Many paradigms for comparing identification thresholds with detection thresholds require the observer to make double judgments. We show that these paradigms can produce misleading results because of response biases and attentional shifts. For example, the subject’s response bias plus correlated noise can mimic inhibition between channels. Some of these same problems can affect single-judgment paradigms. A detailed analysis of the double-judgment forced-choice paradigm reveals that there are a multiplicity of optimal strategies, some of which enhance identification over detection. Several improved analysis techniques for minimizing the effects of cognitive factors are proposed for both the double-judgment forced-choice paradigm and the double-judgment rating-scale paradigm. A classification scheme for distinguishing different types of interactions and correlations is developed. When the new rating-scale algorithm is applied to the detection of well-separated spatial frequencies, substantial masking but negligible inhibition is found. The rating-scale paradigm is shown to be useful in revealing not only the sensitivity and the interactions of the underlying mechanisms but also the observer’s information-processing strategies.
You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
Krauskopf.8
Stromeyer and Klein9 and Lawden.10
Watt11 and Levi and Klein.12
Levi et al.13
Julesz and Tyler.14
Levi and Klein12 and Allik et al.15
Tolhurst and Dealy.16
Table 2
Data Set for Single-Knob Experiment of Allik et al.a (Observer MR)
Example of How Alternating Attention Affects 2 × 2 AFC
Stimulus
Attend to 3 c/deg
Attend to 12 c/deg
Detect.
Identif.
Detect.
Identif.
Interval 1, 3 c/deg
92%
80%
50%
80%
Interval 1, 12 c/deg
50%
80%
92%
80%
Interval 2, 3 c/deg
92%
80%
50%
80%
Interval 2, 12 c/deg
50%
80%
92%
80%
Total
71%
80%
71%
80%
Table 5
Six Goals for Double Judgment Forced-Choice Paradigm (2 × 2 AFC)a
Goal
Probabilities
z Scores
Efficiency
+D,+I
−D,+I
+D,−I
−D,−I
D(±I)
I(±D)
D(+I)
I(+D)
Max. Ratio
I(−D)
D Obs./D Exp. √2D/V
IObs./I Exp. 2I/2B
a
b
c
d
a + c
a + b
a/(a + b)
a/(a + c)
a/(a + d)
b/(b + d)
√2D/V
2I/2B
2zI/zD
M = 0.5, B = 0.5, (V = 0.7071)
1
44.3%
20.3%
20.3%
15.2%
0.372
0.372
0.484
0.484
0.655
0.177
74.3%
74.3%
1.414
2
45.5%
17.8%
19.1%
17.7%
0.372
0.337
0.580
0.537
0.581
0.001
74.3%
67.4%
1.283
3
44.2%
20.3%
15.3%
20.2%
0.241
0.372
0.482
0.651
0.486
0.004
48.1%
74.3%
2.183
4
45.8%
18.0%
18.1%
18.1%
0.356
0.354
0.576
0.574
0.575
0.000
71.2%
70.9%
1.408
5
29.8%
29.7%
29.9%
10.6%
0.244
0.241
0.001
0.002
0.636
0.635
48.9%
48.2%
1.394
6
40.8%
23.0%
23.2%
13.0%
0.357
0.352
0.355
0.351
0.669
0.355
71.3%
70.4%
1.396
M= 1.5, B = 0.5, (V = 1.581)
1
58.9%
8.0%
26.8%
6.3%
1.067
0.436
1.176
0.487
1.303
0.152
95.5%
87.3%
0.578
2
59.3%
7.2%
26.4%
7.1%
1.067
0.424
1.239
0.501
1.240
0.001
95.5%
84.8%
0.562
3
57.8%
9.1%
24.0%
9.1%
0.907
0.436
1.097
0.543
1.098
0.000
81.1%
87.3%
0.681
4
59.4%
7.2%
26.2%
7.2%
1.060
0.429
1.234
0.507
1.235
0.000
94.8%
85.7%
0.572
5
42.4%
11.1%
42.1%
4.3%
1.018
0.089
0.815
0.005
1.325
