Abstracts
of the Psychonomic Society 44th Annual Meeting, Vol. 8, p. 67, 2003.
Letter Identification:
Contrast Polarity and Speed-Accuracy Trade-Off Strategies
Albert
J. Ahumada, NASA Ames Research Center, Moffett Field, CA
Lauren F. V. Scharff, Stephen F. Austin State
University, Nacogdoches, TX
Summary
Observers
were asked to identify which of 12 letters was presented on a uniform
background. The letters varied in
contrast polarity (positive vs. negative) and in contrast relative to the
background (10%, 20%, or 40%). To allow
observers to maintain a consistent perceptual strategy for each polarity, each
observer ran the polarity conditions blocked, first 5 replications of all three
contrast levels at one polarity, then the other.
Both
latency and percent correct scores in general showed better performance for
negative polarity. However, strong
differences in the speed-accuracy trade-off strategies appeared across polarity
for the two groups of observers. The
observers who had the more difficult positive polarity first, took more time
(had longer latencies), but the observers who had the more difficult polarity
second, took less time. Combined
speed-accuracy scores helped to measure the increased identifiability of the
negative contrast letters over that of the positive contrast letters in the
presence of the changing strategies.
Introduction
Our
previous experiments on text readability and letter identification (Scharff
and Ahumada, 2002; 2003a) measured performance for positive and negative contrast
text on a uniform background. Both studies found better performance for negative contrast stimuli
than positive contrast stimuli. We decided to repeat the letter identification
study (Scharff and Ahumada, 2003b) with more careful control of the contrast so
that we could include an accurate contrast polarity factor in our quantitative
index of text readability.
Methods
Observers were asked to identify the Scharff &
Ahumada (2003a) twelve lower case letters (acegilnqrstu) on a uniform
background. A letter remained onscreen until the participant typed a response.
Within each block of 36 trials, each letter was presented at 3 contrast levels:
10%, 20%, and 40%. Six observers ran the 5 negative contrast blocks first;
seven observers ran the 5 positive contrast blocks first.
Results
As Fig. 1 shows, both performance measures,
latency and accuracy, were better for the negative contrast conditions at 20%
and 40% contrast, but were not different at 10% contrast, even though the
accuracy performance was better than chance.
Fig.
1: Left: Letter identification accuracy
vs. contrast. Right: Letter identification latency vs. contrast. Error bars are
95% confidence intervals based on observer x treatment interaction, except for
the lower bars on the 0.1 contrast points in the left figure that are based on
the pooled observer variances for those points to allow comparison with chance.
The speed accuracy trade-off graph (Fig. 2)
shows that while combined speed-accuracy performance was better in the second set
of 5 blocks (circles), the observers did not improve in accuracy; they
shortened their latencies instead. In the first blocks (squares), the observers
given the more difficult positive contrast task (light squares) took more time
to be more accurate, but when this positive contrast task was second (light
circles), observers gave it even less time than was given by the other
observers doing the easier negative contrast task second (dark circles).
Fig. 2: Letter
identification accuracy vs. latency (speed-accuracy trade-off). Square symbols
indicate conditions run in first group of 5 blocks. Circles indicate second group of 5 blocks. Colors indicate the contrast in percent. Error bars are 95% confidence intervals
based on the observer x treatment interaction. Red lines show constant
performance curves for our speed-accuracy trade-off model.
Speed-Accuracy Trade-Off
Assumptions
1) The detectability d’ of the stimuli
increases as the square root of the observation time,
d’
= B T 0.5 ,
where T = the observation time
(observer’s latency). B, the ‘rate’ of information accumulation, is
fixed for a given stimulus condition.
2) The differences among the 12 signals are
orthogonal and equally detectable so that the probability of a correct response
PC can be computed from
d’ by the approximation
PC
= F( 0.87 d’ – 1.38 ),
where F( ) is the cumulative standard
normal distribution function, and the approximating constants are from Elliott
(1964).
The red lines
in Fig. 2 are the speed-accuracy trade-off lines for B = 0.5, 1, 1.5, 2.
Fig. 3 shows the average B estimates as a
function of contrast and polarity.
Fig. 3: Average combined speed-accuracy scores B as a function of contrast and polarity for comparison with Fig. 1. Error bars are 95% confidence intervals based on pooled group variance at each contrast. The polarity effect at the high contrast is now larger in effective contrast.
