Download The Performance/Intensity Function - Rohan Accounts

The Performance/Intensity Function: An Underused
Resource
Arthur Boothroyd
The purpose of this tutorial is to demonstrate the
potential value of the Performance versus Intensity
(PI) function in both research and clinical settings.
The PI function describes recognition probability
as a function of average speech amplitude. In effect,
it shows the cumulative distribution of useful
speech information across the amplitude domain,
as speech rises from inaudibility to full audibility.
The basic PI function can be modeled by a cubed
exponential function with three free parameters
representing: (a) threshold of initial audibility, (b)
amplitude range from initial to full audibility, and
(c) recognition probability at full audibility. Phoneme scoring of responses to consonant-vowel-consonant words makes it possible to obtain complete
PI functions in a reasonably short time with acceptable test–retest reliability. Two examples of research
applications are shown here: (a) the preclinical behavioral evaluation of compression amplification
schemes, and (b) assessment of the distribution of
reverberation effects in the amplitude domain.
Three examples of clinical application show data
from adults with different degrees and configurations of sensorineural hearing loss. In all three
cases, the PI function provides potentially useful
information over and above that which would be
obtained from measurement of Speech Reception
Threshold and Maximum word recognition in
Phonectically Balanced lists. Clinical application can
be simplified by appropriate software and by a routine to convert phoneme recognition scores into estimates of the more familiar whole-word recognition
scores. By making assumptions about context effects,
phoneme recognition scores can also be used to estimate word recognition in sentences. It is hard to
escape the conclusion that the PI function is an
easily available, potentially valuable, but largely
neglected resource for both hearing research and
clinical audiology.
1968a), the form of this function is determined
initially by the acoustic properties of the speech
signal. Speech amplitude varies from moment to
moment— over a range of 30 to 40 dB. As the speech
level is raised from below audibility, the highest
amplitude components are heard first and recognition probability begins to rise above zero. Further
level increases add audibility of lower amplitude
components. But it requires an increase of 30 or 40
dB above the threshold of initial audibility before all
of the acoustic signal is audible to the listener. Thus
the threshold of initial audibility is determined by
the highest amplitude components of the speech
signal, whereas the range from initial to full audibility is determined by the range over which sound
energy is distributed in the amplitude domain. This
process is illustrated in Figure 1, which shows the
transformation of an acoustic waveform: first to an
amplitude versus time plot; then to an amplitude
distribution; and finally to a cumulative amplitude
distribution.
What is remarkable about the cumulative amplitude distribution of speech is how well it can predict
the morphology of the normal PI function for phoneme recognition. The data from Figure 2, for example, are taken from a recent study by Haro (2007) in
which 12 normally hearing young adults listened to
the same consonant-vowel-consonant (CVC) words
used to develop the data in Figure 1. Recordings of
two female talkers were used. Ten words were
presented at each of seven levels (dBleq) in a steadystate noise of 55 dB SPL. The spectrum of the noise
was matched to that of the relevant talker. Differences in the forms of the two PI functions (or
PSNR functions) follow closely the differences
between the cumulative amplitude distributions
of the two recordings.*
Recognition probability, however, depends not
just on the audibility of sound, but also on the
amount of useful information it contains. The PI
(Ear & Hearing 2008;29;479– 491)
INTRODUCTION
The Performance versus Intensity (PI) function is
the relationship between speech recognition probability and average speech amplitude. Although influenced by noise spectra (Studebaker, et al., 1994)
and pure-tone threshold configuration (Boothroyd,
*The difference between these two cumulative amplitude distributions may reflect differences in the productions of the two
talkers. It may also, however, reflect differences in recording
technique. For talker 1, the microphone was placed at 0 degrees
in both the horizontal and vertical planes. For talker 2, a clip-on
microphone was used and this was at 90 degrees in the vertical
plane—probably leading to attenuation of some high-frequency
speech components.
City University of New York, New York, New York; San Diego
State University, San Diego, California; and House Ear Institute.
0196/0202/08/2904-0479/0 • Ear & Hearing • Copyright © 2008 by Lippincott Williams & Wilkins • Printed in the U.S.A.
479
480
BOOTHROYD / EAR & HEARING, VOL. 29, NO. 4, 479 –491
Fig. 1. The source of the normal PI function. The
top panel shows the waveform of a sample of
speech consisting of a string of monosyllabic
words without intervening silences (pressure as
a function of time). The second panel shows the
RMS amplitude of this sample, measured over a
moving 100 msec window (dB as a function of
time). The third panel shows the distribution of
instantaneous amplitudes, with high levels on
the left and low levels on the right (number of
samples at each dB level). The bottom panel
shows the cumulative amplitude distribution,
that is, the percentage of the total energy in the
speech signal that is available to a listener as the
speech level (in dB) increases from initial audibility to full audibility.
function may be seen, therefore, as a behavioral
measure of the cumulative distribution, across amplitude, of useful information in the speech signal.
Knowledge of this distribution has potential value in
both research and clinical applications.
MATHEMATICAL MODELING
The utility of the PI function can be enhanced by
fitting empirical data to a valid underlying mathematical model. The benefits include smoothing data
across several measurements, thereby improving
test–retest reliability, and the reduction of these
measurements to a smaller number of key parameters. Such a model is represented by the cubed
exponential function of Eq. (1), the full development
of which is given in Appendix A.
p ⫽ m/0.99 * (1 ⫺ e(⫺(x⫺t)/r 5.7))3
*
(1)
where p is the phoneme recognition probability at
amplitude x, m is the optimum score at full audibility, e is the base of natural logarithms (⬃2.72), x is
the speech amplitude in dB, t is the threshold amplitude in dB, and r is the amplitude range from initial to
full audibility in dB.
