In Experiment 1a, individual participants searched for an unknown number of coin targets placed in open grassland terrain. We were interested in how search strategy was related to both target detection accuracy and search time for the task. The grassland was 75 m2 in size. Participants searched the open space in any manner they chose and for however long they wished to search. Accuracy was measured as the number of targets detected and search time was calculated as the time from when the participants started the task until they told the experimenters they had finished.
It is important to understand that it was not possible for participants to detect all but very few targets from their starting point. Target detection required moving through the search area. More than the detection of targets per se, or the type of targets searched for, it is the need to conduct an exhaustive search through a search area for targets that are very hard to find that connects this task most directly with that of finding clues to a crime or to the presence of an IED. Analysis of the systematicity of search was enhanced by using data extracted from a Total Station theodolite system. These data allow for visual representation of the routes taken by participants (henceforth ‘route maps’: see Fig. 3). They can also be processed using Fourier analysis to provide some quantitative evidence for general trends apparent when inspecting representations of routes taken by participants. This approach is helpful as participants are free to move in any direction and it captures the underlying spatio-temporal properties of their movements overall.
The Fourier analysis transforms the data from the time domain to the frequency domain and enables calculation of multiple measures derived from the frequency components of movement along the x-axes and y-axes of the search area: (1) The dominant frequency component is an index of the modal speed of movement along each axis. The reciprocal of the dominant frequency component (1/dominant frequency) converts this to seconds and can be used as an approximate measure of participant’s modal time before changing direction; (2) Dividing participant’s overall search time by the modal time before changing direction gives an estimate of the number of changes of direction. Plotting the number of changes of direction along the x-axis against those on the y-axis allows determination of whether participants tended to move systematically along x-axes or y-axes (i.e. left to right or top to bottom) or use a hybrid strategy. Furthermore, by dividing the number of changes of direction by the length of the axis being travelled across provides an estimate of the width of the search corridor used by participants; and finally (3) dividing participants’ modal time before changing direction by the next most commonly occurring time before changing direction indexes variability in speed of searching.
In addition to basic data around search accuracy and time, we show typical route maps and analyze the width of search corridors used, modal movement speed, and variability in speed of movement. We predicted that more accurate search would be reliant on: (1) increased regularity, systematicity of search following a structured path (Dalmaijer et al., 2014; Donnelly et al., 1999; Gilchrist & Harvey, 2006; Keech & Resca, 2010); (2) narrower search corridors (Koopman, 1946, 1980); and (3) slower, more consistently paced movement (Koopman, 1946, 1980).
Method
Participants
Thirty participants (7 men and 23 women, mean age = 23.5 years, SD = 4.73) recruited from the University of Southampton community, with normal or corrected-to-normal color vision, took part in the study for course credit. Participants were screened to ensure visual acuity and normal color vision using Snellen (1862) chart for visual acuity and the Ishihara (1917) color plates. The study was performed in accordance with the Declaration of Helsinki and was approved by the University of Southampton, School of Psychology ethics committee. Informed consent was obtained from all participants.
Apparatus
Experimenters used a grid representing the larger-scale search space to record accuracy. When participants found a target, they pointed to the target and informed the experimenter, who then marked off the corresponding target on the grid. Overall search time was recorded using a stopwatch. Search was deemed to have finished once participants reported to the experimenter that they were done.
Participant movement over space and time was recorded using a Total Station theodolite (Leica TPS1200, Heerbrugg, Switzerland). The Total Station used electronic distance measurement technology and an angle-measurement system to calculate the coordinate of an unknown point relative to a known coordinate point. A signal was sent from a fixed recording station to a reflector prism mounted on a 1.8-m staff held by the participants. A coordinate was recorded every 2 s and accuracy was within 3 mm per km of distance (SD = 1.5). The output of time-stamped coordinates was processed using Environmental Systems Research Institute’s ArcGIS software (ESRI, 2011).
