Electronic Supplementary Material For s1
Experimental Brain Research
Electronic Supplementary Material for:
Information processing bottlenecks in macaque posterior parietal cortex: an attentional blink?
Ryan T. Maloney1,4, Jaikishan Jayakumar1, Ekaterina V. Levichkina1,3, Ivan N Pigarev1,3 & Trichur R Vidyasagar1,2.
1Department of Optometry & Vision Sciences, University of Melbourne, Parkville, Australia.
2Dept of Anatomy & Neuroscience, University of Melbourne, Parkville, Australia.
3 Institute for Information Transmission Problems (Kharkevich Institute), Russian Academy of Sciences, Moscow, Russia.
4School of Psychology, The University of Sydney, Sydney, Australia.
Address correspondence to
Trichur R. Vidyasagar
Department of Optometry and Vision Sciences,
The University of Melbourne,
Melbourne, Victoria 3010
Australia
Email:
Tel:+61-3-83447004
Fax:+61-3-90359905
Analysis of single-monkey behavior: linear contrast tests
This method allows tests of specific polynomial trends when the values of the independent variable are sampled from a continuous scale (in this case, time). For the tests used here, orthogonal contrast coefficients for the linear and quadratic trend components of the delay factor were constructed. The specific set of contrasts for each test is given below. For each experimental variable, tests of significance for each set of contrasts were determined with the chi-square statistic (here given in the case of d’):
, (S1)
where wi are the contrast weights for the particular hypothesis (Smith, 2000), and
, (S2)
is the variance estimate for the ith d’ value calculated using the asymptotic formula of Gourevitch and Galanter (1967). In this expression, P(·|·) are the conditional probabilities of hits (S|s), misses (N|s), correct rejections (N|n) and false alarms (S|n) at the particular delay/condition; z(·|·) are the corresponding standard normal deviates (z-scores),is the standard normal density evaluated at those z-scores, and ns and nn are the numbers of signal (matched) and noise (non-matched) trials, respectively. For each test of the delay factor, the chi-squared statistics for the linear and quadratic components were summed to provide omnibus tests of the effect of delay across conditions, and the resulting statistic was evaluated against a critical chi-squared value with two degrees of freedom (Smith, 2000). Because there were no a priori hypotheses concerning the specific form of the effect of varying delay, only the results of the omnibus tests are reported here.
In the case of P(C) for each stimulus condition, the variance estimate in the denominator of Equation S1 was replaced by the binomial variance for each proportion across delays:
(S3)
(Gould et al., 2007), where n is the number of trials in each condition.
Weights used in linear contrast tests
The method of planned linear contrasts (Smith, 2000) allows within-subject tests of the main effects and interactions in a factorial design to be conducted for single subjects in a way analogous to the tests performed in the analysis of variance across multiple subjects. Orthogonal contrasts for the linear and quadratic trend components for the effect of T1-T2 delay are given here. Higher-order polynomial trend components were not tested.
Analyses of proportions correct: P(C)
Let Pc be the vector of P(C) values calculated for a given monkey at each delay and in each stimulus condition:
Pc = {P(C)Match,50, P(C) Match,150, P(C) Match,300, P(C) Match,450, P(C) Match,600,…
P(C)NmO,50, P(C) NmO,150, P(C) NmO,300, P(C) NmO,450, P(C) NmO,600,…
P(C)NmL,50, P(C) NmL,150, P(C) NmL,300, P(C) NmL,450, P(C) NmL,600,…
P(C)DblNm,50, P(C) DblNm,150, P(C) DblNm,300, P(C) DblNm,450, P(C) DblNm,600},
where the first subscript gives the stimulus condition: matched orientation and location (Match), non-matched orientation (NmO), non-matched location (NmL), or the double non-match condition (DblNm), and the second subscript gives the T1-T2 delay (50, 150, 300, 450, 600 ms). These tests cover the main effect of delay within each stimulus condition. The tests are analogous to separate one-way ANOVAs.
Define the contrast coefficients for tests of the linear and quadratic trend components of the main effect of delay, for each stimulus condition:
wDelay(lin),Match = {-2.6, -1.6, -0.1, 1.4, 2.9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
wDelay(quad),Match = {3.54, -0.94, -3.9, -2.37, 3.67, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
wDelay(lin),NmO = {0, 0, 0, 0, 0, -2.6, -1.6, -0.1, 1.4, 2.9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
wDelay(quad),NmO = {0, 0, 0, 0, 0, 3.54, -0.94, -3.9, -2.37, 3.67, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
wDelay(lin),NmL = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2.6, -1.6, -0.1, 1.4, 2.9, 0, 0, 0, 0, 0},
wDelay(quad),NmL = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3.54, -0.94, -3.9, -2.37, 3.67, 0, 0, 0, 0, 0},
wDelay(lin),DblNm = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2.6, -1.6, -0.1, 1.4, 2.9},
wDelay(quad),DblNm = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3.54, -0.94, -3.9, -2.37, 3.67}.
These weight vectors define tests of the linear trend in the matched orientation and location (Match) condition, the quadratic trend in the matched orientation and location condition, the linear trend in the non-matched orientation (NmO) condition, the quadratic trend in the non-matched orientation condition, the linear trend in the non-matched location (MmL) condition, the quadratic trend in the non-matched location condition, the linear trend in the double non-match (DblNm) condition, and the quadratic trend in the double non-match condition, respectively. The results of these tests are given in Table S1.
Analyses of sensitivity: d’
Contrast tests were also conducted on the d’ measures for both monkeys. These involved tests of the main effect of delay.
Let d be the vector of d’ values at each delay:
d = {d’50, d’150, d’300, d’450, d’600},
where the subscript denotes the T1-T2 delay (50, 150, 300, 450, 600 ms).
Define the vectors of contrast weights for the main effect of delay:
wdDelay(lin) = {-2.6, -1.6, -0.1, 1.4, 2.9},
wdDelay(quad) = {3.54, -0.94, -3.9, -2.37, 3.67},
where the weight vectors define tests of the linear main effect of delay and the quadratic main effect of delay, respectively.
Table S1
Results of significance tests for effects of delay for each condition, P(C)
MonkeyContrast test / 1 / 2
χ2Delay, Match(2) / 140.97* / 64.49*
χ2Delay, Non-match Orientation(2) / 191.75* / 1.75
χ2Delay, Non-match Location(2) / 42.98* / 40.66*
χ2Delay, Double non-match (2) / 49.53* / 21.83*
Each χ2 (d.f. in parentheses) statistic represents a test for the main effect of delay in each stimulus condition. See online methods for details of the method of linear contrasts used, and the supplementary material for the contrast weights used in each test. *P < 0.001.
Supplementary References
Gould IC, Wolfgang BJ, Smith PL (2007) Spatial uncertainty explains exogenous and endogenous attentional cuing effects in visual signal detection. J Vis 7:1-17
Gourevitch V, Galanter E (1967) A significance test for one parameter isosensitivity functions. Psychometrika 32:25-33
Smith PL. 2000. Attention and luminance detection: effects of cues, masks, and pedestals. J. Exp. Psychol. Hum. Percept. Perform. 26: 1401-1420.