The eye tracker was only used in this experiment as a monitoring device to control the gaze restrictions imposed on subjects in the assessment phase of the peripherally presented target position marker. The eye-gaze data recorded here does not provide any valuable contribution to the understanding of the assessment process and will consequently not be analysed.
During the subsequent phase of adjustment of the comparison marker, the execution of eye movements could be expected as the gaze restriction did not apply any more. Although the visual strategy pursued in the adjustment phase was not the prime interest of this investigation, we consider it worthwhile to at least informally introduce two respective options. The first possible strategy could see subjects that continue fixating the center of the display while peripherally adjusting the comparison marker – i.e they do not actually execute eye movements. The idea here might be that the preservation of the viewing conditions and the possibility of matching the comparison with some sort of an after-image of the target stimulus facilitates the adjustment. However, the analysis of eye-movement data does not support this strategy, but favours an alternative approach. This second
5.2 Results 79
strategy suggests that the subjects’ gaze guides the comparison marker movements and, vice versa, that the current marker position provides feedback to the eyes on the progress of the adjustment. Indeed, subjects seem to follow this second strategy.
As a consequence, we will not further analyse this eye-movement data, which obviously experiences interference from the adjustment procedure when the comparison marker is moved across the screen. Eye-movement data is mainly influenced by the marker move-ment – which suggests a smooth pursuit tracking eye-movemove-ment “mode” – rather than by the previous peripheral viewing condition. Certainly, this renders an interpretation difficult – or impossible – with regard to the effects of eccentricity on position assessment acuity. Instead, only the conventional psychophysical data, measured in the dependent variables as discussed in Section 3.4.2, are entered in an analysis of variance. The influ-ence of the factors eccentricity region and meridial position is tested on the dependent variables reaction time RT, radial deviation DX, tangential deviation DY and Euclidean deviation DXY of the comparison marker position from the target marker position in a two-factorial analysis of variance. For all subsequent analyses of variance the α-level for the significance of effects is set to p= 0.05.
5.2.1 Dependent Variables
Reaction Time RT
Figure 5.3 (left) shows a histogram of all measured reaction times RT that subjects re-quired in order to assess the position of the target marker under restricted gaze. The rela-tive frequencies are charted irrespecrela-tive of the eccentric and meridial locations of the target marker. RT varies from a minimum of 155 ms to a maximum of 3100 ms, with approxi-mately 95% of the measured reaction times lying within the interval of 250 to 1350 ms.
The histogram peaks at approximately 410 ms and subjects needed 662.1 ms on average to assess the marker position. A suitable fitting function would be asymmetrical (e.g.
the χ2 distribution or the Gamma-function (for details see Section 12.3)) with a positive skewness of +1.98.
In order to test the influence of the factors eccentricity and meridial position of presen-tation, RT is subjected to an analysis of variance. This detailed analysis of reaction times reveals a significant effect of the region of eccentricity on RT (F(3; 42) = 9.88;p < 0.001):
The assessment of the target marker position took increasingly longer from Eccentric-ity I (624.9 ms) to Eccentricities II (652.8 ms), III (662.2 ms) and IV (696.3 ms). Fur-thermore, a post-hoc comparison of means using the Newman-Keuls test (for details see Hochberg & Tamhane, 1987; Toothaker, 1991; Glass & Hopkins, 1996) is computed.
For this and subsequent post-hoc comparisons of means the α-level for critical ranges is set to p = 0.05. It reveals that no significant difference in RT exists between the two parafoveal Eccentricities II and III (Rcrit = 26.618;p = 0.321) whereas RT sig-nificantly differs between all other eccentricity regions: (Rcrit = 32.125;p = 0.034) for the comparison of RT between the Eccentricities I and II, (Rcrit = 33.010;p = 0.013) for I vs. III, (Rcrit = 36.451;p < 0.001) for I vs. IV, (Rcrit = 35.432;p = 0.005) for II vs. IV and (Rcrit = 32.578;p = 0.024) for III vs. IV. No significant main effect on
80 Experiment E0: Location Assessment in Peripheral Vision
reaction time RT (ms)
relative frequency
0 0.02 0.04 0.06 0.08 0.10
0 500 1000 1500 2000 2500 3000
eccentricity
reaction time RT (ms)
600 620 640 660 680 700 720
I II III IV
horizontal meridian vertical meridian
Figure 5.3: Left: Relative frequency distribution of reaction times RT, aggregated over all eccentricity regions and all meridial marker positions. Right: Reaction time RT as a function of eccentricity when position markers are presented either along the horizontal or the vertical meridian.
