Traditional Analysis

5.3.1.1 Experiment 1

The data-trimming scheme resulted in a 2% rejection rate, removing those trials with RTs less than 0.2s and greater 2s RTs. The RTs were then averaged across trials within a condition, resulting in 320 mean RTs (20 × 4 × 2 × 2;

participants × display sizes × fixed/varied cues × left/right stimulus). The mean RTs then were subjected to ANOVAs, which reported the factors showing significant differences. Only when the sphericity assumption was untenable did I report p values corrected with the Greenhouse-Geisser method. The degrees of freedoms are reported as their original values before the correction.

For the mean RTs, the three-way ANOVA showed reliable effects of display size, F(3, 57) = 183.7, η2p = .906, p = 3.23 × 10^-12, (GG-corrected) and cue, F(1, 19) = 8.27, η2p = .303, p = 9.67 × 10^-3 (fixed vs. varied, 524 ms vs. 552 ms), and two interactions: cueing × display size, F(3, 57) = 5.19, η2p = .215, p = 3.05 × 10

-3 and a stimulus × display size interaction, F(3, 57) = 3.04, η2p = .138, p = 3.64

×10^-2. The more items a search display contained (3, 5, 7, vs. 9), the slower participants responded (438, 502, 564, vs. 649 ms). The cue × display size interaction was due to a stronger display size effect for the varied cue than the fixed cue condition. The RT differences between the two cue levels were 12, 24, 40, and 38 ms, going from the small to the large display sizes (Figure 5-2).

Post-hoc t tests indicated that the fixed cue resulted in quicker RTs than the varied cue at display sizes 5, 7 and 9, t(19) = 2.76, 3.23, 2.65, ps = .013, .004, 016, but not at display size 3, t(19) = 1.61, p = .125. Participants responded slightly faster towards the right target – though the effect was marginal, t(19) = 1.96, p = .065 (657 ms vs. 689 ms) in the varied cue condition when the display size was large (9).

Figure 5-2. Mean correct RTs and percent accuracy in Experiments 1, 2 and 3.

No display size 5 was tested in Experiments 2 and 3. Error ribbons are drawn at ±1 SE.

For the accuracy rate data, the ANOVA showed a reliable display size effect, F(3, 57) = 5.53, η2p = .225, p = .005 (3, 5, 7, vs. 9; .985, .984, .977, vs. .977) and a marginal cue effect, F(1, 19) = .355, η2p = .158, p = .07 (F vs. V; .983 vs. .978). Two marginal interactions were also observed: display size × stimulus, F(3, 57) = 2.95, η2p = .134, p = .06 and the three-way interaction, F(3, 57) = 2.54, p = .073. Participants tended to respond more accurately towards a right target, when the cue was unchanged. The average data showed no obvious

speed-accuracy trade-off.

5.3.1.2 Experiment 2

Experiment 2 used a similar protocol to analyse the average data. The RTs were averaged across trials, resulting in 456 mean RTs (19 × 3 × 2 × 2 × 2;

participants × display sizes × cue × ISIs × left/right stimulus).

For the mean RTs, the ANOVA showed a reliable display size effect (3, 7 vs. 9; 495, 678, vs. 777 ms), F(2, 36) = 148.12, η2p = .892, p = 1.65 × 10^-10 (G-G correction), an effect of the ISI (short vs. long; 657 ms vs. 643 ms), F(1, 18) = 15.23, η2p = .458, p = 1.04 × 10^-3, and the cue (fixed vs. varied; 673 ms vs. 627 ms), F(1, 18) = 10.42, η2p = .367, p = 4.67 × 10^-3. Participants responded marginally faster when the target letter was on the left side (639 ms) than on the right side [661 ms; F(1, 18) = 4.19, η2p = .189, p = 0.06]. There were two two-way interactions, for display size × cue, F(2, 36) = 5.92, η2p = .247, p = .01 (G-G correction) and display size × stimulus, F(2, 36) = 4.27, η2p = .192, p = .04 (G-G correction). The former interaction again was due to the increasing differences between the fixed and varied cue conditions as the display size increased. This time, however, a stronger effect of display size was observed in the fixed cue condition. The interaction of display size × ISI only reached a marginal level, F(2, 36) = 2.82, η2p = .135, p = .08 (Figure 5-2).

Separate ANOVAs at each display size showed a reliable cue effect at all display sizes, F(1, 18) = 6.05, 10.78, 10.31; η2p = .251, .375, .364, ps = .02, .004, 005. The RT differences between the fixed cue and varied cue conditions, respectively, at display sizes 3, 7 and 9, were 27, 47, and 62 ms. The ISI effect were observed at the display size 3 and 7, Fs(1, 18) = 29.57, 13.28; η2p

= .622, .427 ps = 3.64 × 10-5, .002. When the display sizes were averaged across, separate ANOVAs at each percentile indicated significant cue × ISI effect [until 0.4 percentiles, Fs(1, 18) = 6.78, 11.02, 7.83, & 7.34, ps = 0.02, 0.004, 0.01,

& 0.01, η2p = 0.27, 0.38, 0.30, & 0.29]. A percentile-by-percentile comparison suggests the interaction is due to significant ISI differences only in the varied cue condition in the leading edge of the RT distribution.