Several points should be noted about Eq.:
1. The quantity (x ⫺ t)/r is the articulation index
(AI), or speech intelligibility index (ANSI, 1969;
French & Steinberg, 1947; Kryter, 1962a,b).
2. The AI is assumed to rise linearly from 0 to 1
as the level of speech rises from initial to full
audibility. There is, therefore, an additional
proviso that (x ⫺ t)/r cannot be less than zero
or greater than one.†
3. The exponent of three at the end of the equation serves two purposes. First, it helps account for the effects of lexical context on phoneme recognition in CVC words (Boothroyd &
Nittrouer, 1988). Second, it helps account for
departures from the assumption that AI rises
†This condition can also be satisfied with the proviso that 0 ⱕ p ⱕ
m. In other words, p cannot be less than zero or greater than the
value obtained when x ⫽ t ⫹ r.
BOOTHROYD / EAR & HEARING, VOL. 29, NO. 4, 479 –491
100
80
60
Initial
audibility
at -21 dB
60
Range
34 dB
40
Full
audibility
at 13 dB
40
CumAmp for t1
CumAmp for t2
Talker 1
Talker 2
20
0
-20
Max
99 %
100
80
481
-15
-10
-5
0
5
10
15
20
20
Least-squares fit to equation 1
Data from Pegan (2007)
25
Fig. 2. Cumulative amplitude distribution as a predictor of the
normal PI function. Data points show group-mean phoneme
recognition scores (ⴞ1 SE), as a function of signal-to-noise
ratio, for 12 young normally hearing adults listening to
recordings of consonant-vowel-consonant word lists recorded by two talkers. These data are shown in relation to
cumulative RMS amplitude distributions (measured over 100
msec windows) derived from the two recordings. The longterm average level of the two recordings differed by less than
1 dB.
linearly with increasing audibility. Most importantly, however, it improves the fit between
predicted and measured scores.
4. The divisor of 0.99 at the beginning of the
equation reflects an assumption that full audibility occurs when p is within 99% of its asymptotic value, as defined by Eq. (1) (but without the
proviso that the AI cannot exceed 1).
5. The multiplier of 5.7 after (x ⫺ t)/r ensures
that the estimate of r represents the range
from initial to full audibility—the latter being
assumed to occur when p reaches 99% of its
asymptotic value.
Figure 3 shows the least-squares fit ‡ of Eq. (1) to
group-mean PI data obtained by Pegan (2007) in a
study of the distribution of reverberation effects
across the intensity range of speech. The data of
Figure 3 were obtained without reverberation.
Twenty-nine young, normally hearing adults listened dichotically, via insert earphones, to CVC
words recorded by a female talker. Each listener
heard one list of 10 words at each of seven speech
levels (dBleq), presented in spectrally matched
steady-state noise that had a constant level of 60 dB
SPL. The choice of word list was varied across
signal-to-noise ratio and across listener. The parameters for a least-squares fit to the data are m ⫽ 99%;
‡Curve-fitting routines are available within Table Curve and
Sigmaplot software from Systat Software, Inc. and within the
CASPA program of Boothroyd (2006).
0
-25
-20
-15
-10
-5
0
5
10
15
20
25
Fig. 3. Least-squares fit of Eq. (1) to group mean PI data for 29
listeners. Data are taken from Pegan (2007). Error bars show
ⴞ1 SE.
t ⫽ ⫺21 dB; and r ⫽ 34 dB. In other words, mean
phoneme recognition rises from zero to a maximum
of 99% as the signal-to-noise ratio rises from ⫺21
dB, over a range of 34 dB, to a value of ⫹13 dB. The
standard error of fit is 0.77 percentage points.
THE PI FUNCTION
AS A
RESEARCH TOOL
The PI function has potential value in the study of
intentional or unintentional changes in the distribution of useful speech information in the amplitude
domain. The following two examples are of amplitude compression in hearing aids and reverberation
in enclosed spaces.
Amplitude Compression
One of the goals of fast-acting amplitude compression is to reduce the amplitude range over which
useful speech information is distributed. Because
the PI function for speech in noise represents an
estimate of this range, it should provide a behavioral
validation of compression schemes. This possibility
was explored by Oruganti (2000) in a study of
amplitude compression. Lists of recorded CVC
words were presented to groups of eight normally
hearing listeners in a background of pink noise
having a constant octave-band level across frequency. The pink noise was used to simulate a
relatively “flat” hearing loss of around 40 dB HL.
Listeners heard the stimuli monaurally via supraaural earphones under four conditions:
1. Unprocessed.
2. High-frequency emphasis (HFE): Frequencies
above 1100 Hz were amplified by 8 dB so as to
compensate for high-frequency roll-off in the
speech spectrum.
482
BOOTHROYD / EAR & HEARING, VOL. 29, NO. 4, 479 –491
Unprocessed
HP
8dB
+
LP
Envelope (over 5 msec window)
High-frequency
emphasis (HFE)
only
Fine structure
10dB
30dB
Fig. 4. Amplitude compression scheme used
by Oruganti (2000).
compress
amplify
HFE plus
1-band
compression
3. HFE ⫹ single-band compression: The top 30
dB of the amplitude distribution was compressed into a 10 dB range. Attack and release
times were 2.5 msec (see Fig. 4).
4. HFE ⫹ two-band compression. The same compression was applied independently to frequencies below and above 1100 Hz.
Figure 5 shows the least-squares fits of Eq. (1) to
Oruganti’s group-mean phoneme recognition scores.
