Sequential Effects on Reaction Time Distributions: Commonalities and Differences Across Paradigms

	M_A	M_R	Δ	95% CI	M_A	M_R	Δ	95% CI
	VS COLOR				VS FORM
RT	524	479	44.7	[36.3;53.1]	645	642	2.4	[–6.0;10.8]
PC	.978	.993	.015	[.008;.021]	.930	.949	.019	[.008;.030]
	2CRT
RT	584	556	36.6	[28.0;45.2]
PC	.955	.969	.013	[.006;.020]
	INT CONGRUENT				INT INCONGRUENT
RT	575	562	13.5	[9.0;17.9]	608	602	5.6	[1.1;10.1]
PC	.961	.961	–.0002	[–.005;.004]	.940	.950	.010	[.003;.017]
	TS COLOR				TS FORM
RT	712	608	103.6	[85.3;121.8]	788	697	91.6	[74.0;109.1]
PC	.931	.980	.048	[.038;.059]	.937	.958	.021	[.012;.031]

[i] Note. VS = visual search paradigm; 2CRT = 2CRT paradigm; Int = interference paradigm; TS = task-switching paradigm; CI = confidence interval.

Mean response time (mean RT) in ms for repetition and alternation trials separately for each stimulus type of the four paradigms.

Vincentized response time (RT) per quantile for repetition and alternation trials separately per paradigm and stimulus type.

Relative frequency histograms of the pooled observed reaction time (RT) percentiles for repetition and alternation trials separately per paradigm and stimulus type.

Table 2

Ex-Gaussian distribution: Mean (M) parameter estimates for alternation (A) and repetition (R) trials, their difference (Δ), and the respective effect size with 95%-confidence interval of the standardized effects for all parameters within each paradigm and stimulus type.

	M_A	M_R	Δ	d_Z	[LOW;UP]	M_A	M_R	Δ	d_Z	[LOW;UP]
	VS COLOR					VS FORM
µ	415	393	21.4	0.42	[0.32;0.51]	454	442	12.0	0.21	[0.12;0.31]
σ	22	20	2.1	0.15	[–0.22;0.52]	29	22	6.3	0.32	[–0.07;0.7]
τ	113	87	26.0	0.46	[0.3;0.62]	200	209	–9.1	0.08	[0;0.17]
	2CRT
µ	423	386	36.5	0.73	[0.59;0.86]
σ	42	33	8.6	0.72	[0.43;1.02]
τ	100	103	–2.7	0.06	[–0.05;0.18]
	INT CONGRUENT					INT INCONGRUENT
µ	442	430	12.0	0.18	[0.13;0.23]	465	461	4.1	0.06	[0.02;0.11]
σ	37	34	2.6	0.17	[–0.07;0.41]	44	43	1.1	0.06	[–0.15;0.27]
τ	133	131	1.8	0.02	[–0.06;0.11]	140	139	0.8	0.01	[–0.06;0.08]
	TS COLOR					TS FORM
µ	497	448	49.2	0.76	[0.62;0.91]	531	483	47.5	0.66	[0.53;0.79]
σ	42	37	5.1	0.19	[–0.18;0.56]	55	54	1.2	0.07	[–0.25;0.39]
τ	209	160	49.4	0.53	[0.38;0.69]	255	211	44.0	0.45	[0.31;0.58]

[i] Note. Significant differences are highlighted using bold font. VS = visual search paradigm; 2CRT = 2CRT paradigm; Int = interference paradigm; TS = task-switching paradigm.

Table 3

EZ model: Mean (M) parameter estimates for alternation (A) and repetition (R) trials for all parameters within each paradigm and stimulus type as well as the respective effect size with 95%-confidence interval of the standardized effects.

	M_A	M_R	d_Z	[LOW;UP]	M_A	M_R	d_Z	[LOW;UP]
	VS COLOR				VS FORM
a	1.842	2.214	0.35	[0.01;0.68]	1.528	1.655	0.16	[–0.11;0.43]
v	3.913	4.881	0.64	[0.34;0.94]	2.265	2.407	0.2	[0.02;0.39]
t₀	0.288	0.243	0.46	[0.19;0.72]	0.338	0.315	0.22	[–0.01;0.45]
w	0.496	0.499	0.45	[0.08;0.82]	0.49	0.491	0.06	[–0.24;0.36]
	2CRT
a	1.135	1.192	0.2	[0.07;0.34]
v	3.03	3.219	0.28	[0.07;0.48]
t₀	0.339	0.3	0.64	[0.47;0.81]
w	0.505	0.499	1.08	[0.59;1.56]
	INT CONGRUENT				INT INCONGRUENT
a	1.393	1.332	0.09	[–0.04;0.21]	1.248	1.273	0.05	[–0.07;0.17]
v	2.923	2.875	0.06	[–0.11;0.23]	2.568	2.674	0.16	[0.01;0.31]
t₀	0.33	0.322	0.08	[–0.03;0.18]	0.368	0.361	0.07	[–0.06;0.19]
w	0.502	0.502	0.08	[–0.23;0.39]	0.506	0.505	0.21	[–0.01;0.44]
	TS COLOR				TS FORM
a	1.427	1.688	0.52	[0.24;0.81]	1.591	1.588	0.01	[–0.16;0.18]
v	2.021	2.798	1.2	[0.95;1.45]	1.872	2.199	0.67	[0.47;0.88]
t₀	0.379	0.297	0.94	[0.65;1.24]	0.39	0.344	0.59	[0.37;0.81]
w	0.506	0.5	0.93	[0.56;1.30]	0.503	0.503	0.03	[–0.29;0.35]