0.580
91.0%
17.7%
0.123
6
54.7%
9.2%
30.9%
5.2%
1.062
0.354
1.062
0.354
1.361
0.356
95.0%
70.9%
0.472
M = 0.5, B = 1.5, (V= 1.581)
1
74.7%
11.6%
3.5%
10.2%
0.778
1.093
1.105
1.696
1.173
0.079
69.6%
72.8%
1.986
2
75.1%
10.9%
3.1%
10.9%
0.778
1.081
1.141
1.758
1.142
0.000
69.6%
72.1%
1.965
3
75.1%
11.2%
2.5%
11.2%
0.758
1.093
1.128
1.851
1.125
0.004
67.8%
72.8%
2.039
4
75.2%
11.0%
2.8%
11.0%
0.774
1.089
1.140
1.797
1.139
0.001
69.2%
72.6%
1.990
5
15.6%
67.0%
15.6%
1.8%
0.487
0.939
0.869
0.002
1.265
1.994
43.6%
62.6%
2.726
6
54.6%
31.0%
9.1%
5.3%
0.350
1.063
0.352
1.067
1.353
1.057
31.3%
70.9%
4.291
M = 1.5, B = 1.5, (V = 2.121)
1
84.4%
5.5%
5.5%
4.6%
1.275
1.274
1.543
1.543
1.628
0.114
85.0%
85.0%
1.414
2
84.6%
5.0%
5.3%
5.1%
1.275
1.262
1.590
1.569
1.582
0.010
85.0%
84.1%
1.400
3
84.4%
5.5%
4.5%
5.6%
1.220
1.274
1.543
1.636
1.536
0.009
81.3%
85.0%
1.477
4
84.7%
5.1%
5.1%
5.2%
1.269
1.269
1.584
1.584
1.578
0.008
84.6%
84.6%
1.414
5
33.0%
33.1%
33.1%
0.8%
0.415
0.415
0.003
0.003
1.992
1.994
27.6%
27.6%
1.415
6
73.3%
12.3%
12.3%
2.1%
1.060
1.062
1.062
1.064
1.910
1.051
70.7%
70.8%
1.417
Columns two through five give the probabilities (in percent) of the four possible outcomes in a 2 × 2 AFC paradigm. For example, the fourth column [c = P(+D, −I)] is the probability of the identification being wrong and the detection being correct. The sixth through eleventh columns are z scores corresponding to combinations of the raw probabilities. The sixth column [probability of correct detection independent of identification, D(±I)] is the z score of the quantity a + c. The eighth column [probability of correct detection contingent on the identification being correct, D(+I)] is the z score of the quantity a/(a + b) that considers only events with correct identification. The twelfth and thirteenth columns compare the observed detection (sixth column) and identification (seventh column) with what would be expected in a single- judgment two-alternative forced-choice paradigm. The last column is the I/D ratio given by the ratio of the seventh and sixth columns times
.
Table 6
Olzak’s Data on Double-Judgment Ratings for 3- and 12-c/deg Gratings
Low Ratings
High-Frequency Ratings
3 c/deg Stimulus
3 + 12-c/deg Stimulus
Totals
1
2
3
4
5
6
Totals
1
2
3
4
5
6
6
211
112
44
30
20
4
1
175
26
12
18
20
26
73
5
179
53
54
58
9
5
0
116
11
16
13
18
23
35
4
76
22
21
16
10
7
0
73
3
7
9
11
17
26
3
24
6
7
2
5
4
0
52
0
3
1
6
18
24
2
5
3
0
2
0
0
0
48
1
0
1
4
18
24
1
5
2
2
0
0
0
1
36
1
0
0
3
12
20
Totals
198
128
108
44
20
2
42
38
42
62
114
202
Blank Stimulus
12-c/deg Stimulus
6
18
5
3
5
3
1
1
13
0
0
0
1
3
9
5
69
18
22
20
5
3
1
41
0
3
7
9
5
7
4
117
51
40
16
8
2
0
79
5
9
10
9
25
21
3
99
45
23
10
16
5
0
79
8
2
3
14
21
31
2
112
54
16
14
19
6
2
132
13
7
8
34
32
38
1
86
67
8
5
1
3
2
156
16
4
4
16
44
72
Totals
240
112
70
52
20
6
42
25
32
83
130
188
Table 7
Center Location of Channel Activity (in d′ Units)
Stimulus Pairs
12-c/deg Channel Activity
3-c/deg Channel Activity
Method: 1 Area
2 Neg. Diag.
3
4
1 Area
2 Neg. Diag.
3
4
Max. Lik.
Max. Lik.