The slope of the PI function increased with HFE—
reflecting compensation for high-frequency roll-off
in the speech spectrum (Cox & Moore, 1988). The
addition of single-band compression increased the
slope further—as one would expect. Switching from
single-band to two-band compression, however, had
only a small additional effect on slope. The derived
100
80
60
40
Unprocessed
High-frequency emphasis (HFE)
HFE + 1-band compression
HFE + 2-band compression
20
0
0
5
10
15
20
25
30
35
40
Fig. 5. Phoneme recognition in pink noise by young hearing
adults as a function of speech amplitude and type of processing. Data points show group-mean data (ⴞ1 SE) from Oruganti (2000). Curves are least-squares fits to Eq. (1).
Apply
compressed
envelope
ranges from initial to full audibility were 43, 34, 24,
and 22 dB for the unprocessed signal, HFE alone,
HFE⫹single-band compression, and HFE⫹doubleband compression, respectively.
What is striking about these data is that the
behaviorally measured compression ratio for singleband compression was only 1.4:1 and not the 3:1
that might be expected from the digital processing.
The discrepancy is easily explained, however, by the
fact that gain changes in single-band compression
are dominated by amplitude at the spectral maximum but are applied to all frequencies (Dillon,
2001). It is usually assumed that this issue can be
resolved by compressing independently in two or
more channels. Oruganti’s data, however, did not
support this assumption—the behavioral compression ratio increased to only 1.5:1 when compression
was applied independently in low- and high-frequency bands. One could argue that the initial HFE
made the two-band compression scheme redundant.
The point here, however, is not to draw conclusions
about compression algorithms but to demonstrate
the potential value of the PI function as a technique
for the preclinical, behavioral evaluation of hearing
aid processing schemes that are designed to change
the distribution of information in the amplitude
domain.
Reverberation
Individuals listening to speech deep into the reverberant field in an enclosed space (at least threetimes the critical distance from the source) rely on
multiple early reflections for audibility of the signal
(Boothroyd, 2004; Bradley, et al., 2003). Unfortunately, these reflections are accompanied by multi-
BOOTHROYD / EAR & HEARING, VOL. 29, NO. 4, 479 –491
ple late reflections that cause speech sounds to
interfere with each other through a combination of
energetic and informational masking (Bradley,
1986; Nabalek, et al., 1989). In modeling this effect,
Boothroyd has treated late-arriving reverberation
as an equivalent self-generated noise, the resulting
signal-to-noise ratio being inferred from data on
consonant recognition reported by Peutz (1997). An
implied assumption of this approach is that the
principal effects of late reflections are confined to
the weaker components of the useful speech signal
and consist of energetic masking. If, however, informational masking plays a major role one would
expect the effects of late reflections to be distributed
across the amplitude range of the useful speech
signal. The study of Pegan mentioned earlier was
designed to test these two hypotheses. If the negative effects of late reflections are confined to the
weaker speech sounds, it was predicted that the PI
functions for reverberated speech would not begin to
separate from that of the unreverberated speech
until fairly high signal-to-noise ratios were reached.
If, on the other hand, the negative effects of late
reflections are distributed throughout the amplitude
range of speech, it was predicted that the PI functions would separate at all signal-to-noise ratios.
Phoneme recognition was measured in sentencefinal CVC words. The sentences were subjected to
simulated reverberation with reverberation times
(RT60) of 1, 2, and 4 sec. After processing, overall
levels were adjusted to equate dBleq levels across
conditions. Stimuli were then mixed with steadystate random noise whose spectrum was matched to
that of the talker. The condition of RT60 ⫽ 0 (i.e., no
reverberation) was also included. Twelve young
normally hearing adults were tested at RT60 ⫽ 0,
2, and 4 sec. An additional 17 listeners were tested
at RT60 ⫽ 0, 1, and 2 sec. Each listener heard one
list of 10 CVC words at each of seven signal-to-noise
ratios, under three reverberation conditions. Signalto-noise ratio was controlled by varying speech level
while keeping noise level constant. After confirming
that there were no significant differences between
the two listener groups at 0 and 2 sec, the data were
pooled.
Figure 6 shows Pegan’s data, together with leastsquares fits to Eq. (1). The findings were clearly in
keeping with the second prediction and strongly
support the conclusion that, for a listener who is
relying on early reflections, the negative effects of
late reflections are distributed throughout the amplitude range of the useful signal. They also strongly
suggest that optimal phoneme recognition for such a
listener requires a signal-to-noise ratio that is
higher than the 15 dB recommended by ANSI
(2002). Once again, however, the purpose here is not
483
80
60
40
20
Reverberation Time (RT60)
0 sec
1 sec
2 sec
4 sec
0
Fig. 6. Phoneme recognition by young hearing adults as a
function of postreverberation signal-to-noise ratio and reverberation time. Data points show group-mean data (ⴞ1 SE)
from Pegan (2007). Curves are least-squares fits to Eq. (1).
to draw conclusions about reverberation itself but to
illustrate the potential power of the PI function as a
behavioral tool for studying the effects of distortions
on the distribution of useful speech information in
the amplitude domain.
THE PI FUNCTION
AS A
CLINICAL TOOL
The PI function underlies the two standard clinical
speech measures—speech reception threshold (SRT)
and word recognition in lists of phonetically balanced
words (PBmax) (Brandy, 2002). SRT is the level giving
50% recognition probability for spondees and is
expressed in dB HL relative to the value for normally hearing listeners. PBmax is the recognition
probability for whole monosyllabic words in phonetically balanced lists when presented at a level believed to provide optimum performance. The SRT is
used (a) to validate pure-tone thresholds, and (b) as
the basis for estimating the optimum listening level.