Stimuli
The experiment was conducted on an open space of grassland (see Fig. 1). The perimeter of a 15 × 5 m search area was marked out at 1-m intervals using 40 colored cones. The position of the cones was calibrated with the Total Station prior to testing. The relative positions of cones allowed definition of 75 m2 grid cells. Testing took place over four consecutive days. The location of the grid was moved each day to avoid excessive trampling of grass. Across days, the conditions of the grass remained broadly similar.
Twenty-five UK sterling two pence coins were used as targets (see Fig. 2). The two pence coins were of a copper color and were 25 mm in diameter. The coins were all matt rather than shiny in appearance. The coins were placed so that they could be detected from standing height, although they were sufficiently small that detection required active exploration of the search grid.
Coins were distributed within the grid so that five coins were placed pseudo-randomly within each 1-m ‘search lane’ (i.e. five coins were placed along each 1-m search lane across the 5-m width of the grid). On average, there was one coin per 3 m2. The targets were placed in the same grid cell locations for all participants. Distractors were not added within the search area but leaves and other natural materials did form naturally occurring distractors and were not removed from the search space.
Procedure
Following the screening, participants were given a brief explanation of the Total Station and were instructed to hold the staff upright and close to their body while searching. The staff was lightweight and easy to carry. Participants were not told how many coins could be found but instructed to search until they were confident they had completed their search (i.e. they had found all the targets). Participants were told not to pick coins up but to point and tell the experimenter that a coin had been found. Participants were not penalized for reporting the same coin on more than one occasion (as the task simulates a task where a conservative approach to finding targets is encouraged) but each target was only counted once when calculating response accuracy. Once participants had completed their search, they were asked to give a score on a ten-point scale to indicate how confident they were that they had found all the coins. A higher score implied high confidence while a lower score indicated lower levels of confidence.
Results
Participants were excluded from data analysis if they failed to detect any coins. While detecting no coins might reflect their best performance, they were removed on the basis that it is impossible to differentiate poor performance from failing to engage with the task. We therefore took a conservative position on removing from analysis. This resulted in the removal of two participants (6.7% of the data) meaning data analysis was conducted on the data from 28 participants. However, the removal of the two participants did not influence the pattern of significance of results. Correlational tests were used to examine if there was a relationship between two variables, simple linear regressions were used to examine whether one variable predicted a second variable, t-tests were used to examine whether the mean scores of two participant groups differed and a Fisher’s exact test was used to test how likely it was that observed distributions were due to chance. All regressions reporting time or frequency use log-transformed data to reduce skew, though this did not, however, affect the underlying pattern of results. For the regressions, significance levels were adjusted for multiple comparisons as regressions compared the same measure across x-axes and y-axes. Only effects reaching a p value of 0.025 were considered significant. The statistical package used to analyze the data was R version 3.3.0 (R Core Team, 2016).
Behavioral data
Basic measures of accuracy and total search time are presented in Table 1. On average, participants found just under half the available targets, despite spending an average of 7.5 min on the task. On average, participants reported a confidence score of 6.89 on a ten-point scale. On average, the first target was found after 39 s and the last target was found 40 s before terminating search. For each participant, a regression was carried out exploring the linear relationship between the time of finding each target against the ordinal number of that target as found by the participant (i.e. 1st, 2nd, 3rd, etc.). This measure explores whether targets were found consistently throughout search or were found more easily at the beginning than the end of search. The range of adjusted R-squared values was 0.842–0.995 (all ps < 0.052) across participants. The result suggests that targets were found at a fixed rate throughout search. Accuracy was predicted by confidence ratings (β1 = 2.448, F(1,26) = 5.195, p = 0.031, adj R2 = 0.135): participants who gave a high confidence rating were more accurate in their search.
Search strategy
Examples of typical route maps are shown in Fig. 3. Visual inspection of these route maps reveals some commonalities across participants. These commonalities were explored using Fourier analysis.
Systematicity of search path
To quantify regularity of search path, a Fourier transformation was carried out for each participant and along both the x- and y- axes (see Donnelly et al., 1999). Our first prediction was that search would be more accurate when participants used a regular, systematic search strategy following a structured path. To explore this prediction, we examined the number of changes of direction (calculated by dividing participant’s overall search time by the modal time before changing direction).
