This paper’s reference:
Howes, D.H. & Solomon, R.L. (1951). Visual duration threshold as a function
of word-probability. Journal of Experimental Psychology, 41, 401-410.
Visual Duration Threshold as
a Function of Word-Probability
Davis H. Howes and Richard
L. Solomon
Harvard University
Conventional
threshold experiments provide a sample of language behavior under highly
controlled conditions. However exclusively E may be interested in S’s vision or
hearing, his observations typically are in units of communicative behavior. Of
particular interest is the threshold experiment in which a word is exposed
tachistoscopically for very brief durations which are gradually lengthened on
successive exposures until the word is correctly reported. In such an
experiment, the observations are in fundamental units (time) and can be
expressed as functions of any measurable properties of behavioral units such as
words. Any general property of words, then, should be operative in the word‑threshold
experiment, and the dependent variable (duration threshold) some function of
it.
This
paper explores experimentally the function relating duration threshold to the
relative frequency with which a word appears in the English language.
Word-probability is an inference from relative frequency of occurrence; the
only operation necessary to estimate the probability of occurrence of a
specific word under any given conditions is to count the frequency of
occurrence of such a word relative to the total number of words occurring in a
specific sample of language recorded under those conditions. In the present
experiment, word-probability will be defined by relative frequency of
occurrence of a given word in certain standard word counts for the English
language.
Any
function which relates visual duration thresholds to word‑probability
tends to emphasize the importance of operational analysis in perceptual
experiments. Those perceptual studies measuring the optical conditions under
which specific linguistic responses occur are clearly based on linguistic at
well as optical operations. As the following experiments will show, the
probability of a word has an enormous effect on its visual duration threshold;
yet the conventional concepts of perception offer no clear interpretation of
such a variable. In this paper we shall confine ourselves to a description of
experimental data. Their theoretical implications will be discussed in later
papers.
Our
experimental problem may be phrased as follows: What is the relationship
between word‑probability and speed of recognition? More specifically,
What is the relationship between the relative frequency of occurrence of
specific words in the English language and the visual duration threshold
necessary ‘for correct report of those words when they are tachistoscopically
exposed?
Method
Word‑frequency. Word‑frequency counts
are made by selecting a sample of language behavior (usually written) that
contains a given number of words, and then tabulating the number of times that
each particular word occurs. The results of several tabulations on large samples of written language are incorporated
in the Thorndike-Lorge Teacher’s Word Book of 30,000 Words. To minimize
the effect of any peculiarities of any individual word counts, the relative
frequency of words in the following experiments was estimated in three cases:
(1) by the Lorge Magazine Count, (2) by the Lorge-Thorndike Semantic Count, and
(3) by the geometric mean of the frequencies in both counts.
The
Magazine Count (4) is based on approximately 4.5 million words taken from
issues of popular magazines that appeared between 1927 and 1938. The Semantic
Count (1) is based on the Encyclopedia Britannica, Bartlett’s Familiar
Quotations, the Literary Digest, and books of fiction and
nonfiction.’ Word-frequencies based on the various counts will hereafter be
designated as follows: Magazine Count, ‘fmg; Semantic Count, fsm; average of
the two counts, fav.
Visual
duration threshold. The 20 Ss in our experiments were given the following instructions:
This
is an experiment to see how keen your vision is when a word is briefly flashed
before your eyes. You will be given words to identify. A number of increasingly
long flashes will be presented for each word. I will notify you before I change
the word that is being flashed.
The
first flashes will be very brief, and you probably will be unable to recognize
the word. I will then gradually increase the duration of the flash for the
successive trials of that word. After each flash, please state clearly and
distinctly whatever you think you saw. There is no objection to guessing; but,
if you have no idea what it is, say so.
Before
I present each flash, I will say, ‘Ready.’ You will then look into the
eye-piece and focus on the area between the two orange lines. After the ready
signal, do not say anything until you have made your response to the flash.
After you have made your response, sit back and relax until I give the ready
signal for the next presentation. We will have a recess after every few words,
or whenever you say you are tired.
The
first few words will be for practice, so that you will become familiar with
this procedure.
Do
you have any question?
It
is important to notice that S was not instructed to respond as quickly as
possible to the exposure, but to respond whenever he felt ready to respond. The
time that E measured and controlled was the duration of the exposure, not the
latency of the S’s response.
The
words were exposed in a modified Dodge tachistoscope designed and built by Mr.
Ralph Gerbrands. The duration of each exposure was controlled to the nearest 10
msec. The range of exposure durations was from 10 to 1,000 msec. The
illumination for exposed words was obtained by two preheated fluorescent lamps
which could be turned on and off almost instantaneously. The pre-exposure
fixation pattern consisted of two horizontal parallel lines of light furnished
by neon glow lamps. The pre-exposure illumination was terminated when the word‑exposure
illumination went on. The S, therefore, saw the fixation lines disappear at the
onset of the exposure, and a pattern of letters appeared in place of the lines.