PBmax is used (a) as an estimate of auditory resolution, (b) as an indicator of communication difficulty,
and (c) sometimes as a measure of hearing aid or
cochlear-implant outcome. These two measures
were adopted in the early days of clinical audiology
in the United States, in part, because obtaining a
complete PI function was considered both impractical and unnecessary (Carhart, 1965). With some
modifications to test procedures, however, a complete PI function can be obtained in a reasonably
short time. Moreover, the resulting information goes
beyond estimates of threshold and optimum performance.
One of the keys to the clinical utility of the PI
function is phoneme scoring—that is, measuring
performance, not as the percentage of whole words
484
BOOTHROYD / EAR & HEARING, VOL. 29, NO. 4, 479 –491
125
0
10
20
30
500
1000 2000 4000 8000
O Right Ear
X Left Ear
Headphone, binaural
Aid, binaural
PTA = 40 dB
O
X O
O
X X
X O
O
X
40
50
60
Fig. 7. Pure-tone audiogram and binaural PI
functions, via headphones and aided, for an
adult with a moderate sensorineural hearing
loss. Note that PRT stands for Phoneme
Recognition Threshold and is the level in dB,
re normal, at which the listener scores 50%
of his maximum. PRT is similar to the more
familiar SRT.
250
O
XO
X
70
80
90
100
Error bars show +/-1 se
PTA = 3-frequency avg.
PRT = phoneme recog. threshold
MCL = most comfortable level
UCL = uncomfortable level
110
Optimum
score
= 99%
100
80
Range of
optimal
listening
60
PRT = 39 dB
Nor
mal
40
20
MCL
UCL
0
0
10
recognized, but as the percentage of the constituent
vowels and consonants recognized. This relatively
simple change has several benefits.
1. It increases the number of test items and,
therefore, improves test–retest reliability and
reduces the confidence limits of a single score
(Boothroyd, 1968a; Gelfand, 1998; Thornton &
Raffin, 1978).
2. It becomes possible to obtain reasonably reliable scores from very short lists and the time
saved can be used for testing at several levels
(Boothroyd, 1968a).
3. The phoneme score is less influenced by the
listener’s vocabulary knowledge than is the
whole-word score and is, therefore, a more
valid measure of auditory resolution (Boothroyd, 1968b; Olsen, et al., 1996).
As noted earlier, by fitting scores obtained at
several levels to an underlying model, one essentially averages several data points, thereby improving overall test–retest reliability. The following
three examples illustrate the potential value of a
complete PI function in clinical applications.
A Flat, Moderate, Sensorineural Hearing Loss
Figure 7 shows pure tone and PI data for an adult
with a moderate sensorineural hearing loss. Binaural phoneme recognition scores were obtained under
headphones. Each score took roughly 1 min to obtain
20
30
40
50
60
70
80
90
100
110
and is based on a 10-word list (i.e., 30 phonemes). §
Equation (1) was fit to the data. For this individual
the estimated optimal score was 99%. The phoneme
recognition threshold ¶ (PRT) was 39 dB HL, which
is very close to the three-frequency-average hearing
loss of 40 dB. The optimum score and the PRT
provide, essentially, the same information as do
PBmax and SRT. Note, however, that additional
information is provided in terms of most comfortable
and uncomfortable levels that are easily determined
during testing. More importantly, one has information on the range of optimal listening (defined here
as the dB range over which the estimated phoneme
recognition probability is at least 90% of optimal).
The aided PRT is some 10 dB better than that
obtained under headphones. Moreover, at a conversational speech level of 60 dB, phoneme recognition
improves from around 65% to over 90%. The aided
data, however, would encourage one to explore the
use of wide dynamic range compression to enhance
audibility of low-amplitude speech. Even though
this is a straightforward case, it can be seen that the
preparation of complete PI functions provides useful
§The error bars in Figures 6, 7, and 8 show ⫾1 SE, estimated
from the normal approximation to the binomial distribution
under the assumption that there are, effectively, 25 independent
phonemes in a 10-word list.
¶Phoneme recognition threshold is defined here as the level, re:
normal, at which the phoneme recognition score is 50% of the
optimum score. For reasonably flat losses, the phoneme recognition threshold and the SRT are almost identical (Walker, 1975).
BOOTHROYD / EAR & HEARING, VOL. 29, NO. 4, 479 –491
125
250
500
1000 2000 4000 8000
O Right Ear
X Left Ear
Headphone, binaural
Aid, binaural
0
10
20
30
40
50
PTA = 72 dB
O
XO
X
XO
O
X
X O
X
O
O
X
60
70
80
90
100
110
100
Error bars show +/-1 se
PTA = 3-frequency avg.
PRT = phoneme recog. threshold
MCL = most comfortable level
UCL = uncomfortable level
Optimum
score
= 87%
80
Range of
optimal
aided
listening
60
Aided
PRT
= 26 dB
Nor
mal
40
485
Range of
optimal
listening
MCL
Unaided
PRT = 67 dB
20
Fig. 8. Pure-tone audiogram and binaural PI
functions, via headphones and aided, for an
adult with a severe sensorineural hearing
loss.
UCL
0
0
10
20
30
40
50
60
70
80
90
100
information over and above estimates of threshold
and optimum performance—for little extra expenditure of time.
A Flat Severe Sensorineural Loss
Figure 8 shows threshold and PI data for a more
challenging case. This is an adult with a flat
severe sensorineural hearing loss. PRT is 67 dB
HL, which compares favorably with the threefrequency average hearing loss of 72 dB. Optimum
phoneme recognition under headphones is around
87%. Unlike with the moderate loss, however,
there is a very narrow range over which this
optimum score is attained. A small increase in
level produces discomfort and a small decrease
lowers performance. In this case, the hearing aids
provide adequate gain—the aided PRT being reduced to 27 dB. More importantly, however, the
range of optimal listening has been extended from
a few dB to around 25 dB—thanks to a combination of high-frequency emphasis and compression
limiting in the hearing aid. Once again, there is
valuable information provided by the PI functions—which in this case took less than 15 min to
prepare—that would not otherwise be available.