Conclusions
Scores
combining speed and accuracy show a different interaction of the polarity
effect with contrast than latency or accuracy alone and generate larger ANOVA
F’s for the polarity effect.
As signal detection theory asks for experiments
to have false alarms and uses them to estimate detectability, speed-accuracy
trade-off theory asks for non-zero error rates and provides measures of
detectability that combine speed and accuracy.
Acknowledgements
The Airspace Operations Systems (AOS) Project of NASA's Airspace Systems Program provided funding. NASA Ames Research Center cooperative agreement NCC 2-1095 with the San Jose State University Foundation provided support. We are grateful for the assistance of Ryan Smith, Robin Rustad, and Lori Shird. John Palmer provided the idea for the speed-accuracy trade-off model.
References
P. B. Elliott (1964) Tables of d’, in J. A.
Swets, ed., Signal Detection and Recognition by Human Observers, p.
651-684.
L.
F.V. Scharff, A. J. Ahumada, Jr. (2002) Predicting the Readability of
Transparent Text, Journal of Vision 2(9), 653-666.
L.
F.V. Scharff, A. J. Ahumada (2003) Contrast measures for predicting text
readability, B. E. Rogowitz and T. N. Pappas, eds., Human Vision and
Electronic Imaging VIII, SPIE Proc. 5007, p. 463-472.
L.
F.V. Scharff, A. J. Ahumada, Jr. (2003) Letter identification latencies are
predicted by an asymmetric contrast metric, Vision Sciences Society Abstracts,
abstract TU752, p. 223.
Contact Information
A.
J. Ahumada, Jr.:
http://vision.arc.nasa.gov/personnel/al/ahumada.html
L.
F.V. Scharff:
http://hubel.sfasu.edu/scharff.html
Appendix
Matlab routines for computing the speed-accuracy
trade-off curves and the measure B.
function Pc = sat(T, B, T0,
n, an, bn, Pe)
%
speed[latency](T)-accuracy(Pc) trade off curve
% B = d' for 1 time unit
% T0 = part of response
time that information is not being accumulated
% n = number of response
alternatives
% an, bn = constants to
approximate Pc(dprime,n)
% Pe = "finger
error" probability
dprime = B*sqrt(T-T0) ;
Pc = (1/n)*Pe +
(1-Pe)*Fnorm(an*dprime - bn) ;
% The routine sat may be
used to plot points (T, Pc(T))
% for a constant
information ‘rate’, B.
% We assume that the
detectability dprime increases proportionately to
% the square root of the
time spent accumulating information TI
% dprime = B/sqrt(TI)
% We assume the latency is
a constant plus the accumulation time
% T = T0 + TI
% We assume that dprime can
be converted to a probability correct
% according to the number
of response alternatives.
% Pc' = f(dprime, n)
% This function can be
approximated by
% Pc' = Fnorm(an*dprime -
bn),
% where a12 = 0.87 (Elliott
(1964) p. 681) and
% Fnorm(-bn)=1/n. So b12 = -znorm(1/12) = 1.3830
% We allow for a finger
error rate so that the observed rate of correct
% responses is
% Pc = (1/n)*Pe +
(1-Pe)*Pc'
% Test: T = 2; B = 1; T0 =
1; n = 12; an = 0.87; bn = 1.383; Pe=0.05
% Pc = 0.2929 ;
Fnorm(1/sqrt(2)) = 0.76
function B = satB(Pc, T,
T0, n, an, bn, Pe)
%
speed[latency](T)-accuracy(Pc) trade off measure
% B = dprime for 1 time
unit
% T0 = time that
information is not being accumulated
% n = response alternatives
% an, bn = constants to
approximate Pc(dprime,n)
% Pe = finger error rate
Pcu = (Pc - Pe/n)/(1-Pe);
B = ((bn +
znorm(Pcu))/an)./sqrt(T-T0) ;
% from sat.m
% dprime = B*sqrt(T-T0) ;
% Pc = (1/n)*Pe +
(1-Pe)*Fnorm(an*dprime - bn) ;
% Test:
% Pc = 0.2929 ; T = 2; T0 = 1; n = 12; an = 0.87; bn = 1.383;
Pe=0.05
% B = 0.9998
function val = Fnorm(z)
val =
0.5*(1+erf(z/1.41421356237310));
function val = znorm(p)
val =
1.41421356237310*erfinv(p+p-1);