The number of changes of direction was plotted across both axes (see Fig. 4). High values on one axis were associated with low values on the other axis (r(26) = –0.558, p = 0.002). Participants turning top to bottom tended to search along fewer, longer corridors and participants turning left to right tending to search along more, shorter corridors. These data are consistent with all participants searching systematically, using an ‘S’-shaped route to cover the search area (as shown in Fig. 3). Their fundamental pattern of movement (the ‘S’ shape) was consistent irrespective of whether they primarily moved top to bottom or left to right. The important result is that all participants exhibited regularity in the path taken to search. Given this, it was not possible to explore variations in accuracy as a function of the presence or absence of regularity (as per our first prediction).
Width of search corridors
Our second prediction was that search would be more accurate as search width narrowed. This hypothesis was based on the idea that a narrow search width would better facilitate the search of close space using the fine-grained spatial acuity of foveal vision. To explore this prediction, participants were split into two groups – those who primarily moved left to right (n = 11) and those who primarily moved top to bottom (n = 16). There was one participant who did not fall into either category, conducting a hybrid strategy, and was therefore removed from subsequent analysis. We took the number of changes of direction made by each participant along their dominant axis (i.e. whether they were in the top-to-bottom or left-to-right group), added 1 (to take into account the number of sweeps both up and down, i.e. five turns would mean six sweeps), and divided the length of the axis being travelled across by this figure (i.e. for those in the top-to-bottom group, the length of the axis being travelled across in meters, which was 5, would be divided by the first figure calculated). This normalized the data, as calculating the search width took into account the length of each axis.
These data are shown in Fig. 5. The striking result is that the search width for the majority of participants lies between 1 and 2 m (alternatively between 50 cm and 1 m to both the left and right of the center). This suggests that there is commonality in search width irrespective of whether participants search top to bottom or left to right across the search grid. Given the limited range of width of search corridors, there is no evidence of search width predicting either accuracy (β1 = –0.534, F(1,25) = 0.356, p = 0.556, adj R2 = –0.025) or total search time (β1 = 0.446, F(1,25) = 2.11, p = 0.159, adj R2 = 0.041). Irrespective of outcome for accuracy or time, participants searched along their ‘S’-shaped path, using a common search width.
Search speed and search speed variability
Our third prediction was that search would be more accurate when participants searched with slow, consistently paced movement (Search Theory; Koopman, 1946, 1980). To examine this prediction, we examined the modal time before changing direction on each axis and variability in time before changing direction (by dividing the modal time before changing direction by the next most commonly occurring time before changing direction). For the left-to-right group, accuracy was not predicted by the modal time before changing direction, nor variability in time before changing direction (β1 = –0.41, F(1,9) = 0.065, p = 0.805, adj R2 = –0.103; β1 = –3.437, F(1,9) = 1.478, p = 0.255, adj R2 = 0.046; see Fig. 6a and b). Total search time was predicted by modal time before changing direction but not variability in time before changing direction (β1 = 1.133, F(1,9) = 8.712, p = 0.016, adj R2 = 0.435; β1 = 0.094, F(1,9) = 0.009, p = 0.928, adj R2 = –0.11; see Fig. 6c and d).
For the top-to-bottom group, there was a very strong trend for accuracy to be predicted by modal time before changing direction and variability in time before changing direction (β1 = 1.229, F(1,14) = 5.926, p = 0.029, adj R2 = 0.247; β1 = 1.982, F(1,14) = 5.716, p = 0.031, adj R2 = 0.239; see Fig. 7a and b). Participants were more accurate when they took longer before changing direction and varied their time before changing direction. Total search time was predicted by modal time before changing direction but not variability in time before changing direction (β1 = 0.956, F(1,14) = 27.21, p < 0.001, adj R2 = 0.636; β1 = 0.507, F(1,14) = 1.047, p = 0.324, adj R2 = 0.003; see Fig. 7c and d). Participants took longer overall to search when they took longer before changing direction. As predicted, increased accuracy was associated with slow search (i.e. longer before changing direction, i.e. turning), but surprisingly, it was variable search speed that was associated with increased accuracy rather than a consistent pace as predicted.