RT can be established for the meridial position factor (F(1; 14) = 1.68;p = 0.215). In-teraction effects of eccentricity and meridial position on RT are not significant either (F(3; 42) = 0.53;p= 0.661). Figure 5.3 (right) shows the reaction time RT as a function of eccentricity and the meridial position of the target marker.
Positional Deviations DX, DY and DXY
The analysis of the mislocation of the comparison marker, relative to the target marker, i.e. the radial as well as the tangential and the Euclidean deviations of the comparison marker position from the target marker position can be accomplished by using one of two possible data sets: Either theabsolute (positive) deviations from the target or a deviation measure that takes into account thedirection of the deviation as well. As results are quite different for both data sets, the choice of the respective set has to be considered carefully with regard to the intended further employment of the findings and interpretation.
The relationship between the target and the comparison marker positions in terms of radial, tangential and Euclidean deviation was already discussed in Section 3.4.2 and is again illustrated in Figure 5.4. If we consider the “directional” data, the radial devia-tion DX will be assigned a positive value in case the radial coordinate of the comparison marker position has a greater value than that of the target marker position, i.e. when the radial position of the target marker is “overestimated”. Accordingly, DX will be negative when the radial coordinate of the comparison marker is closer to the fixation point than that of the target marker, i.e. when the radial position of the target marker is “underes-timated”.
Regarding the tangential deviation, we determine DY as positive when the tangential coordinate of the target marker position has to be shifted clockwise – rotation of the radial axis around the fixation point – to match that of the comparison marker, and negative when shifted counter-clockwise. Here, it obviously does not make sense to classify the deviations as “overestimation” or “underestimation”.
The Euclidean deviation DXY is assigned a positive value if the Euclidean distance
5.2 Results 81
Figure 5.4: Radial and tangential axes and the respective deviations DX (pink) and DY (black) of the comparison marker from the target marker. DXY (light blue) denotes the Euclidean distance between the target (green) and the comparison marker (red).
between the fixation point and the comparison marker is greater than that between the fixation point and the target marker – and negative otherwise. Figure 5.4 thus shows a configuration where all DX, DY and DXY are positive. The “absolute” data sets ignore the directional information and are represented by the positive deviations only, i.e. directional and absolute data would be identical for the sample scenario in Figure 5.4.
As we will later be interested in modelling the distribution of the positional assess-ments of the target, information from both data types is required. If the distribution is thought of as being bivariate in nature, the analysis of directional data yields information on the origin and the orientation of the distribution whereas the distributions “extent”
can be more reliably determined through the absolute data – this is particularly true for symmetric distributions such as the normal distribution. The following paragraphs detail the results for DX, DY and DXY when both absolute and directional analyses are performed.
Absolute Radial Deviation DXp
Let us first consider the absolute radial deviation DXp. As the case with reaction time RT before, we enter DXp into a two-factorial analysis of variance in order to test the influence of the independent variables eccentricity and meridial position on the radial deviation.
The results show that an increase of DXp coincides with the target marker presentation in increasingly peripheral locations. The mean absolute radial deviations (all given in degrees of visual angle) measure 0.47o for Eccentricity I, 0.79o for Eccentricity II, 0.91o for Eccen-tricity III and 1.06ofor Eccentricity IV. The standard deviations for DXp are computed as 0.39, 0.62, 0.70 and 0.84o for the Eccentricities I–IV, respectively. The differences between the eccentricity levels are highly significant (F(3; 42) = 1.37;p < 0.001). A post-hoc com-parison of means using the Newman-Keuls test reveals that significant differences exist be-tween all eccentricity levels: (Rcrit = 0.149;p <0.001) for the comparison of DXp between the Eccentricities I and II, (Rcrit = 0.147;p <0.001) for I vs. III, (Rcrit = 0.147;p <0.001)
82 Experiment E0: Location Assessment in Peripheral Vision
eccentricity absolute radial deviation DXp (degrees)
0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
I II III IV
horizontal meridian vertical meridian
Figure 5.5: Absolute radial deviation DXp of the comparison marker position from the target marker position for all eccentricities and meridial positions.
for I vs. IV, (Rcrit = 0.101;p= 0.040) for II vs. III, (Rcrit = 0.142;p < 0.001) for II vs. IV and (Rcrit = 0.128;p= 0.009) for III vs. IV.
