96 Experiment E1: Length Assessment in Peripheral Vision
orientation. The effects of these factors are tested on the dependent variables reaction time RT and the length deviation DL of the comparison line segment from the target line segment.
6.2.1 Dependent Variables
Reaction Time RT
The relative frequencies for RT are distributed in Experiment E1 almost identical to the distribution of reaction times RT measured in the previous experiment. The measured reaction times range from a minimum of 156 ms to a maximum of 3976 ms. The overall mean RT, averaged over all values, is computed at 660.7 ms and the histogram peaks at 430 ms. As before, an asymmetrical function with a positive skewness of +1.98 would be appropriate to fit the distribution of RT. Approximately 95% of the values lie within the interval of 250 to 1450 ms. Figure 6.3 (left) shows the respective histogram for RT.
As in the previous experiment, the factor eccentricity exerts a significant effect on the reaction time RT required for the assessment of line segment lengths (F(3; 33) = 4.54;p= 0.009). The mean RT increases from 640.1 ms for Eccentricity I, through 655.3 ms and 671.0 ms for the Eccentricities II and III, to 683.2 ms for Eccentricity IV. A post-hoc comparison of means using the Newman-Keuls test reveals that significant differences exist between the following eccentricity levels: (Rcrit = 32.198;p= 0.039) for the comparison of RT between the Eccentricities I and III, (Rcrit = 37.514;p= 0.012) for I vs. IV, (Rcrit = 30.992;p= 0.047) for II vs. III and (Rcrit = 35.672;p = 0.035) for II vs. IV. In contrast, only tendencies for the existence of significant differences in RT can be found between the Eccentricities I and II (Rcrit = 25.401;p = 0.080) and between the Eccentricities III and IV (Rcrit = 27.941;p= 0.078).
Both target line segment length and orientation factors do not show a significant main effect on RT, the analysis of variance yields (F(2; 22) = 1.00;p = 0.383) and (F(2; 22) = 2.50;p = 0.125), respectively. Furthermore, no significant effects can be observed for all possible two- and three-way interactions. However, there appears to
reaction time RT (ms)
relative frequency
0 0.02 0.04 0.06 0.08 0.10
0 500 1000 1500 2000 2500 3000 3500 4000
eccentricity
reaction time RT (ms)
600 620 640 660 680 700 720
I II III IV
short intermediate long
Figure 6.3: Left: Cumulative relative frequency distribution of reaction times RT over all eccentricity regions, line segment lengths and orientation levels. Right: Reaction time RT as a function of eccentricity, separated for short, intermediate and long line segments.
6.2 Results 97
be a tendency towards an interaction between eccentricity and line segment length (F(6; 66) = 2.04;p = 0.072) which suggests that short and intermediate lines require less processing time for length assessment only when presented at near-foveal locations (Eccentricities I and II). Furthermore, a closer inspection of the data reveals that RT remains at a high level between 667.3 and 689.3 ms for long line segments, independent of the eccentric presentation position of the target line segments. Figure 6.3 (right) illus-trates the means of RT as a function of the Eccentricities I–IV and the target line segment lengths (short, intermediate, long).
Length Deviation DL
Similar to theabsolute (positive) anddirectional value types for the radial, tangential and Euclidean positional deviations in Experiment E0, we also distinguish between these two types here. Whereas the absolute values give a better impression of how much the lengths of the comparison line segments differ from those of the target line segments, the analysis of the directional data is indispensable in determining whether target lengths were under- or overestimated. For the following analyses, we will thus consider the length deviations DLp, which represents the positive deviations between the lengths of the comparison and the target line segments. DL, the directional pendant, will be negative in case the length of the comparison line segment is shorter than that of the target, and positive otherwise.
Both DL and DLp are relative measures that correlate the deviation to the target length.
Example: A comparison line segment that is adjusted to LC = 110 pixels when the target is LT = 100 pixels long constitutes
DL= (LC−LT)/LT = 0.1, (6.1)
i.e. a length deviation of (+)10%.
Positive Relative Length Deviation DLp
In order to test the effects of the eccentricity region, the target line segment length and orientation on DLp, a three-way analysis of variance is conducted. Significant main effects can be established for the factors eccentricity (F(3; 33) = 11.82;p < 0.001) and target line segment length (F(2; 22) = 33.25;p < 0.001). A post-hoc comparison of means using the Newman-Keuls test reveals that significant differences exist between the following eccentricity levels: (Rcrit = 0.038;p = 0.040) for the comparison of DLp between the Eccentricities I vs. II, (Rcrit = 0.045;p= 0.001) for I vs. III, (Rcrit= 0.049;p <0.001) for I vs. IV, (Rcrit = 0.041;p= 0.035) for II vs. III and (Rcrit = 0.043;p= 0.002) for II vs. IV.