A Severe High-Frequency Sensorineural
Hearing Loss
The final example (Fig. 9) is of an adult with a
severe high-frequency sensorineural hearing loss.
110
For losses like this, the PI function typically has
two sections (Boothroyd, 1968a). As speech amplitude increases, low-frequency speech information
first becomes audible but phoneme recognition
quickly stabilizes at a low value (note the upper
speech area on the audiogram). With further increase in level, high-frequency speech information
eventually becomes audible and phoneme recognition begins to rise again—in this case to an optimum level of around 86% (note the lower speech
area on the audiogram). Figure 9 shows a leastsquares fit of Eq. (1) to scores obtained between 25
and 70 dB and a second fit to scores obtained
between 75 and 95 dB. The SRT, using spondees,
would most likely have been in the region of 25 dB
HL for this subject and a rule of SRT ⫹30 or ⫹40
would have resulted in a search for PBmax at a
level below the optimal listening range. In cases
such as this, a full PI function may provide information that is not only richer than that provided
by SRT and PBmax— but more valid.储
COMPUTER ASSISTANCE
Although phoneme scoring makes it possible to
obtain complete PI functions in a reasonably short
time (typically 1 min for a 10-word list) it does add
储Note, however, that several researchers have recognized the
shortcomings of SRT as a basis for predicting the optimal listening level and some of the proposed alternatives would work well
in this case (Guthrie, 2007; Kamm, et al., 1983).
486
BOOTHROYD / EAR & HEARING, VOL. 29, NO. 4, 479 –491
125
250
500
1000 2000 4000 8000
O Right Ear
X Left Ear
Headphone, binaural
0
10
20
O
X O
X
30
40
50
X
O
Speech
area
X OO XO
X OO
XX
O
XX O
60
70
80
90
Fig. 9. Pure-tone audiogram and binaural PI
function, via headphones, for an adult with
a severe high-frequency sensorineural hearing loss.
100
Error bars show +/-1 se
PTA = 3-frequency avg.
PRT = phoneme recog. threshold
MCL = most comfortable level
UCL = uncomfortable level
110
100
Optimum
score
= 86%
80
Range of
optimal
listening
Nor
mal
60
40
MCL
UCL
20
0
0
10
a little complexity to the processes of recording
responses, logging data, averaging scores, estimating confidence limits, and graphing. These
processes can be handled effectively, however, by
custom software. An example is the CASPA program developed by the author and used to generate most of the behavioral data reported here
(Boothroyd, 2006; Mackersie, et al., 2001). This
program uses the AB isophonemic word lists (see
Appendix B). There are 20 lists, each consisting of
10 CVC words. The 10 vowels and 20 consonants
occurring most frequently in English CVC words
appear once in each list. All stimuli exist as digital
sound files. For aided and unaided sound-field
testing, speech amplitude is controlled by the
software and normally covers the range from 45 to
75 dB SPL (leq) in 5 dB steps. For testing over a
wider range— either in the sound field or under
headphones—the computer output is routed to an
audiometer. The listener’s repetition of a test word
is entered by the tester who is then shown the
word in text form. The three phonemes are scored
as correct or incorrect—additions, omissions, or
substitutions counting as errors— before moving
to the next word. After 10 words have been presented and scored, the results are automatically
logged, together with the test words, the responses, and the test conditions. Data for a given
listener can be recalled and specific runs selected
for averaging (if more than one list was presented
20
30
40
50
60
70
80
90
100
110
at the same level under the same test condition),
estimation of standard errors, graphing, and
curve-fitting.
RECONCILING PHONEME AND WHOLE-WORD
RECOGNITION
Although preparing a complete PI function in a
clinical context is made possible by phoneme scoring, the resulting scores are not simple substitutes
for whole-word scores. They can, however, be used to
estimate whole-word scores using the following
equation:
w ⫽ 100 * (p/100)2.5
(2)
where w is the whole-word recognition score in
percentage and p is the phoneme recognition score
in percentage.
The exponent of 2.5 in Eq. (2) is the j-factor
(Boothroyd & Nittrouer, 1988), and represents the
effective number of independent phonemes per
word. For meaningful CVC words, j is less than
three (the actual number of phonemes in a word)
because of the influence of word context on phoneme
recognition.
Equation (2) was used to generate the conversion
chart of Table 1. This chart will be helpful to
clinicians who have developed an implicit understanding of whole-word recognition scores in terms
of their relationship to communication difficulties.
BOOTHROYD / EAR & HEARING, VOL. 29, NO. 4, 479 –491
487
TABLE 1. Chart for converting percent phoneme recognition scores (p) into equivalent percent whole-word scores (w) and estimated
word-in-sentence scores (s)
p
w
s
p
w
s
p
w
s
p
w
s
p
w
s
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
2
0
0
0
0
0
0
0
1
1
1
1
2
2
2
3
3
4
5
5
6
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
2
2
2
3
3
3
3
4
4
5
5
5
6
6
7
7
8
8
9
9
7
8
9
10
11
12
13
14
16
17
18
20
21
23
24
26
28
29
31
33
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
10
11
11
12
13
14
14
15
16
17
18
19
19
20
21
22
23
25
26
27
35
37
38
40
42
44
46
48
50
52
54
56
58
60
62
64
66
68
69
71
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
28
29
30
32
33
34
35
37
38
40
41
42
44
46
47
49
50
52
54
55
73
75
76
78
80
81
83
84
85
87
88
89
90
91
92
93
94
95
95
96
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
57
59
61
63
65
67
69
71
73
75
77
79
81
83
86
88
90
93
95
98
100
97
97
98
98
98
99
99
99
99
100
100
100
100
100
100
100
100
100
100
100
100
PREDICTING WORD RECOGNITION
SENTENCES
IN
One can also use phoneme recognition scores to
estimate word-recognition probability in sentences
using the k-factor (Boothroyd & Nittrouer, 1988):
s ⫽ 100 * (1 ⫺ (1 ⫺ (p/100)2.5)k
(3)
where s is the percent word recognition in sentences,
p the phoneme recognition score in percentage, and
k is the effect of sentence context, expressed as a
proportional increase in the effective number of
independent channels of information (k is equivalent to the proficiency factor in AI theory).
