A Hierarchy of Binary Sequences perception1

Appendix 1

Experiment 2

Grouping of alternation rates in accordance with a post hoc Tukey analysis

B
Human Performance
P(a) / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8
1.93 3.47
3.47 5.17
5.17 6.73
6.73 8.13 8.27 8.67
/ A
Chance Mechanisms
P(a) / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8
2.20
3.97 5.10
7.40
9.40 10.13 10.27
C
Traits and Preferences
P(a) / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8
3.87 5.33 6.00
5.33 6.00 7.20 7.30
6.00 7.20 7.73 7.87 7.30
/ D
Periods and Processes
P(a) / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8
6.63 6.34 6.47 6.27
5.90 4.93 4.33

Mean frequencies of alternation rate (p (a)) attribution to each of the single categories, classified in accordance with the Tukey test (p < 0.05). Means connected with a line do not significantly differ from each other.

Experiment 3

A Comparison of Chance Mechanisms and Human Performance

Chance Mechanisms
P(a) / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8
4.43 4.57 5.13 6.20
5.13 6.20 6.97
6.20 6.97 7.62 7.67
/ Human Performance
P(a) / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8
7.57 7.43 6.87 5.80
6.87 5.80 5.03
5.80 5.03 4.38 4.33

B Comparison of Chance Mechanisms and‘Traits and Preferences’

Chance Mechanisms
P(a) / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8
2.10 3.17 3.73
3.73 5.83
5.83 7.87
7.87 8.97 9.50
/ Traits and Preferences
P(a) / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8
9.90 8.83 8.27
8.27 6.17
6.17 4.13
4.13 3.03 2.50

C Comparison of Chance Mechanisms and‘Periods and Processes’Jovi

Chance Mechanisms
P(a) / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8
1.90 2.30 3.73
6.17
8.37 10.17
10.17 10.40
/ Periods and Processes
P(a) / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8
10.10 9.70 8.27
5.83
3.63 1.83
1.83 1.60

D Comparison of Human Performance and‘Periods and Processes’

Periods and Processes
P(a) / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8
8.83 8.53 7.43
7.43 5.93
5.93 4.63
4.63 3.80 3.03
/ Human Performance
P(a) / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8
3.17 3.47 4.57
4.57 6.07
6.07 7.37
7.37 8.20 8.97

F Comparison of‘Traits and Preferences’ and‘Periods and Processes’

Traits and Preferences
P(a) / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8
2.63 3.10 4.00
7.10 8.63
8.63 9.70 9.77
/ Periods and Processes
P(a) / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8
9.37 8.90 8.00
4.90 3.37
3.37 2.30 2.33

E Comparison of Human Performance and‘Traits and Preferences’

Human Performance
P(a) / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8
4.93 5.33 5.77 5.63 5.70 6.00 5.90
/ Traits and Preferences
P(a) / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8
7.07 6.67 6.23 6.37 6.30 6.00 6.10

Mean frequencies of alternation rate (p (a)) attribution to each category within a category pair, classified in accordance with the Tukey test (p < 0.05). Means connected with a line do not significantly differ from each other.

Experiment4

A. Comparison of Chance Mechanisms, Human Performance, and ‘Traits and Preferences’
Chance Mechanisms
P(a) / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8
0.87 1.40 2.17
3.80
6.47 6.43 7.67
/ Human Performance
P(a) / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8
7.83 7.57
7.57 5.87
5.87 4.57
1.93 2.67 1.60
Traits and Preferences
P(a) / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8
3.30 3.03 3.97 3.63 3.60 2.90 2.73
B. Comparison of Chance Mechanisms, Human Performance, and ‘Periods and Processes’
Chance Mechanisms
P(a) / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8
0.93 2.10 2.17
3.77
6.83 7.73
7.73 8.40
/ Human Performance
P(a) / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8
1.73 2.83 2.90 3.13
2.83 2.90 3.13 3.97
3.97 4.67
4.67 5.73
Periods and Processes
P(a) / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8
9.33
7.07
5.17
2.50
1.20 1.13 0.7
C. Comparison of‘Periods and Processes’, ‘Traits and Preferences’, and Chance Mechanisms
Periods and Processes
P(a) / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8
6.67 6.23
6.23 4.67
4.67 3.87
3.87 2.50
2.50 1.77 1.13
/ Chance Mechanisms
P(a) / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8
.33 .73
.73 1.93
1.93 3.13
5.73
7.50
8.97
Traits and Preferences
P(a) / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8
5.00 5.03 5.40 5.00 3.77
3.77 2.73
2.73 1.90
D. Comparison of‘Periods and Processes’, ‘Traits and Preferences’, and Human Performance
Periods and Processes
P(a) / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8
6.97 6.2
6.2 4.87
4.87 3.13
3.13 2.67 1.90 2.03
/ Traits and Preferences
P(a) / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8
2.97 2.97 3.23 4.37
3.23 4.37 5.07
4.37 5.07 5.60 5.83
Human Performance
P(a) / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8
2.07 2.57
2.57 4.17
4.17 4.27 4.27 4.37 4.50

Mean frequencies of alternation rate (p (a)) attribution to each category within a category triplet, classified in accordance with the Tukey test (p < 0.05). Means connected with a line do not significantly differ from each other.