[i] Note. Significant differences are highlighted using bold font. VS = visual search paradigm; 2CRT = 2CRT paradigm; Int = interference paradigm; TS = task-switching paradigm.

Table 4

Four-parameter diffusion model: Mean (M) parameter estimates for alternation (A) and repetition (R) trials for all parameters within each paradigm and stimulus type as well as the respective effect size with 95%-confidence interval of the standardized effects.

	M_A	M_R	d_Z	[LOW;UP]	M_A	M_R	d_Z	[LOW;UP]
	VS COLOR				VS FORM
a	1.8	2.21	0.46	[0.16;0.76]	1.48	1.6	0.21	[–0.06;0.48]
v	3.7	4.65	0.73	[0.45;1]	2.04	2.1	0.08	[–0.09;0.25]
t₀	0.34	0.32	0.47	[0.25;0.68]	0.38	0.37	0.06	[–0.09;0.21]
w	0.58	0.63	0.32	[0.04;0.59]	0.56	0.6	0.33	[0.09;0.57]
	2CRT
a	1.47	1.39	0.36	[0.15;0.57]
v	4.12	3.89	0.25	[0.07;0.43]
t₀	0.29	0.28	0.17	[–0.01;0.35]
w	0.32	0.4	1.11	[0.76;1.46]
	INT CONGRUENT				INT INCONGRUENT
a	1.5	1.43	0.15	[–0.06;0.36]	1.43	1.45	0.06	[–0.08;0.2]
v	3.39	3.39	0	[–0.11;0.11]	3.13	3.27	0.16	[0.01;0.31]
t₀	0.33	0.33	0.11	[0;0.22]	0.34	0.33	0.06	[–0.07;0.19]
w	0.43	0.42	0.05	[–0.1;0.2]	0.39	0.39	0.01	[–0.17;0.19]
	TS COLOR				TS FORM
a	1.51	1.75	0.49	[0.2;0.78]	1.71	1.7	0.01	[–0.22;0.24]
v	2.4	3.17	1.03	[0.82;1.23]	2.23	2.6	0.61	[0.4;0.82]
t₀	0.37	0.32	0.93	[0.72;1.14]	0.36	0.33	0.6	[0.32;0.87]
w	0.43	0.46	0.4	[0.08;0.72]	0.42	0.42	0.02	[–0.26;0.3]

[i] Note. Significant differences are highlighted using bold font. VS = visual search paradigm; 2CRT = 2CRT paradigm; Int = interference paradigm; TS = task-switching paradigm.

Table 5

Seven-parameter diffusion model: Mean (M) parameter estimates for alternation (A) and repetition (R) trials for all parameters within each paradigm and stimulus type as well as the respective effect size with 95%-confidence interval of the standardized effects.