The value of k reflects several factors (a) semantic
and syntactic redundancy in the sentence material,
(b) the perceiver’s world and linguistic knowledge,
and (c) the perceiver’s language processing skills.
It can range from around 2 for complex, unfamiliar language to 10 or more for informal conversation. A value of 4 is used in the conversion chart of
Table 1, representing relatively easy sentence
material—at least from the perceiver’s perspective. The data in Table 1 are also shown graphically in Figure 10.
SUMMARY
The PI function represents the cumulative distribution of useful speech information in the amplitude
domain. Its form is well predicted by a cubed exponential equation with three free parameters: (a) the
threshold of initial audibility, (b) the amplitude
range from initial to full audibility, and (c) the
optimum recognition probability at full audibility.
Phoneme scoring makes it possible to obtain PI
functions in a reasonably short time. Moreover,
phoneme recognition scores provide a more valid
estimate of auditory resolution than do whole-word
scores. Generation of complete PI functions can have
value in research contexts by providing information
on the effects of intentional or unintentional changes
to the distribution of useful speech information
Whole CVC words
in isolation
Words in relatively
easy sentences
80
60
40
20
0
0
20
40
60
80
100
Fig. 10. Estimated word recognition in isolation and in
sentence context, as functions of phoneme recognition in
CVC words.
488
BOOTHROYD / EAR & HEARING, VOL. 29, NO. 4, 479 –491
across the amplitude domain. It can also have value
in clinical contexts by providing information over
and above estimates of threshold and optimum performance. The PI function is an easily available,
potentially valuable, but largely neglected resource
for both hearing research and clinical audiology.
ACKNOWLEDGMENTS
The contributions of Balaji Oruganti, Bethany Mulhearn, Nina
Guerrero, Nancy Plant, Kathryn Pegan, Noemi Haro, Eddy
Yeung, and Gary Chant to the work underlying this article are
gratefully acknowledged.
This work was supported, in part, by NIDRR RERC grant No.
H1343E98 to Gallaudet University and by NIH grant No.
DC06238 to the House Ear Institute. The CASPA software was
developed by the author to facilitate the presentation and scoring
of short isophonemic word lists for the generation of PerformanceIntensity functions. Interested clinicians and researchers may
obtain a copy of this software, for a fee, by contacting the author.
Based on the Raymond Carhart Memorial Lecture to the Annual
meeting of the American Auditory Society, 2000.
Address for correspondence: Arthur Boothroyd. 2550 Brant Street, San
Diego, CA 92101. E-mail: aboothroyd@ cox.net.
Received June 26, 2007; accepted January 14, 2008.
Derivation of a Model of the PI Function
This derivation begins with AI theory. The AI is a
transform of recognition probability and is given by:
(A1)
where ai is the articulation index and p is the
recognition probability in percentage.
The motivation behind development of the AI was
to bypass the tedious and expensive process of as-
Fig. A1. Showing the identity of the AI-based
and exponential functions and the fact that
cubing either function provides a better fit to
the experimental data.
ai ⫽ (x ⫺ t)/r
(A2)
where ai is the articulation index when the speech
level is x, x is the speech level in dB, t is the threshold
of initial audibility in dB, and r is the range from
initial to full audibility in dB with the restriction
that
0 ⬍ ⫽ ai ⬍ ⫽ 1
APPENDIX A
ai ⫽ ⫺log(1 ⫺ p/100)
sessing early telephone systems with actual listeners (Fletcher, 1953). A principal virtue of the AI
transform is that it is additive—meaning that if two
independent sources of information have articulation indices of AI1 and AI2, the AI for the combination is simply the sum of the two. It was found that
good prediction of behavioral outcomes was obtained
if it was assumed that the useful speech information
within a given band of frequencies was distributed
uniformly over a limited range of amplitudes (originally 30 dB). For the moment, we will consider the
band of frequencies to be very wide— covering the
whole frequency range over which useful information is available. Under these assumptions, the
cumulative AI rises linearly from 0 to 1 as the
speech signal rises from initial audibility to full
audibility. Thus
Equation (A3) converts AI into recognition probability
by reversing Eq. (A1) and combining with Eq. (A2):
p ⫽ 100 * (1 ⫺ E((x⫺t)/r))
(A3)
where p is the recognition probability in percentage,
E is the residual error probability at full audibility.
The broken line in Figure A1 shows a leastsquares fit of Eq. (A3) to the group-mean PI data of
BOOTHROYD / EAR & HEARING, VOL. 29, NO. 4, 479 –491
Figure 3. The parameters for a least-squares fit to
the data are:
Residual error at full audibility ⫽ 0.9%
Threshold of audibility ⫽ ⫺17 dB SNR
Range from zero to full audibility ⫽ 34 dB
The standard error of fit is 1.9 percentage points.
