Julia Trommershäuser, Laurence T. Maloney, and Michael S. Landy, "Statistical decision theory and the selection of rapid, goal-directed movements," J. Opt. Soc. Am. A 20, 1419-1433 (2003)
We present two experiments that test the range of applicability of a movement planning model (MEGaMove) based on statistical decision theory. Subjects attempted to earn money by rapidly touching a green target region on a computer screen while avoiding nearby red penalty regions. In two experiments we varied the magnitudes of penalties, the degree of overlap of target and penalty regions, and the number of penalty regions. Overall, subjects acted so as to maximize gain in a wide variety of stimulus configurations, in good agreement with predictions of the model.
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Data reported for the five subjects individually; spatial motor variability
reaction and movement times (± one standard deviation), and constant response bias in the x
direction
(± one standard error of the mean) computed by averaging across all conditions (∼720 data points per subject); the score indicates the cumulative sum of wins across all trials.
Table 2
Experiment 1, Comparison of Results with Model Predictionsa
Subject
Performance (%)
Slope
p
Slope
p
S1
1.38 ± 0.08*
<0.0001
0.97 ± 0.05
0.5824
98.60
S2
1.03 ± 0.11
0.7740
0.86 ± 0.05
0.0067
104.92
S3
0.73 ± 0.08*
<0.0001
0.68 ± 0.05*
<0.0001
97.57
S4
0.76 ± 0.08*
0.0003
0.74 ± 0.04*
<0.0001
107.67
S5
0.86 ± 0.09
0.1298
1.00 ± 0.05
0.8886
98.91
Model predictions were computed for each of the five subjects individually by using estimates of individual subjects’ motor variability
as given in Table 1
. See text for details.
Data reported for the five subjects individually; motor variability
response bias in the x
and y
directions
± one standard error of the mean), computed by averaging across all conditions (∼384 data points per subject); the score indicates the cumulative sum of wins across all trials. Performance is computed by dividing the score by the score of an optimal performer with the same motor variability.
Table 4
Experiment 2, Comparison of Results with Model Predictionsa
Subject
(%)
Slope
p
Slope (r
)
p
Performance (%)
S1
75.31
0.94 ± 0.02
0.0076
1.10 ± 0.02*
<0.0001
77.0*
S2
67.53
0.98 ± 0.02
0.3608
1.06 ± 0.03
0.0542
91.0*
S3
68.09
0.99 ± 0.02
0.6105
0.87 ± 0.03*
<0.0001
90.3*
S4
65.39
1.03 ± 0.02
0.1995
1.30 ± 0.03*
<0.0001
79.5*
S5
73.31
0.96 ± 0.02
0.0723
1.15 ± 0.03*
<0.0001
95.1
Model predictions were computed for each of the five subjects individually by using estimates of individual subjects’ motor variability
as given in Table 3
.
Data reported for the five subjects individually; spatial motor variability
reaction and movement times (± one standard deviation), and constant response bias in the x
direction
(± one standard error of the mean) computed by averaging across all conditions (∼720 data points per subject); the score indicates the cumulative sum of wins across all trials.
Table 2
Experiment 1, Comparison of Results with Model Predictionsa
Subject
Performance (%)
Slope
p
Slope
p
S1
1.38 ± 0.08*
<0.0001
0.97 ± 0.05
0.5824
98.60
S2
1.03 ± 0.11
0.7740
0.86 ± 0.05
0.0067
104.92
S3
0.73 ± 0.08*
<0.0001
0.68 ± 0.05*
<0.0001
97.57
S4
0.76 ± 0.08*
0.0003
0.74 ± 0.04*
<0.0001
107.67
S5
0.86 ± 0.09
0.1298
1.00 ± 0.05
0.8886
98.91
Model predictions were computed for each of the five subjects individually by using estimates of individual subjects’ motor variability
as given in Table 1
. See text for details.
Data reported for the five subjects individually; motor variability
response bias in the x
and y
directions
± one standard error of the mean), computed by averaging across all conditions (∼384 data points per subject); the score indicates the cumulative sum of wins across all trials. Performance is computed by dividing the score by the score of an optimal performer with the same motor variability.
Table 4
Experiment 2, Comparison of Results with Model Predictionsa
Subject
(%)
Slope
p
Slope (r
)
p
Performance (%)
S1
75.31
0.94 ± 0.02
0.0076
1.10 ± 0.02*
<0.0001
77.0*
S2
67.53
0.98 ± 0.02
0.3608
1.06 ± 0.03
0.0542
91.0*
S3
68.09
0.99 ± 0.02
0.6105
0.87 ± 0.03*
<0.0001
90.3*
S4
65.39
1.03 ± 0.02
0.1995
1.30 ± 0.03*
<0.0001
79.5*
S5
73.31
0.96 ± 0.02
0.0723
1.15 ± 0.03*
<0.0001
95.1
Model predictions were computed for each of the five subjects individually by using estimates of individual subjects’ motor variability
as given in Table 3
.