The flash illumination at the eyepiece was about .07 ft.-candles (Macbeth
illuminometer reading), which was sufficiently low that no S responded
correctly to a word which was exposed for less than 30 msec.
The
list of experimental words was typed on an adding-machine roll, which was
attached to some rollers at the back of the tachistoscope, and each of the
words could be centered, one by one, in the exposure slot in a standard order.
The letters were capitals of block type, 1/8 in. high, and were exposed
approximately 23 in. from S’s eyes.
Practice
has an enormous effect on this species of tachistoscopy. Four familiar words,
all referring to the academic environment (HARVARD, UNIVERSITY, TEACHER, and
PROFESSOR served as preliminary words to absorb the most striking practice
effects, but only a much longer prefatory list could have stabilized the
thresholds. To distribute the remaining effects of practice, the standard order
in which the words were arranged was counterbalanced for order and staggered
for initial position in the list. For example, in a 60‑word list used in
Experiment 1, the word order for successive Ss followed these patterns (numbers
represent words and their standard order): 1, 2, 3 . . . 59, 60; 60, 59, 58 . .
. 2, 1; 5, 6, 7 , . . 3, 4; 56, 55, 54 . . . 58, 57; 9, 10, 11 . . . 7, 8; 52,
51, 50 . . . 54, 53; etc. About 20 or 30 thresholds could be measured in an
hour. Despite recesses and short rest periods, the last portion of long
sessions found the Ss fatigued, but as thresholds showed a regular decline with
practice down to the last word, it would seem that whatever effect fatigue had
on thresholds was masked by the large practice effect.
A
rhythm was forced by the time required for E to record the response to the
previous exposure, to set the duration of the next, and to give the ready
signal. During this period between flashes (lasting from 15 to 45 sec.) S
looked around in an experimental room kept at its normal illumination (5
ft.-candles). In this way, S was light‑adapted to a fairly constant level
after each exposure. A brief period (0.5 to 1.0 sec.) between the moment S’s
eyes were sealed against the eyepiece of the tachistoscope and the instant of
the flash did permit some dark adaptation to occur, but its degree was
unrelated to any properties of the stimulus words used in our experiments.
Permitting S to look wherever he wished between exposures also improved his
temper during the long session.
Correct
responses began to occur with exposures ranging from 30 to 1,000 msec.,
depending on the individual S and on the word being exposed. No rigid schedule
of progression from short to long exposures could cope with such an extensive
range. For each S the exposure time for the first flash was chosen so that it
was at least 40 msec. below the very minimum duration at which correct
responses could be expected for the particular S, word, and stage of practice.
Below 200 msec. the step interval used was 10 or 20 msec.; from 200 to 450
msec. the interval was 20 or 30 msec.; and above 450 msec. the step interval
was 50 msec. Two exposures were usually given at each flash duration, before
the exposure time was lengthened. The number of exposures preceding the
threshold criterion ranged from zero to 48. If this variable had any practice
effect on thresholds (and none were observed), it would have been to obscure
differences between high- and low-threshold words, rather than to exaggerate
them; for the former were, on the average, preceded by many more exposures.
Following
the ascending method of limits, the flash duration was systematically
lengthened until the exposed word was accurately reported. Three successive correct
responses was taken for the criterion for a duration threshold. Quantitatively,
threshold was defined as the duration halfway between the duration of the
longest exposure to which an incorrect response was made and the duration of
the three criterion exposures.
A
few Ss’ thresholds were quite high, compared to the remainder of the group,
making the distribution of duration thresholds markedly skewed for each word,
To indicate the central tendencies of the thresholds, therefore, both means and
medians were used. A third average threshold measure was derived by taking the
mean of the 10 lowest thresholds for each word. Means for these abridged
distributions were almost identical with the medians. The time of exposure at
which the threshold criterion was reached will, hereafter, be referred to as t;
and tM, tMd, and tL will, hereafter, stand for
the three indices of central tendency for thresholds.
Experiment
1
Table
1 presents alphabetically 60 words used in Experiment 1. Another study (Solomon
& Howes, 1951) required that the list include 30 relatively common
words--five representing each of six different value or interest
categories--and 30 words of relative rarity, similar to, and preferably
synonyms of, the common ones. Synonyms and words of the same value category
were separated in the standard order of word presentation to minimize their
interactions. The frequencies of these words in the three word counts were
converted into logarithms to facilitate their manipulation, since the range of
frequencies was from zero to 3,000.
Results
Product‑moment
correlation coefficients relating the three measures of central tendency of
threshold to the logarithms of the three measures of word‑frequency are
shown in Table 2. The coefficients range from ‑ .68 to ‑ .75;
covariance of log word. frequency with duration threshold accounts for an
average of 50.9 per cent of the total variance. …[Any differences among
correlation coefficient are not statistically significant]…
Scatter-plots
of the correlations (Fig. 1) justify the calculation of linear (product‑moment)
correlations between the frequency variable and the threshold variable. The
data of Experiment 1 demonstrate a strong inverse relationship between relative
word‑frequency and duration threshold. Words of high frequency of
occurrence require shorter exposure durations for correct report than do words
of low relative frequency of occurrence.
