Response times results for experiments
Screening of RT with two SDs of the mean for each participant resulted in the removal of 3.66% and 3.85% in experiment 1, 3.39% and 2.08% in experiment 2, and 5.22% and 2.56% in experiment 3, for older and younger adults, respectively.
Figure 2 shows the results of RT in experiment 1. The 3-way mixed ANOVA on RTz revealed a significant main effect of age group, F(1,28) = 4.68, ηp2 = 0.14, p = .039, that is, older adults responded more slowly than did younger adults. Also, a longer response for the collinear condition than non-collinear condition, F(1,28) = 19.25, ηp2 = 0.29, p < .001; and a longer response for the overlap condition than for the non-overlap condition, F(1,28) = 67.55, ηp2 = 0.59, p < .001. The two-way interactions and the three-way interactions were all significant, ps < .001. Interestingly, the simple main effect of the three-way interactions revealed that younger adults had significant search impairment (longer response to the overlap than the non-overlap conditions) in the collinear condition, F(1,56) = 9.08, ηp2 = 0.04, p = .004, while no significant effect was observed in the non-collinear condition, p = .86. Meanwhile, older adults not only had a significant search impairment in the collinear condition, F(1,56) = 162.55, ηp2 = 0.70, p < .001, but also a significant attentional capture effect in the non-collinear condition, F(1,56) = 5.37, ηp2 = 0.02, p = .024.
Figures 3E and 3F show the results of experiment 2 for younger and older adults, respectively. The three-way mixed ANOVA revealed a significant main effect on target type, F(1,22) = 60.34, ηp2 = 0.71, p < .001, suggesting that the search impairment was generally obtained. A main effect of the distractor length was also found, F(3,66) = 4.00, ηp2 = 0.13, p = .011, showing that RT became longer as distractor length increased. The two-way interactions and the three-way interactions were also significant, ps < .05. The simple main effect analysis of the three-way interaction showed that search impairment was significant in all four distractor lengths in younger adults: F(1, 88) = 6.23, 11.10, 17.80, and 20.85, ηp2 = 0.02, 0.04, 0.06 and 0.07; ps < .01 for the distractor lengths of three, five, nine, and 13, respectively; and older adults, F(1, 88) = 5.50, 23.57, 52.35, and 67.15; ηp2 = 0.02, 0.08, 0.18 and 0.23; ps < .05, for the distractor lengths of 3, 5, 9, and 13, respectively.
To understand whether the size of search impairment increased with distractor length, a two-way mixed ANOVA was performed for RTz differences between the overlap and non-overlap conditions (the size of search impairment). Results showed a significant main effect for age, F(1,22) = 6.19, ηp2 = 0.22, p = .021; distractor length, F(3,66) = 18.68, ηp2 = 0.40, p < .001; and the interaction, F(3,66) = 6.60, ηp2 = 0.14, p < .001. Importantly, a significant linear trend in distractor length was observed for younger adults, F(1,66) = 4.36, ηp2 = 0.06, p = .040; and older adults, F(1,66) = 65.01, ηp2 = 0.48, p < .001, indicating that the search impairment increased with distractor length for both age groups.
Figures 4E and 4F show results of experiment 3 for younger and older adults, respectively. The three-way mixed ANOVA on RTz showed a main effect of target type, F (1, 34) = 71.44, ηp2 = 0.65, p < .001, indicating that search impairment was observed regardless of whether curved or straight distractors were used. A main effect of age group was also observed, F (1, 34) = 5.35, ηp2 = 0.14, p = .026, showing that older adults took longer than younger adults did. In addition, an interaction between target type and distractor type was found, F (1, 34) = 4.51, ηp2 = 0.60, p < .001, suggesting that the search impairment was larger in the straight than the curved conditions. The simple main effect revealed that younger adults showed significant search impairment in the straight condition, F (1, 68) = 39.27, ηp2 = 0.19, p < .001, but not in the curved condition, p = .42. However, a pair-wise t-test showed significantly longer overlap responses (727 ms) than the non-overlap (709 ms) responses in the curved condition, t (17) = 2.52, p = .022, Cohen’s d = 0.15. Older adults, however, exhibited search impairment in both straight, F (1, 68) = 88.03, ηp2 = 0.44, p < .001, and curved conditions, F (1, 68) = 5.94, ηp2 = 0.03, p = .017.
Accuracy results for experiments
Table 1 shows the accuracy in three experiments. In experiment 1, three-way mixed ANOVA revealed a significant main effect for age group, F(1,28) = 9.73, ηp2 = 0.26, p = .004; target type, F(1,28) = 24.25, ηp2 = 0.33, p < .001; distractor type, F(1, 28) = 24.27, ηp2 = 0. 28, p < .001; as well as three two-way interactions and the three-way interactions, ps < .001. In other words, older adults had more errors than younger adults did, the collinear condition was more difficult than the non-collinear condition, and the overlapping condition was more difficult than the non-overlapping condition. The simple main effect of the three-way interactions showed that the older adults had search impairment in accuracy in the collinear condition, F(1,56) = 105.63, ηp2 = 0.65, p < .001, and no significant effects were found for younger adults and older adults in the non-collinear condition, ps > .05.