Figure 5-3. The percentile plot shows the small ISI effect in Experiment 2 is due to the RT differences at the early percentiles in the varied cue condition. Error bars were drawn at ±1 SE.

For the accuracy data, the ANOVA showed reliable effects of display size, F(2, 36) = 5.84, η2p = .245, p = .015 (G-G correction), cue, F(1, 18) = 7.89, η2p

= .305, p = .012 and stimulus, F(1, 18) = 16.46, η2p = .478, p = .0007. Participants showed a tendency to respond better towards the right targets, comparing to the left targets (.984 vs. .975).

There were two two-way interactions: stimulus × display size, F(2, 36) =

4.73, ,η2p = .208, p = .016, and ISI × cue, F(1, 18) = 9.85, η2p = .354, p = .0057.

The stimulus × display size interaction is due to a larger advantage when responding for a right target in a 7-item display (1.59% increase; 1.16% increase in the marginal effect in Experiment 1), comparing to other display sizes (in average 0.48% increase). The ISI × display size interaction reached only marginal difference, F(2, 36) = 3.52, η2p = .164, p = .052.

The ISI × cue interaction stems from a reliable difference in the two cue conditions at the short ISI (fixed vs. varied; .985 vs. .975), but not at the long ISI (fixed vs. varied; .981 vs. .980). Accuracy was higher for the fixed target than for the varied target. The effect was mainly due to significant accuracy differences at display size 9, F(1, 18) = 9.31, η2p = .341, p = .007 and at display size 7, F(1, 18) = 6.30, η2p = .259, p = .002 when the ISI was 50 ms.

5.3.1.3 Experiment 3

Experiment 3 replicated Experiment 2, thereby using an identical protocol to analyse the average data, with 480 mean RTs (20 × 3 × 2 × 2 × 2;

participants × display sizes × cue × ISIs × left/right stimulus).

For the mean RTs, the ANOVA showed a reliable display size effect (3, 7 vs. 9; 447, 575, vs. 648 ms), F(2, 38) = 140.71, η2p = .881, p = 1.01 × 10^-10, an effect of the ISI (short vs. long; 562 ms vs. 552 ms), F(1, 19) = 7.66, η2p = .287, p = 1.22 × 10^-2. The cue factor is not significant (fixed vs. varied; 561 vs. 553) nor the interactions was found significant.

For the accuracy data, the ANOVA showed reliable effects of display size, F(2, 38) = 13.84, η2p = .42, p = 4.65 × 10^-4. The cue factor showed only marginal effect, F(1, 19) = 4.04, η2p = .175, p = .06 (fixed vs. varied; .971

vs. .966). The stimulus × display size interaction replicated the finding in Experiment 2, F(2, 38) = 11.35, η2p = .208, p = 5.77 × 10^-4. The ISI × cue only reached marginal level, F(1, 19) = 3.48, η2p = .155, p = .08. The marginal ISI × display size interaction found in Experiment 2 was not significant in Experiment 3. One three-way interaction, cue × ISI × display size, was found marginally significant, F(1, 19) = 3.10, η2p = .14, p = .06. This interaction is due to the display size dependent differences between the varied and fixed cue, which observed only in short ISI.

As for the slope, when fitted using linear regression models, the search slopes across the three experiments did not differentiate fixed and varied cue condition (p > .3).

Table 5-2. Summary table for search slope. The slopes were calculated based on simple linear regression model, using display sizes regressed on mean RT.

Slope comparisons between the two cue conditions were conducted using a null model, presuming that two lines were parallel, comparing to an alternative model, presuming that the cue factor interacts with the display size factor.

Cue 50-ms ISI 400-ms ISI

Overall, the participants in Experiment 1 (538 ms) responded quicker than those in Experiment 2 (650 ms), but relative to Experiment 1, the

participants in Experiment 3 slowed only slightly (557 ms). Participants in Experiment 2 showed a reversed cue effect at mean RTs, though this effect did not suppress significant level in Experiment 3 when per-condition observation was doubled.

The accuracy advantage for the fixed condition consistently emerged across the three experiments, but reduced to non-significant difference in the condition of 400-ms ISI. This suggests that a long ISI might allow one to consolidate the varied, trial-by-trial updated search template and to strengthen it to a similar level as a consistently-mapped template (i.e., fixed condition).

Nevertheless, when considering with the data of accuracy rate, one may argue that the reverse pattern in the mean RT suggests that participants might trade speed with accuracy (or vice versa). I suggest that this is a matter of adjusting decision threshold and decision rate (Forstmann et al., 2008). In the following, I used the two decision-making models – LBA and DDM – to approach an optimal fit solution for the data and propose an account for how the WM strength of a search template relates to the decision parameters.