Experiment 2
Several
uncontrolled factors were forced upon the previous experiment by the selection
of words for a planned subsequent experiment. The words varied from 6 to 12
letters in length. Plurals and ing forms, it has already been observed, cannot
be distinguished from their roots in the published Thorndike‑Lorge
tables, and the frequencies for such words in Experiment 1 are probably
inaccurate. For a few words, the frequencies based on the two counts are so
disparate that even their ranks in the hierarchy of relative frequencies may be
called into question. Strong associations, moreover, interrelate many of the
words. For a pair of synonyms (or for words classified in the same value
category), one following closely upon the other in the tachistoscopic list, the
repetition of the first word during the measurement of its threshold might be
expected to raise the probability (add lower the threshold) of the second. For
example, the probability of lawyer might be raised by the repetition of’
barrister, during measurement of the threshold of the latter a few seconds
before. Scattering related pairs throughout the list was designed to minimize
these effects; but how successfully this was accomplished cannot be determined
from the evidence of Experiment 1 alone.
Experiment
2 was designed to control these factors. The range of word‑frequencies in
the Semantic and Magazine Counts was divided into 15 intervals, with central
frequencies at roughly equal logarithmic distances. For each interval, a page
number was selected from a table of random numbers, and the first seven‑letter
word on that page whose frequency lay within that interval, both in the
Magazine and Semantic Counts, was chosen. Contextual words (prepositions,
conjunctions, auxiliary verbs, pronouns, articles, etc.) were omitted, for
there is some indication that their probabilities, outside. connected
discourse, do not behave like those of other words. In this way, the following
list (arranged in order of decreasing frequency) was constructed: country,
promise, example, balance, deserve, venture, welfare, testify, dwindle, surmise
vulture, irksome, titular, figment, and machete.
In
random order, these 15 words were presented for threshold determination to the
20 Ss, exactly as were the 60 words of the main list of Experiment 1. Each S
was given the words of Experiment 2 at a session separated by two weeks or more
from Experiment 1. Half of the Ss were first given the 15‑word list, and
half received the 60‑word list of Experiment 1 first. Despite the
identical procedures, the comparative brevity of the 15‑word list swelled
the relative effect of practice on duration thresholds. Only. two preliminary
words (HARVARD and TEACHER) preceded the shorter list of Experiment 2, instead
of the four words used for Experiment 1.
Thresholds
were computed as in Experiment 1. Means and medians for the complete data were
supplemented by the means of the 10 lowest thresholds for each word.
Results
The
product‑moment correlations obtained in Experiment 2 appear in Table 3.
That the various uncontrolled variables in Experiment 1 introduced no important
error is suggested by the fact that the correlations for that experiment are,
on the whole, higher than those for Experiment 2. The differences are too small
to be of statistical significance. The average covariance of visual duration
threshold with log word frequency is only 44.5 percent for Experiment 2,
compared with 50.9 per cent for Experiment 1.
[A
detailed analysis of practice effects is deleted here.]
On
the basis of practice effects alone, therefore, the differences between
Experiments 1 and 2 can be predicted. Consequently, we can assume that the
various factors uncontrolled in Experiment 1 but controlled in Experiment 2
(length of word, associated interaction between synonym pairs, etc.) have only
negligible effects upon the function relating duration threshold to word‑frequency.
Moreover, the fact that the differences between two experiments can be resolved
with good accuracy lends credence to the generality of the relationship between
duration threshold and log word‑frequency. At present, the most likely
form of this relationship appears to be given by the equation:
t = – k log f,
where
[t is the duration threshold, f is the normative frequency of the word,
and k is the slope constant;]
…the slope constant k depends upon what measure of central tendency
happens to be used to represent the distribution of thresholds.
[Some
very detailed analyses deleted here.]
Summary
1. Data from two experiments, using 75 words, show that the visual
duration threshold of a word, measured tachistoscopically by an ascending
method of limits, is an approximately linear function of the logarithm of the
relative frequency with which that word occurs in the Thorndike‑Lorge
word counts.
2. Product‑moment correlations between the two variables range
from ‑ .68 to ‑ .75 in the main experiment. Empirical corrections
for certain physical characteristics of the words and of their component
letters were found to raise the range of those correlations to ‑ .76 to ‑
.83.
3. Viewed as a correlation between language behavior in a highly
specific situation (duration threshold determination) and in general usage
(Thorndike‑Lorge counts), these data are of significance for the
experimental analysis of language behavior. In addition, they point to the
necessity for operational interpretation of a large number of perceptual
experiments, since the size of threshold is found to be a function of a
property (relative frequency) of the responses (words) that operationally
define perceptual threshold.
(Manuscript
received April 26, 1950.)
References