The fit is improved if we cube the estimated
recognition probability in Eq. (A3) before converting
to percentage. Thus
p ⫽ 100 * (1 ⫺ Fai)3
(A4)
F ⫽ 1 ⫺ (1 ⫺ E)1/3
(A5)
where
The fit of Eq. (A4) to Pegan’s data is shown by the
solid line in Figure A1. The parameters for best fit
are now:
F ⫽ 0.0027 (still giving residual error at full
audibility of E ⫽ 0.9%)
Threshold of audibility ⫽ ⫺21 dB SNR
Range from zero to full audibility ⫽ 35 dB
It will be seen from Figure A1 that the cubed AI
function more closely resembles the typical PI function in that it predicts a linear portion between 20%
and 60%. Moreover, the exponent of three can be
justified as helping account for the influence of
phonological and lexical redundancy on phoneme
recognition—as in the j-factor of Boothroyd and
Nittrouer (1988). It may also help deal with departures from the assumption that the AI rises linearly
with increasing audibility. More importantly, however, the standard error of fit is reduced, here, from
1.9 to 0.77% pts.
Unfortunately, the parameters of range and residual error in Eqs. (A4) and (A5) are not entirely
independent. And if one wished to account for distortions of the signal or proficiency of the listeners,
one would need to add a fourth parameter— equivalent to the k-factor of Boothroyd and Nittrouer
(1988), or the proficiency factor of traditional AI
theory.
A small modification to Eq. (A4), however, can
deal with these two problems. This modification
involves replacing the variable F with e (the base of
natural logarithms), adding a parameter representing recognition at full audibility, and introducing a
couple of constants. The result is the following cubed
exponential equation [Eq. (1) in the body of the text]:
p ⫽ m/0.99 * (1 ⫺ e(⫺(x⫺t)/r 5.7))3
*
(A6)
where p is the phoneme recognition probability, m is
the recognition probability at full audibility, x is the
speech level in dB, e is the base of natural loga-
489
rithms (⬃2.72), t is the threshold of initial audibility
in dB, and r is the amplitude range in dB from initial
to full audibility.
Note the constraint that 0 ⱖ (x ⫺ t)/r ⱕ 1.
If (x ⫺ t)/r is not restricted to an upper limit of 1, the
value of p will approach an asymptotic value of m/0.99.
The constant (5.7) forces r to take the value at which
recognition probability reaches 0.99 of this asymptote.
Similarly, the constant (0.99) at the beginning of Eq.
(5) forces m to take the value of the % recognition
probability at full audibility. Thus the whole function
is now defined by three parameters: the threshold of
initial audibility in dB (t), the amplitude range between initial and full audibility in dB (r), and the
percent phoneme recognition probability at full audibility (m).
The least-squares fit of Eq. (A6) is shown in the
Pegan data in Figure A1 but is indistinguishable
from the fit to the cubed AI function. The fitting
parameters are:
m ⫽ 99%
t ⫽ ⫺21 dB SNR
r ⫽ 34 dB
The standard error of fit is 0.77%pts.**
Putting the limitation of 0 ⱕ ai ⱕ 1 into equation
form can be accomplished with logarithmic addition.
The equation is complicated but the result is simple—ai cannot fall below 0 or rise above 1:
ai ⫽ 1 ⫺ log共1 ⫹ 10∧共共1 ⫺ log共1 ⫹ 10∧
⫻ 共100 * 共x ⫺ t兲/r兲兲/100兲 * 100兲兲/100 (A7)
Once the parameters of m, t, and r have been
obtained, they can be used to estimate other quantities of possible interest. For example
PRT ⫽ t ⫹ r * 0.275
(A8)
where PRT is the amplitude at which the phoneme
recognition score is 50% of the optimum value
s ⫽ 234/r
(A9)
where s is the slope of the PI function between 20%
and 60% of the maximum.
o⫽t⫹r
(A10)
where o is the level at which the optimum recognition probability of m is first attained.
**The two equations are, in fact, equivalent over most of their
range. It can be shown that the amount by which AI is multiplied
in Eq. (5) is 1/logF(e), which is ⫺5.9 (using the fitting data from
Fig. 3). The shift from ⫺5.9 to ⫺5.7 ties the range to 0.99 of the
asymptote of the exponential function and accounts for the 1 dB
difference of range for the fits to Eqs. (A4) and (A6).
490
BOOTHROYD / EAR & HEARING, VOL. 29, NO. 4, 479 –491
This is a single-band model, but it can be expanded to account for frequency-dependence of
speech amplitude, hearing aid gain, signal-to-noise
ratio, or pure-tone threshold.
APPENDIX B
AB isophonemic word lists used in CASPA and to
generate the behavioral data reported in this article.
List 1
List 2
List 3
List 4
List 5
List 6
List 7
List 8
List 9
List 10
ship
rug
fan
cheek
haze
dice
both
well
jot
move
fish
duck
path
cheese
race
hive
bone
wedge
log
tomb
thug
witch
teak
wrap
vice
jail
hen
shows
food
bomb
fun
will
vat
shape
wreath
hide
guess
comb
choose
job
fib
thatch
sum
heel
wide
rake
goes
shop
vet
June
fill
catch
thumb
heap
wise
rave
got
shown
bed
juice
badge
hutch
kill
thighs
wave
reap
foam
goose
not
shed
bath
hum
dig
five
ways
reach
joke
noose
pot
shell
hush
gas
thin
fake
chime
weave
jet
rob
dope
lose
jug
latch
wick
faith
sign
beep
hem
rod
vote
shoes
List 11
math
hip
gun
ride
siege
veil
chose
shoot
web
cough
List 12
have
wig
buff
mice
teeth
jays
poach
rule
den
shock
List 13
kiss
buzz
hash
thieve
gate
wife
pole
wretch
dodge
moon
List 14
wish
Dutch
jam
heath
laze
bike
rove
pet
fog
soon
List 15
hug
dish
ban
rage
chief
pies
wet
cove
loose
moth
List 16
wage
rag
beach
chef
dime
thick
love
zone
hop
suit
List 17
jade
cash
thief
set
wine
give
rub
hole
chop
zoom
List 18
shave
jazz
theme
fetch
height
win
suck
robe
dog
pool
List 19
vase
cab
teach
death
nice
fig
rush
hope
lodge
womb
List 20
cave
rash
tease
jell
guide
pin
fuss
home
watch
booth
Note: Each list contains 1 instance of each of the same 30 phonemes. These are the 10 vowels and 20 consonants that occur most frequently in English CVC words. The lists are balanced
only for phonemic content - not for word frequency or lexical neighborhood size. No word appears twice in the corpus of 200.