In contrast, only a tendency towards the existence of a significant difference in DLp can be found between the Eccentricities III and IV (Rcrit = 0.034;p= 0.089). The differences between all levels of the factor target line segment length are significant (Newman-Keuls post-hoc test) with respect to DLp: (Rcrit = 0.084;p <0.001) for the comparison between short and intermediate lengths, (Rcrit = 0.080;p < 0.001) for short vs. long lengths and (Rcrit = 0.069;p= 0.042) for intermediate vs. long lengths.
98 Experiment E1: Length Assessment in Peripheral Vision
When data is averaged over lengths and orientations (for all subjects), comparison line segment lengths deviate from the target lengths by 16.6% for Eccentricity I, 18.6% for Eccentricity II, 21.9% for Eccentricity III and 23.8% for Eccentricity IV. A cumulation of data over the factors eccentricity and orientation yields that subjects (incorrectly) adjust the length of the comparison line segment with deviations of 31.8% (short), 17.2% (inter-mediate) and 11.8% (long) on average. The factor orientation does not yield a significant main effect on DLp (F(2; 22) = 0.22;p= 0.800).
eccentricity positive relative length deviation DLp
-0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
I II III IV
short intermediate long
Figure 6.4: Positive relative deviation DLpof the length of the comparison from the target line segment as a function of Eccentricity I–IV and target line segment length (short, intermediate, long).
In addition, the interaction between eccentricity and target line segment length reaches significance level (F(6; 66) = 3.87;p= 0.002). This can be attributed to the fact that DLp
constantly increases with greater eccentricities for short and intermediate line segments, whereas it remains unaffected for long line segments. For short line segments, DLp is com-puted to be 0.28, 0.31, 0.35, 0.36, for intermediate length 0.11, 0.14, 0.21., 0.24, and for long line segments 0.11, 0.11, 0.11, 0.14 – each for the respective Eccentricities I–IV. This is supported by a post-hoc comparison of means using a Newman-Keuls test. It reveals significant differences between the four eccentricity levels for targets with short and in-termediate lengths. In contrast, such differences cannot be found between the eccentricity levels for long targets1. No other interactions show significant effects on DLp. Figure 6.4 shows the positive relative length deviation DLp as a function of eccentricity and target line segment length.
1Due to the large number of results for the factor combinations of the Newman-Keuls test in the form (Rcrit=...;p=...), these individual values are not explicitly reported here.
6.2 Results 99
Relative Length Deviation DL
In order to investigate the directional extent of the line segment length assessment, DL is subjected to an identical multi-factorial analysis of variance as was conducted for DLp
before.
The analysis yields a significant main effect of the factor eccentricity on DL (F(3; 33) = 19.57;p <0.001). The target line segment length is generally overestimated, increasingly so with increasingly eccentric presentation. The overestimation effect reaches the following values: 4.8% when the target line segment is presented within the eccentricity region I, 9.6% in eccentricity region II, 15.7% in eccentricity region III and 17.9% in eccentricity region IV. A post-hoc comparison of means using the Newman-Keuls test reveals that significant differences exist between the following eccentricity levels: (Rcrit = 0.052;p = 0.014) for the comparison of DL between the Eccentricities I vs. II, (Rcrit = 0.059;p <
0.001) for I vs. III, (Rcrit = 0.058;p < 0.001) for I vs. IV, (Rcrit = 0.056;p = 0.004) for II vs. III and (Rcrit = 0.059;p < 0.001) for II vs. IV. In contrast, no significant difference in DL can be found between the Eccentricities III and IV (Rcrit= 0.044;p= 0.120).
Another significant main effect on DL can be found for target line segment length (F(2; 22) = 60.37;p < 0.001). If we average over eccentricity and orientation, a mean overestimation of 28.9% for short and of 8.9% for intermediate line lengths emerges. Long line segments are underestimated by 1.9% on average. According to a Newman-Keuls post-hoc test, the differences between all levels of the factor target line segment length are significant with respect to DL: (Rcrit = 0.090;p <0.001) for the comparison between short and intermediate lengths, (Rcrit = 0.092;p < 0.001) for short vs. long lengths and (Rcrit = 0.075;p= 0.006) for intermediate vs. long lengths.
Again, no significant main effect for the factor orientation can be observed (F(2; 22) = 0.66;p = 0.524). The further analysis shows that the previously (for DLp) significant
eccentricity
relative length deviation DL
-0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
I II III IV
short intermediate long
Figure 6.5: Relative deviation DL of the length of the comparison from the target line segment as a function of eccentricity and target line segment length.
100 Experiment E1: Length Assessment in Peripheral Vision
interaction between eccentricity and target line segment length prevails for DL (F(6; 66) = 2.86;p = 0.015), again confirmed by post-hoc comparisons of means using a Newman-Keuls test. In analogy to Figure 6.4, Figure 6.5 illustrates the relative length deviation DL as a function of eccentricity and target line segment length.