Again, no main effect for the meridial position can be observed (F(1; 14) = 0.13;p = 0.070). However, there appears to be a tendency towards less absolute radial deviation when the target markers are presented in proximity to the horizontal meridian than in proximity to the vertical meridian. Interaction effects of eccentricity and meridial position on DXp are not significant (F(3; 42) = 0.02;p = 0.663). Figure 5.5 shows the mean absolute radial deviation DXp as a function of eccentricity and meridial position of the target marker.
Absolute Tangential Deviation DYp
Analogous to DXp, the absolute tangential deviation DYp is subjected to an analysis of variance. Similar to the previous findings, differences between the Eccentricities I–IV are highly significant for DYp (F(3; 42) = 3.26;p < 0.001). A post-hoc comparison of means using the Newman-Keuls test reveals that significant differences exist between all eccentricity levels: (Rcrit = 0.071;p < 0.001) for the comparison of DYp between the Eccentricities I and II, (Rcrit = 0.067;p < 0.001) for I vs. III, (Rcrit = 0.072;p <0.001) for I vs. IV, (Rcrit = 0.057;p <0.001) for II vs. III, (Rcrit = 0.064;p < 0.001) for II vs. IV and (Rcrit = 0.070;p < 0.001) for III vs. IV. The least tangential deviation is found for Eccentricity I (0.31o) and then constantly increases for Eccentricities II (0.45o), III (0.60o) and IV (0.73o). The standard deviations for DYp are computed as 0.26o, 0.36o, 0.49o and 0.59o for the Eccentricities I–IV, respectively. The meridial position does not exert a significant effect on DYp (F(1; 14) = 0.10;p = 0.098), but the tendency towards a more accurate assessment of absolute tangential position of the target markers in proximity to the horizontal meridian – compared with those presented in proximity to the vertical
5.2 Results 83
eccentricity absolute tangential deviation DYp (degrees)
0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
I II III IV
horizontal meridian vertical meridian
Figure 5.6: Absolute tangential deviation DYpof the comparison marker position from the target marker position for all eccentricities and meridial positions.
meridian – prevails as for DXp. No interaction effects between eccentricity and meridial position on DYp can be observed (F(3; 42) = 0.03;p = 0.384). Figure 5.6 illustrates the mean values of DYp for the different peripheral regions and the meridial positions.
Qualitatively comparing the magnitudes of DXp and DYp already suggests that these two measures are significantly different from each other: The radial deviation is larger than the tangential deviation. When we enter the distinction between these two axes as an additional factor into the analysis of variance, the ad-hoc hypothesis is confirmed
eccentricity
deviation (degrees)
0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
I II III IV
radial deviation DXp tangential deviation DYp
Figure 5.7: The absolute radial deviations DXp and the absolute tangential deviations DYp of the comparison marker position from the target marker position as functions of eccentricity.
84 Experiment E0: Location Assessment in Peripheral Vision
(F(1; 14) = 1.04;p < 0.001). Figure 5.7 shows the means of DXp in comparison with those of DYp for all eccentricity regions I–IV, collapsed over the horizontal and meridial presentation positions.
