15) = 16.3,
p = .001,
ηpartial_squared = 0.521;
F(1, 15) = 39.6,
p < .001,
ηpartial_squared = 0.725;
F(1, 15) = 36.4,
p < .001,
ηpartial_squared = 0.708, respectively). The three-way interaction was also significant (
F(1, 15) = 15.3,
p = .001,
ηpartial_squared = 0.505). The most notable result (highlighted in
Figure 6) is that during conjunction foraging with fingers, observers have a strong tendency to choose the same target as on the last trial, and they will “travel” far in the display to choose such a target, presumably not choosing closer targets of the other type. Such a difference is not seen for gaze foraging.
Finishing Time and Traveling Distance
For finger foraging, the average finishing time for each trial was 12.6 s for the feature condition and 17.6 s for the conjunction condition (paired t(15) = 6.5, p < .001). This indicates that conjunction foraging was, on average, more difficult than feature foraging. The average traveling distance for each trial was 5346 pixels during feature foraging and 6436 for conjunction foraging (paired t(15) = 8.8, p < .001). This is not surprising since if observers use longer runs of foraging the same target, they will by necessity travel longer. The gaze foraging data mirror the finger foraging data: Average finishing time for each trial was 6.7 and 10.2 s for feature and conjunction foraging, respectively (paired t(15) = 6.9, p < .001). For feature foraging, the average traveling distance was 2922 and 3261 pixels for conjunction foraging (paired t(15) = 4.2, p < .001).
Foraging Organization
Finally, we analyzed foraging organization. Calculating the correlation between the Cartesian coordinates of the targets and the sequence of how the targets are selected provides information on search organization (
Woods et al., 2013). A high correlation between x-coordinates and selection sequence suggests that foraging was performed with horizontal sweeps across the search space. Similarly, a high correlation between the y-coordinates and the selection sequence suggests that participant foraged in vertical sweeps. If the correlation is low, the foraging is disorganized. The highest correlation (irrelevant of axis) is the Best R and yields an estimate of the degree to which foraging was organized (shown in
Figure 7). A two-way repeated measures ANOVA revealed a significant main effect of condition (
F(1, 15) = 42.3,
p < .001,
ηpartial_squared = 0.74) and of foraging method (
F(1, 15) = 12.1,
p = .002,
ηpartial_squared = 0.45) and a significant interaction (
F(1, 15) = 22.3,
p < .001,
ηpartial_squared = 0.60). A post-hoc test showed that the differences were always significant except between foraging methods in the feature condition. Overall, foraging appears to be highly organized during feature foraging, indicating that participants utilize consistent horizontal or vertical sweeps through the display when attentional load is low. Such tendencies are generally reduced during conjunction foraging, but the drop is much more marked for finger foraging. This differential pattern of organization is again suggestive that the conjunction manipulation has less of an impact on eye foraging than it does on finger foraging.
Error-Rates
Error-rates were defined as the proportion of total number of incorrect taps or fixations divided by the total number of targets. Using Wilcoxon signed-rank tests, no significant differences (p = .426) in error-rates between feature (Median = .014, range .003–.07) and conjunction (Median = .019, range 0–.065) conditions were found for finger foraging, but for gaze foraging the error-rates in the conjunction task (Median = .084, range .013–.094) were significantly higher (p < .001) than in the feature task (Median .013, range 0–.031). While significant, a difference of only 6 percentage points is unlikely to account for the strong difference in the observed foraging patterns. Specifically, there was little or no nonrandom gaze foraging while for finger foraging the majority of trials were nonrandom. If the gaze pattern reflected a speed–accuracy trade-off, the difference in error rates should be far larger.