Pairs
Joint
Pairs
Joint
B – 3
0.13
0.21
0.11
0.11
1.59
1.71
1.68
1.50
B – 12
1.62
1.86
1.71
1.72
−0.39
−0.46
−0.40
−0.38
B – 3 & 12
1.55
1.70
1.64
1.71
0.91
0.84
0.94
1.00
3 – 12
1.61
1.97
1.69
1.61
1.91
2.01
2.01
1.88
3 – 3 & 12
1.52
1.81
1.61
1.60
−0.37
−0.19
−0.46
−0.50
12 – 3 & 12
0.00
0.07
0.00
−0.01
1.20
1.23
1.25
1.38
Table 8
Results of Double-Judgment Rating-Scale Algorithm
Stimulus pairs
Starting Edge
Boundary
No. Correct
d′
Stim.1
Stim. 2
Algorithm
Method 2
Method 3
B – 3
Bottom
(4, 4, 4, 3, 3, 6)
405
406
1.758
1.72
1.68
(4, 4, 4, 4, 3, 6)
413
396
1.747
B – 12
Left
(1, 3, 3, 2, 3, 4)
396
418
1.787
1.92
1.77
(1, 3, 3, 3, 3, 4)
412
408
1.826
3 – 3 & 12
Left
(0, 0, 1, 2, 3, 2)
370
412
1.569
1.82
1.67
(0, 0, 1, 2, 3, 3)
400
394
1.636
12 – 3 & 12
Bottom
(4, 2, 3, 3, 2, 3)
349
392
1.232
1.23
1.25
(4, 2, 3, 3, 3, 3)
370
364
1.245
B – 3 & 12
Left
(3, 4, 4, 3, 1, 0)
424
437
2.169
1.90
1.89
(3, 4, 4, 3, 3, 0)
444
424
2.240
B – 3 & 12
Bottom
(5, 4, 5, 3, 0, 0)
423
437
2.161
(5, 5, 5, 3, 0, 0)
445
421
2.225
3 – 12
Left
(0, 0, 0, 4, 3, 5)
444
453
2.530
2.81
2.63
(0, 0, 0, 4, 4, 5)
453
444
2.530
12 – 3
Bottom
(3, 2, 3, 3, 6, 6)
445
456
2.577
(3, 2, 3, 4, 6, 6)
454
446
2.563
Controls
B(3 & 12) – B(3 & 18)
Bottom
(0, 4, 6, 6, 6, 6)
235
313
0.244
0.33
0.16
(1, 4, 6, 6, 6, 6)
302
244
0.232
B(3 & 18) – B(3 & 12)
Left
(1, 0, 0, 1, 6, 6)
267
295
0.310
(1, 0, 0, 2, 6, 6)
307
255
0.312
Tables (8)
Table 1
Bipolar and Monopolar Cues in Single-Knob Experiments
Krauskopf.8
Stromeyer and Klein9 and Lawden.10
Watt11 and Levi and Klein.12
Levi et al.13
Julesz and Tyler.14
Levi and Klein12 and Allik et al.15
Tolhurst and Dealy.16
Table 2
Data Set for Single-Knob Experiment of Allik et al.a (Observer MR)
Example of How Alternating Attention Affects 2 × 2 AFC
Stimulus
Attend to 3 c/deg
Attend to 12 c/deg
Detect.
Identif.
Detect.
Identif.