Table 1
The accuracy (%) and the standard error of the mean (in parentheses, %) in each condition in the three experiments.
|
Younger adults
|
Older adults
|
|
Overlap
|
Non-overlap
|
Overlap
|
Non-overlap
|
Experiment 1
|
|
|
|
|
Collinear
|
95.00
(1.12)
|
95.65
(0.81)
|
80.37
(2.02)
|
96.94
(0.76)
|
Non-collinear
|
94.81
(0.93)
|
94.54
(0.89)
|
97.41
(0.99)
|
95.56
(0.72)
|
Experiment 2
|
|
|
|
|
Collinear 3-bar
|
94.44
(1.81)
|
95.37
(1.25)
|
92.13
(2.10)
|
96.30
(0.86)
|
Collinear 5-bar
|
97.22
(1.08)
|
93.06
(0.94)
|
93.06
(2.48)
|
95.60
(1.05)
|
Collinear 9-bar
|
95.83
(1.55)
|
94.68
(0.99)
|
86.57
(2.77)
|
95.83
(1.16)
|
Collinear 13-bar
|
93.06
(1.55)
|
93.75
(2.00)
|
82.87
(2.86)
|
97.22
(0.76)
|
Experiment 3
|
|
|
|
|
Curved collinear
|
96.53
(0.81)
|
96.25
(0.54)
|
81.48
(3.65)
|
83.33
(5.44)
|
Straight collinear
|
91.53
(1.46)
|
94.40
(0.84)
|
84.72
(3.68)
|
80.69
(5.22)
|
In experiment 2, the three-way mixed ANOVA showed that younger adults in general were more accurate than older adults, F(1,22) = 5.88, ηp2 = 0.21, p = .024. The target type main effect was also obtained, F(1,22) = 11.11, ηp2 = 0.22, p = .003, suggesting that search impairment was observed in all distractor length conditions. Furthermore, the longer the collinear distractor was, the lower the accuracy was, F(3,66) = 2.87, ηp2 = 0.11, p = .043. The interaction between age group and target type as well as the interaction between target types and distractor lengths were significant, ps < .05. The simple main effect showed that the accuracy of older adults generated search impairment in distractor lengths of 9- and 13-bars, F(1,88) = 14.43 and 34.67, ηp2 = 0.10 and 0.24, ps < .001, respectively.
In experiment 3, a three-way mixed ANOVA showed that older adults had a lower accuracy than younger adults, F (1, 34) = 11.09, ηp2 = 0.25, p = .002. A significant interaction between age group and distractor type was also found, F (1, 34) = 5.38, ηp2 = 0.13, p = .027, suggesting that younger adults had higher accuracy in the curved condition than in the straight condition, F (1, 34) = 9.10, ηp2 = 0.21, p = .005. Older adults, however, did not exhibit differences in terms of accuracy for the two types of distractors, p = .79. The three-way interaction was significant, F (1, 34) = 7.48, ηp2 = 0.17, p = .009; however, there was no significant search impairment in accuracy for both age groups, ps > .05.
The Brinley plot and state trace
Figure 5 illustrates the results of the meta-analysis of the three experiments. The Brinley plot (Fig. 5A) showed that the variance of the two age groups can be explained by a simple linear regression, R2 = .97. Separately fitting for non-overlap (R2 = .98) and overlap (R2 = .99) conditions did not considerably increase R2. Thus, a more parsimonious explanation was concluded by taking the single linear regression, in that the performance of older adults was a function of younger adults in certain expansions of RTs, from an easier to more difficult condition.
Figure 5B shows the state trace for the three experiments. The linear regression of the total data reached the highest explanation, R2 = .89. Separation of fitting revealed less well-fit for younger (R2 = .80) and older (R2 = .81) adults; thus, a single regression can fit the data. The slope of regression was 1.51, suggesting a multiplicative complexity for older adults in dealing with the more difficult condition (overlap condition) relative to the less difficult one (non-overlap condition). The slope ratio for conditions (overlap over non-overlap, which is 7.24 over 5.32) in Fig. 5A and that for the groups (older over younger, which is 1.48 over 1.09) in Fig. 5B was equal, which was 1.36 (7.24/5.36 ≈ 1.48/1.09 ≈ 1.36). The equivalent ratio is also a characteristic of the multiplicative complex argument of the relationship between the two groups21, suggesting that the increment of RTs of older adults was not simply an additive manner from younger adults; rather, multiple steps/processing were postponed in older adults.