E. Comparison of all four identified categories

Chance Mechanisms
P(a) / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8
0.48 1.13 1.52
1.13 1.52 2.35
4.30 5.74
5.74 6.96
/ Human Performance
P(a) / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8
1.52 2.17 2.48 2.78 2.91 2.61 2.48
Periods and Processes
P(a) / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8
7.35
5.78
3.95 3.09
3.09 1.70
1.70 1.09 0.74
/ Traits and Preferences
P(a) / 0.2 / 0.3 / 0.4 / 0.5 / 0.6 / 0.7 / 0.8
2.65 2.91 3.04 2.57 1.83
2.65 2.91 4.00 3.78 3.04 2.57

Mean frequencies of alternation rate (p (a)) attribution to each category within a four categories set, classified in accord with the Tukey test (p < 0.05). Means connected with a line do not significantly differ from each other.

Appendix 2

Trend line equations and explained variances for Figure 1

Chance mechanisms: y = 0.52 p(a) + 0.17, R² = 0.60; human performance the trend line is not significant; periods and processes: y = 0.85 p(a)2 - 1.69 p(a) + 0.86, R² = 0.77; traits and preferences: y = 0.39 p(a) + 0.30, R² = 0.37; for the 'other' responses the trend line is not significant.

Trend line equations and explained variances for Figure 2

Chance mechanisms: y = -5.56 p(a)3+ 7.27 p(a)2- 1.49p(a) + 0.25, R² = 0.99; human performance: y = -1.57p(a)2 + 2.53p(a) - 0.31, R² = 0.99; periods and processes: y = -0.25 p(a) + 0.61, R² = 0.71; traits and preferences: y = -1.57p(a)2+ 2.53p(a) - 0.31, R² = 0.98.Bold components are significant at p < .05.

Trend line equations and explained variances for Figure 3

For chance mechanisms: y = 0.53p(a) + 0.24, r² = 0.95 vs. human performance:y = -0.53p(a) + 0.76, r² = 0.95l; for chance mechanisms:y = -5.86p(a)3+ 8.78p(a)2 - 2.85p(a) + 0.45, r² = 0.99 vs.traits and preferences:y = 5.86p(a)3- 8.78p(a)2 + 2.85p(a) + 0.55, r² = 0.99; for chancemechanisms:y = -9.26p(a)3+ 13.94p(a)2 - 4.98p(a) + 0.67, r² = 0.99vs.periodsandprocesses: y = 9.26p(a)3- 13.94p(a)2 + 4.98p(a) + 0.33, r² = 0.99; for humanperformance:y = 0.88p(a) + 0.06, r² = 0.98 vs. periodsandprocesses:y = -0.88p(a) + 0.94, r² = 0.9; for traitsandpreferences:y = -9.80p(a)3+ 14.24p(a)2 - 5.04p(a) + 0.74, r² = 0.99vs.periodsandprocesses:y = 9.65p(a)3- 14.04p(a)2 +4.96p(a) + 0.27,r² = 0.99; the humanperformance vs.traitsandpreferencestrends are non-significant. Bold components are significant at p < .05.

Trend line equations and explained variances for Figure 4

For chancemechanisms:y = -5.86p(a)3 + 8.96p(a)2 - 3.11p(a) + 0.39, R² = 0.98 vs.human performance: y = 6.02p(a)3- 8.48p(a)2 + 2.58p(a) + 0.44,R² = 0.96 vs.traitsandpreferences: n.s.;for chancemechanisms:y = -6.56p(a)3 + 10.29p(a)2 - 3.78p(a) + 0.50, R² = 0.97 vs. humanperformance: y = -2.55p(a)2+ 2.65p(a) - 0.29, R² = 0.80 vs.periodsandprocesses: y = 2.09p(a)2 - 3.33p(a) + 1.38, R² = 0.99; for chancemechanisms:y = -4.48p(a)3+ 7.80p(a)2 - 2.84p(a) + 0.33, R² = 0.99 vs.periodsandprocesses: y = -0.82p(a) + 0.73, R² = 0.98 vs.traitsandpreferences: y = -1.29p(a)2 + 0.83p(a) + 0.30, R² = 0.97;forhumanperformance: y = -1.10p(a)2 + 1.4p(a) - 0.07, R² = 0.91vs.periodsandprocesses: y = 0.98p(a)2 - 1.74p(a) + 0.92, R² = 0.98 vs.traitsandpreferences: y = 0.45p(a) + 0.13, R² = 0.88. Bold components are significant at p < .05.

For chance mechanismsy = 1.02p(a)2 - 0.09p(a) + 0.01, R² = 0.99 vs.periodsandprocesses y = 1.10p(a)2 - 2.04p(a) + 0.98, R² = 0.99 vs.traitsandpreferences y = -1.38p(a)2 + 1.25p(a) + 0.02, R² = 0.88.Bold components are significant at p < .05. The humanperformance trends are non-significant.