Interval 1, 3 c/deg
92%
80%
50%
80%
Interval 1, 12 c/deg
50%
80%
92%
80%
Interval 2, 3 c/deg
92%
80%
50%
80%
Interval 2, 12 c/deg
50%
80%
92%
80%
Total
71%
80%
71%
80%
Table 5
Six Goals for Double Judgment Forced-Choice Paradigm (2 × 2 AFC)a
Goal
Probabilities
z Scores
Efficiency
+D,+I
−D,+I
+D,−I
−D,−I
D(±I)
I(±D)
D(+I)
I(+D)
Max. Ratio
I(−D)
D Obs./D Exp. √2D/V
IObs./I Exp. 2I/2B
a
b
c
d
a + c
a + b
a/(a + b)
a/(a + c)
a/(a + d)
b/(b + d)
√2D/V
2I/2B
2zI/zD
M = 0.5, B = 0.5, (V = 0.7071)
1
44.3%
20.3%
20.3%
15.2%
0.372
0.372
0.484
0.484
0.655
0.177
74.3%
74.3%
1.414
2
45.5%
17.8%
19.1%
17.7%
0.372
0.337
0.580
0.537
0.581
0.001
74.3%
67.4%
1.283
3
44.2%
20.3%
15.3%
20.2%
0.241
0.372
0.482
0.651
0.486
0.004
48.1%
74.3%
2.183
4
45.8%
18.0%
18.1%
18.1%
0.356
0.354
0.576
0.574
0.575
0.000
71.2%
70.9%
1.408
5
29.8%
29.7%
29.9%
10.6%
0.244
0.241
0.001
0.002
0.636
0.635
48.9%
48.2%
1.394
6
40.8%
23.0%
23.2%
13.0%
0.357
0.352
0.355
0.351
0.669
0.355
71.3%
70.4%
1.396
M= 1.5, B = 0.5, (V = 1.581)
1
58.9%
8.0%
26.8%
6.3%
1.067
0.436
1.176
0.487
1.303
0.152
95.5%
87.3%
0.578
2
59.3%
7.2%
26.4%
7.1%
1.067
0.424
1.239
0.501
1.240
0.001
95.5%
84.8%
0.562
3
57.8%
9.1%
24.0%
9.1%
0.907
0.436
1.097
0.543
1.098
0.000
81.1%
87.3%
0.681
4
59.4%
7.2%
26.2%
7.2%
1.060
0.429
1.234
0.507
1.235
0.000
94.8%
85.7%
0.572
5
42.4%
11.1%
42.1%
4.3%
1.018
0.089
0.815
0.005
1.325
0.580
91.0%
17.7%
0.123
6
54.7%
9.2%
30.9%
5.2%
1.062
0.354
1.062
0.354
1.361
0.356
95.0%
70.9%
0.472
M = 0.5, B = 1.5, (V= 1.581)
1
74.7%
11.6%
3.5%
10.2%
0.778
1.093
1.105
1.696
1.173
0.079
69.6%
72.8%
1.986
2
75.1%
10.9%
3.1%
10.9%
0.778
1.081
1.141
1.758
1.142
0.000
69.6%
72.1%
1.965
3
75.1%
11.2%
2.5%
11.2%
0.758
1.093
1.128
1.851
1.125
0.004
67.8%
72.8%
2.039
4
75.2%
11.0%
2.8%
11.0%
0.774
1.089
1.140
1.797
1.139
0.001
69.2%
72.6%
1.990
5
15.6%
67.0%
15.6%
1.8%
0.487
0.939
0.869
0.002
1.265
1.994
43.6%
62.6%
2.726
6
54.6%
31.0%
9.1%
5.3%
0.350
1.063
0.352
1.067
1.353
1.057
31.3%
70.9%
4.291
M = 1.5, B = 1.5, (V = 2.121)
1
84.4%
5.5%
5.5%
4.6%
1.275
1.274
1.543
1.543
1.628
0.114
85.0%
85.0%
1.414
2
84.6%
5.0%
5.3%
5.1%
1.275
1.262
1.590
1.569
1.582
0.010
85.0%
84.1%
1.400
3
84.4%
5.5%
4.5%
5.6%
1.220
1.274
1.543
1.636
1.536
0.009
81.3%
85.0%
1.477
4
84.7%
5.1%
5.1%
5.2%
1.269
1.269
1.584
1.584
1.578
0.008
84.6%
84.6%
1.414
5
33.0%
33.1%
33.1%
0.8%
0.415
0.415
0.003
0.003
1.992
1.994
27.6%
27.6%
1.415
6
73.3%
12.3%
12.3%
2.1%
1.060
1.062
1.062
1.064
1.910
1.051
70.7%
70.8%
1.417
Columns two through five give the probabilities (in percent) of the four possible outcomes in a 2 × 2 AFC paradigm. For example, the fourth column [c = P(+D, −I)] is the probability of the identification being wrong and the detection being correct. The sixth through eleventh columns are z scores corresponding to combinations of the raw probabilities. The sixth column [probability of correct detection independent of identification, D(±I)] is the z score of the quantity a + c. The eighth column [probability of correct detection contingent on the identification being correct, D(+I)] is the z score of the quantity a/(a + b) that considers only events with correct identification. The twelfth and thirteenth columns compare the observed detection (sixth column) and identification (seventh column) with what would be expected in a single- judgment two-alternative forced-choice paradigm. The last column is the I/D ratio given by the ratio of the seventh and sixth columns times
.
Table 6
Olzak’s Data on Double-Judgment Ratings for 3- and 12-c/deg Gratings
Add to BibSonomy