	M_A	M_R	d_Z	[LOW;UP]	M_A	M_R	d_Z	[LOW;UP]
	VS COLOR				VS FORM
a	1.45	1.61	0.23	[–0.08;0.54]	1.38	1.49	0.22	[–0.01;0.44]
v	3.62	5.22	1.08	[0.65;1.51]	2.31	2.34	0.02	[–0.24;0.28]
t₀	0.35	0.33	0.45	[0.27;0.64]	0.38	0.38	0.05	[–0.13;0.23]
w	0.67	0.65	0.11	[–0.18;0.39]	0.64	0.67	0.19	[–0.04;0.43]
*σ_v*	0.56	1.19	0.63	[0.24;1.01]	0.66	0.63	0.03	[–0.28;0.33]
$σ_{t_{0}}$	0.08	0.07	0.36	[0.08;0.64]	0.12	0.12	0.02	[–0.22;0.25]
σ_w	0.19	0.19	0.05	[–0.33;0.42]	0.24	0.25	0.12	[–0.25;0.5]
	2CRT
a	1.44	1.31	0.33	[0.14;0.53]
v	5.93	5.36	0.49	[0.11;0.87]
t₀	0.28	0.27	0.11	[–0.05;0.27]
w	0.29	0.42	1.49	[0.94;2.03]
σ_v	1.8	1.7	0.11	[–0.17;0.4]
$σ_{t_{0}}$	0.12	0.12	0.12	[–0.18;0.42]
σ_w	0.1	0.13	0.27	[–0.1;0.65]
	INT CONGRUENT				INT INCONGRUENT
a	1.42	1.41	0.03	[–0.18;0.24]	1.39	1.46	0.13	[–0.03;0.28]
v	4.71	4.82	0.07	[–0.23;0.37]	4.46	5.08	0.38	[0.13;0.63]
t₀	0.32	0.31	0.16	[–0.01;0.32]	0.32	0.32	0.07	[–0.06;0.2]
w	0.41	0.4	0.07	[–0.19;0.34]	0.37	0.35	0.14	[–0.09;0.37]
*σ_v*	1.46	1.5	0.03	[–0.25;0.3]	1.37	1.69	0.22	[0.01;0.44]
$σ_{t_{0}}$	0.12	0.11	0.09	[–0.16;0.35]	0.14	0.14	0.02	[–0.22;0.26]
*σ_w*	0.12	0.12	0	[–0.37;0.38]	0.11	0.12	0.1	[–0.23;0.43]
	TS COLOR				TS FORM
a	1.63	1.86	0.38	[0.08;0.68]	1.85	1.83	0.03	[–0.19;0.26]
v	3.89	5.04	0.69	[0.32;1.05]	3.53	4.11	0.37	[0.07;0.66]
t₀	0.34	0.3	0.69	[0.44;0.93]	0.34	0.3	0.56	[0.31;0.8]
w	0.38	0.44	0.48	[0.11;0.84]	0.38	0.37	0.08	[–0.22;0.38]
*σ_v*	1.61	1.71	0.08	[–0.25;0.42]	1.4	1.41	0	[–0.29;0.29]
$σ_{t_{0}}$	0.14	0.14	0.04	[–0.31;0.38]	0.15	0.15	0.05	[–0.27;0.37]
*σ_w*	0.1	0.14	0.48	[0.12;0.83]	0.11	0.11	0.08	[–0.29;0.44]

[i] Note. Significant differences are highlighted using bold font. VS = visual search paradigm; 2CRT = 2CRT paradigm; Int = interference paradigm; TS = task-switching paradigm.

Table 6

Results of the χ²-test computed jointly for alternation and repetition trials as well as from the Kolmogorov-Smirnov test computed separately for alternation and repetition trials for each paradigm, stimulus type, and model.

	χ²(99)(P)	D_A(P)	D_R(P)	χ²(99)(P)	D_A(P)	D_R(P)
	VS COLOR			VS FORM
ExGauss	136(.008)	0.0179(.056)	0.0177(.056)	108(.246)	0.0072(.919)	0.0077(.912)
EZ	185(< .001)	0.0341(< .001)	0.034(< .001)	127(.029)	0.0113(.444)	0.0121(.412)
Diff4	175(< .001)	0.0274(< .001)	0.0269(.001)	114(.143)	0.0085(.789)	0.0091(.768)
Diff7	100(.467)	0.0092(.729)	0.009(.744)	109(.232)	0.0062(.979)	0.0069(.958)
	2CRT
ExGauss	184(<.001)	0.011(.001)	0.0111(.001)
EZ	1494(< .001)	0.0252(< .001)	0.0256(< .001)
Diff4	299(< .001)	0.0228(< .001)	0.0232(< .001)
Diff7	244(< .001)	0.0151(< .001)	0.0153(< .001)
	INT CONGRUENT			INT INCONGRUENT
ExGauss	103(.371)	0.0038(.973)	0.0038(.974)	123(.051)	0.004(.959)	0.0039(.967)
EZ	139(.005)	0.0081(.251)	0.0079(.266)	155(< .001)	0.0072(.378)	0.0073(.362)
Diff4	117(.101)	0.0085(.204)	0.0083(.211)	138(.006)	0.0086(.187)	0.0086(.186)
Diff7	112(.170)	0.0075(.331)	0.0074(.338)	131(.018)	0.0069(.425)	0.0069(.436)
	TS COLOR			TS FORM
ExGauss	196(< .001)	0.0124(.015)	0.0124(.015)	110(.219)	0.0028(>.999)	0.003(.999)
EZ	344(< .001)	0.0268(< .001)	0.0267(< .001)	128(.027)	0.0083(.227)	0.0083(.231)
Diff4	250(< .001)	0.0175(< .001)	0.0175(< .001)	142(.003)	0.0119(.023)	0.0123(.018)
Diff7	127(.032)	0.0039(.972)	0.0039(.969)	120(.072)	0.0075(.332)	0.0076(.325)

[i] Note. VS = visual search paradigm; 2CRT = 2CRT paradigm; Int = interference paradigm; TS = task-switching paradigm; ExGauss = ex-Gaussian distribution; EZ = EZ-diffusion model; Diff4 = four-parameter diffusion model, Diff7 = seven-parameter diffusion model.