Absolute Euclidean Deviation DXYp
The Euclidean deviation DXYp is the last dependent variable that is tested in Experi-ment E0 with respect to possible interactions with the peripheral and meridial presenta-tion posipresenta-tions. DXYp, which is computed from DXp and DYp as the Euclidean distance between the target and comparison marker positions, increases with increasing eccentric-ity. This highly significant effect (F(3; 42) = 2.37;p <0.001) is manifested by mean values for DXYp of 0.60ofor Eccentricity I, 0.98o for Eccentricity II, 1.18o for Eccentricity III and 1.40o for Eccentricity IV. The standard deviations for DXYp are computed as 0.40o, 0.59o, 0.70o and 0.84o for the Eccentricities I–IV, respectively. A post-hoc comparison of means using the Newman-Keuls test reveals that significant differences again exist between all eccentricity levels: (Rcrit = 0.153;p < 0.001) for the comparison of DXYp between the Eccentricities I and II, (Rcrit = 0.153;p < 0.001) for I vs. III, (Rcrit = 0.158;p <0.001) for I vs. IV, (Rcrit = 0.114;p= 0.001) for II vs. III, (Rcrit = 0.153;p < 0.001) for II vs. IV and (Rcrit = 0.160;p <0.001) for III vs. IV.
In accordance with the results of the analyses of variance for DXp and DYp, a cor-responding tendency towards an effect of the meridial position on DXYp can be noted (F(1; 14) = 0.31;p = 0.064): The Euclidean deviation of the comparison from the target marker appears to be slightly less when the target marker is presented in proximity to the horizontal meridian. This tendency is qualitatively visible in Figure 5.8 where the Euclidean deviation DXYp is shown as a function of eccentricity and the meridial posi-tion of the target marker. There is no interacposi-tion effect between eccentricity and meridial
eccentricity absolute Euklidian deviation DXYp (degrees)
0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
I II III IV
horizontal meridian vertical meridian
Figure 5.8: Absolute Euclidean deviation DXYp of the comparison marker position from the target marker position for all eccentricities and meridial positions.
5.2 Results 85
position on DXYp (F(3; 42) = 0.02;p= 0.537).
As already briefly mentioned, the distribution of the comparison marker positions – which can be thought of as sketched in Figure 5.9 (left) – requires more than just knowl-edge of the “extent” of the distribution. The origin of the distribution, i.e. its “anchor point”, for example, constitutes essential information for describing the distribution func-tion. The analyses of DXp, DYp and DXYp do not yield this data. Instead, an analysis of the “directional” data sets is required to obtain the direction of the deviation of the comparison marker relative to the target marker. These deviations will again be anal-ysed separately for the radial (DX), tangential (DY) and Euclidean (DXY) dimensions.
In Figure 5.9 (left), the green dot highlights the target marker position that the subjects had to assess, the black dots show all positions (for all subjects and repetitive measures by subjects) where they placed the comparison marker. The red dot marks the averaged comparison marker position. The ellipsis illustrates the results of a principal component analysis (PCA) that approximates the (orientation of the) distribution of the compar-ison marker positions. If the relative frequencies of assessment positions are also taken into account and charted on an axis perpendicular to the x–y–coordinate (paper) plane, a distribution shaped similarly to that shown in Figure 5.9 (right) emerges. The exact procedure will be discussed later in Chapter 8.
Figure 5.9: Left: Approximation of a sample distribution of comparison marker positions using principal component analysis (PCA). Right: Original distribution of the same comparison marker positions and their relative frequencies.
As the analyses of DXp, DYp and DXYp revealed, the meridial position of the target marker does not have a significant effect on the absolute radial, tangential or Euclidean deviations of the comparison marker position from the target marker position. We will thus collapse the data over the factor meridial position and only test the effect of the eccentricity region on the “directional” deviations DX, DY and DXY.
Radial Deviation DX
An analysis of variance yielded a significant eccentricity effect on the radial deviation DX (F(3; 42) = 0.09;p= 0.048) and the means for DX are computed to -0.17o for Eccentric-ity I, -0.34o for Eccentricity II, -0.37o for Eccentricity III and -0.43o for Eccentricity IV.
86 Experiment E0: Location Assessment in Peripheral Vision
A post-hoc comparison of means using the Newman-Keuls test reveals that significant differences exist between almost all eccentricity levels: (Rcrit = 0.285;p = 0.012) for the comparison of DX between the Eccentricities I and II, (Rcrit = 0.267;p = 0.021) for I vs. III, (Rcrit = 0.255;p= 0.029) for I vs. IV, (Rcrit= 0.267;p= 0.021) for II vs. IV and (Rcrit = 0.284;p = 0.015) for III vs. IV. Only when comparing DX between the eccen-tricity levels II and III the Newman-Keuls test does not produce a significant difference (Rcrit = 0.213;p= 0.065).