Discussion
In Experiment 1a, we examined how searching for an unknown number of coins in an open space of grassland terrain was conducted. We predicted that accurate search would be reliant on: (1) a regular, systematic search strategy following a structured path (Dalmaijer et al., 2014; Donnelly et al., 1999; Gilchrist & Harvey, 2006; Keech & Resca, 2010); (2) narrow search corridors (Koopman, 1946, 1980); and (3) slow, consistently paced movement (Koopman, 1946, 1980).
The basic behavioral data showed the task to be extremely challenging, with task accuracy being at 45%. Many targets were missed despite participants taking a significant amount of time to explore the search area (on average, 7 min 33 s). Targets were, however, detected at a fixed rate throughout search. Furthermore, accuracy was predicted by the confidence ratings given by the participants, suggesting participants had some idea of how accurate they had been in the task.
The route maps showed participants tended to search using an ‘S’-shaped strategy, though sometimes embedded within a more complex pattern (see Fig. 3). This was confirmed in the analysis of data extracted using the Fourier analysis. Given that all participants exhibited regularity in their search path, we were unable to explore whether a regular search path predicted higher accuracy or not. However, the regularity of the ‘S’-shaped path made it possible for participants to define a search path that rarely contained crossovers and where the search width varied between 1 and 2 m. Following an ‘S’-shaped path minimized the memory demands inherent in the task relative to if a more irregular path was followed (Gilchrist et al., 2001). Presumably this width of search corridor adopted by participants was set according to their beliefs about the salience of targets in the context of the environment in which they were being sought. More or less salient targets would, respectively, lead to use of a wider or narrower search corridor.
Given that participants opted to search using a common search width, an important question is, how exhaustive is each participants’ search within their search corridor? Accuracy varied markedly across participants despite using the common search width and so using the common search width did not ensure that search was exhaustive. At least for some participants, the failure to search exhaustively was associated with a faster movement time reflected in the reduced modal time before turning. The implication of speeded search is that areas of the search corridor were left unexplored as forward body motion occurred at a rate too fast for the sweep of left-to-right head movements and associated eye movements. The fact that accuracy was associated with confidence is consistent with participants having some insight into the likelihood of the success or failure of their attempt at an exhaustive search (metacognitive awareness).
One might think of the relationship between time before changing direction and accuracy as reflecting a speed-accuracy trade-off but its observation is important. An observer tasked with ensuring or judging the quality of a search is unlikely to be able to make such a determination from the search path but it may follow from measuring differences in the time taken for search. Interestingly, slowed search distinguishes experts from novices in airport baggage-screening tasks (Biggs, Cain, Clark, Darling, & Mitroff, 2013). Calibrating how long a search task requires is, we suggest, a skill to be learnt both in complex visual searches and searches for targets placed in a more complex physical environment.
Variable search speed was also associated with increased accuracy, rather than a consistent pace, as predicted. This variability of search speed and accuracy found for the top-to-bottom participants was unexpected. On reflection, however, it is likely to be an effect associated with the task itself. Careful searchers slowed to ensure targets were clearly identified and marked as detected by the experimenters leading to variability in search speed as being identified with increased accuracy.
It is possible that the failure to find a relationship in the left-to-right group for time before changing direction and variability in time before changing direction for accuracy may be accounted for by the shorter time and distance between turns that participants had to make when moving left to right than top to bottom. Given that participants searching top to bottom were more accurate when they took longer before changing direction, the shorter distance before having to turn when searching left to right may have led to less efficient search. Measures based on participants movement through space may require sufficient movement time along axes, unfettered by the noise introduced by the slowing and speeding of turning itself, to become reliable indices of performance. In other words, the failure to find a relationship for accuracy for the participants moving left to right is likely to be a form of signal-to-noise problem.