REFERENCES
ANSI. (1969). American national standard method for calculation
of the articulation index (S3.5–1969). New York: American
National Standards Institute.
ANSI. (2002). Acoustical performance criteria, design requirements, and guidelines for classrooms (ANSI S12.6-2002). New
York: American National Standards Institute.
Boothroyd, A. (1968a). Developments in speech audiometry. Br J
Audiol (Formerly Sound), 2, 3–10.
Boothroyd, A. (1968b). Statistical theory of the speech discrimination score. J Acoust Soc Am, 43, 362–367.
Boothroyd, A. (2004). Room acoustics and speech perception.
Semin Hear, 25, 155–166.
Boothroyd, A. (2006). CASPA 5.0. Software. San Diego: A Boothroyd.
Boothroyd, A. & Nittrouer, S. (1988). Mathematical treatment of
context effects in phoneme and word recognition. J Acoust Soc
Am, 84, 101–114.
Bradley, J. S. (1986). Predictors of speech intelligibility in rooms.
J Acoust Soc Am, 80, 837– 845.
Bradley, J. S., Sato, H., & Picard, M. (2003). On the importance of
early reflections for speech in rooms. J Acoust Soc Am, 113,
3233–3244.
Brandy, W. T. (2002). Speech audiometry. In J. Katz (Ed.),
Handbook of clinical audiology (5 ed., pp. 96 –110). Baltimore:
Lippincott Williams & Wilkins.
Carhart, R. (1965). Problems in the measurement of speech
discrimination. Arch Otolaryngol, 82, 253–260.
Cox, R. M. & Moore, J. R. (1988). Composite speech spectrum for
hearing aid gain prescriptions. J Speech Hear Res, 31, 102–107.
Dillon, H. (2001). Compression systems in hearing aids. In
Hearing aids (pp. 169). New York: Theime.
Fletcher, H. (1953). Speech and hearing in communication.
New York: Van Nostrand [edited by Jont Allen and republished in 1995 by the Acoustical Society of America. Woodbury, NY].
French, N. R. & Steinberg, J. C. (1947). Factors governing the
intelligibility of speech sounds. J Acoust Soc Am, 19, 90 –119.
Gelfand, S. (1998). Optimizing the reliability of speech recognition scores. J Speech Lang Hear Res, 41, 1088 –1102.
Guthrie, L. A. (2007). Optimizing presentation level for speech
recognition testing. Unpublished AuD research thesis. San
Diego: San Diego State University.
Haro, N. (2007). Development and evaluation of the Spanish
computer-assisted speech perception assessment test
(CASPA). Unpublished AuD research thesis. San Diego: San
Diego State University.
Kamm, C. A., Morgan, D. E., & Dirks, D. D. (1983). Accuracy of
adaptive procedure estimates of PB-Max level. J Speech Hear
Disord, 48, 202–209.
Kryter, K. D. (1962a). Methods for the calculation and use of the
articulation index. J Acoust Soc Am, 34, 1689 –1697.
Kryter, K. D. (1962b). Validation of the articulation index.
J Acoust Soc Am, 34, 1698 –1702.
Mackersie, C. L., Boothroyd, A., & Minnear, D. (2001). Evaluation
of the computer-assisted speech perception test (CASPA). J Am
Acad Audiol, 12, 390 –396.
Nabalek, A. K., Letowski, T. R., & Tucker, F. M. (1989). Reverberant overlap- and self-masking in consonant identification.
J Acoust Soc Am, 86, 1259 –1265.
BOOTHROYD / EAR & HEARING, VOL. 29, NO. 4, 479 –491
Olsen, W. O., Van Tasell, D. J., & Speaks, C. E. (1996). Phoneme
and word recognition for words in isolation and in sentences.
Ear Hear, 18, 175–188.
Oruganti, B. (2000). The effects of high-frequency emphasis and
amplitude compression on the short-term intensity range of
speech. Unpublished Doctoral dissertation. New York: City
University of New York.
Pegan, K. (2007). Interactive effects of noise and reverberation on
speech perception. Unpublished AuD research thesis. San Diego: San Diego State University.
Peutz, V. (1997). Speech reception and information. In D. Davis &
491
C. Davis (Eds.), Sound system engineering (2 ed., pp. 639 – 644).
Boston: Focal Press.
Studebaker, G. A., Taylor, R., & Sherbecoe, R. L. (1994). The
effect of noise spectrum on speech recognition performanceintensity functions. J Speech Hear Res, 37, 439 – 448.
Thornton, A. R. & Raffin, M. J. M. (1978). Speech discrimination
scores modeled as a binomial variable. J Speech Hear Res, 21,
507–518.
Walker, J. (1975). A comparative study of two test procedures in
speech audiometry. Unpublished Masters Thesis, MA: University of Massachusetts, Amherst.