Thus, for all eccentricities, subjects on average placed the comparison marker closer to the fixation point on the radial axis. The standard deviations for DX are computed as 0.59o, 0.92o, 1.08oand 1.28o for the Eccentricities I–IV, respectively. Figure 5.10 illustrates the means of the radial deviations DX for the Eccentricities I–IV.
eccentricity
radial deviation DX (degrees)
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3
I II III IV
Figure 5.10: Radial deviation DX of the comparison marker position from the target marker position for all eccentricities, collapsed over the horizontal and vertical meridial locations.
Tangential Deviation DY
When the data for the tangential deviation DY is entered into an analysis of variance, a significant effect of eccentricity thereupon emerges (F(3; 42) = 0.20;p = 0.002). How-ever, as the computation of means for the four eccentricities shows, no steady tendency for direction for the mislocation is visible. Means are -0.02o for Eccentricity I, 0.02o for Eccen-tricity II, -0.08o for Eccentricity III and 0.02o for Eccentricity IV. A post-hoc comparison of means using the Newman-Keuls test reveals that significant differences exist only be-tween the following eccentricity levels: (Rcrit = 0.079;p = 0.003) for the comparison of DY between the Eccentricities II and III and (Rcrit = 0.080;p= 0.003) for III vs. IV. In contrast, differences between the eccentricity levels I and II (Rcrit = 0.059;p = 0.192), between I and III (Rcrit = 0.067;p = 0.055), I and IV (Rcrit = 0.062;p = 0.141) and II
5.2 Results 87
eccentricity
tangential deviation DY (degrees)
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3
I II III IV
Figure 5.11: Tangential deviation DY of the comparison marker position from the target marker position as a function of eccentricity.
and IV (Rcrit = 0.040;p= 0.790) are not significant.
The tangential deviations are significantly smaller than the radial deviations (F(1; 14) = 0.30;p = 0.010). The standard deviations for DY are computed as 0.41o, 0.57o, 0.78o and 0.94o for the Eccentricities I–IV, respectively. Figure 5.11 shows the means of the tangential deviations DY for the Eccentricities I–IV.
Euclidean Deviation DXY
The analysis of variance for the Euclidean deviation DXY yields a significant effect for the tested factor eccentricity (F(3; 42) = 0.07;p = 0.039). A post-hoc comparison of means using the Newman-Keuls test reveals that significant differences again exist between all eccentricity levels: (Rcrit = 0.240;p = 0.026) for the comparison of DXY between the Eccentricities I and II, (Rcrit = 0.220;p = 0.015) for I vs. III, (Rcrit = 0.213;p = 0.010) for I vs. IV, (Rcrit = 0.251;p = 0.045) for II vs. III, (Rcrit = 0.251;p = 0.030) for II vs. IV and (Rcrit = 0.256;p = 0.039) for III vs. IV. The computed means are -0.15o for Eccentricity I, -0.33o for Eccentricity II, -0.38o for Eccentricity III and -0.44o for Eccentricity IV. The standard deviations for DXY are computed as 0.71o, 1.06o, 1.31o and 1.57o for the Eccentricities I–IV, respectively.
As could be expected from the result of the analyses of DX and DY, the greater mag-nitudes of the radial deviations – compared to the tangential deviations – dominate the Euclidean deviations and yield a steadily increasing Euclidean deviation with more pe-ripheral target marker positions. The negative values of DXY account for the fact that subjects positioned the comparison markers closer to the fixation point than where the target markers were located. Figure 5.12 illustrates the means of the Euclidean devia-tions DXY for the Eccentricities I–IV.
88 Experiment E0: Location Assessment in Peripheral Vision
eccentricity
Euklidian deviation DXY (degrees)
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3
I II III IV
Figure 5.12: Euclidean deviation DXY of the comparison marker position from the target marker po-sition as a function of eccentricity.