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Acoustic Continua and
Phonetic Categories
Frequency - Tones
Frequency - Tones
Frequency - Tones
Frequency - Tones
Frequency - Complex Sounds
Frequency - Complex Sounds
Frequency - Vowels
• Vowels combine acoustic energy at a number of
different frequencies
• Different vowels ([a], [i], [u] etc.) contain acoustic
energy at different frequencies
• Listeners must perform a ‘frequency analysis’ of
vowels in order to identify them
(Fourier Analysis)
Any function can be decomposed in terms of sinusoidal (=
sine wave) functions (‘basis functions’) of different
frequencies that can be recombined to obtain the original
function. [Wikipedia entry on Fourier Analysis]
Time -->
Amplitude
Frequency
Joseph Fourier (1768-1830)
Frequency - Male Vowels
Frequency - Male Vowels
Frequency - Female Vowels
Frequency - Female Vowels
Synthesized Speech
•Allows for precise control of sounds
•Valuable tool for investigating perception
Timing - Voicing
Voice Onset Time (VOT)
60 msec
English VOT production
• Not uniform
• 2 categories
Perceiving VOT
‘Categorical Perception’
Discrimination
Same/Different
0ms 60ms
Same/Different
0ms 10ms
Same/Different
40ms 40ms
A More Systematic Test
D
0ms
20ms
D
D
20ms
40ms
T
T
40ms
60ms
T
Within-Category Discrimination is Hard
Cross-language Differences
R
R
L
L
Cross-Language Differences
English vs.
Japanese R-L
Cross-Language Differences
English vs. Hindi
alveolar [d]
retroflex [D]
?
Russian
-40ms
-30ms
-20ms
-10ms
0ms
10ms
Kazanina et al., 2006
Proceedings of the National
Academy of Sciences, 103, 11381-6
Quantifying Sensitivity
Quantifying Sensitivity
• Response bias
• Two measures of discrimination
– Accuracy: how often is the judge correct?
– Sensitivity: how well does the judge distinguish the categories?
• Quantifying sensitivity
– Hits
False Alarms
Misses
Correct Rejections
– Compare p(H) against p(FA)
Quantifying Sensitivity
• Is one of these more impressive?
– p(H) = 0.75, p(FA) = 0.25
– p(H) = 0.99, p(FA) = 0.49
• A measure that amplifies small percentage differences at
extremes
z-scores
Normal Distribution
Dispersion
around mean
Standard Deviation
A measure of dispersion
around the mean.
Mean (µ)
Carl Friederich Gauss (1777-1855)
√(
∑(x - µ)2
n
)
The Empirical Rule
1 s.d. from mean: 68% of data
2 s.d. from mean: 95% of data
3 s.d. from mean: 99.7% of data
Normal Distribution
Standard deviation
 = 2.5 inches
Heights of American
Females, aged 18-24
Mean (µ)
65.5 inches
Quantifying Sensitivity
• A z-score is a reexpression of a data point in units of standard
deviations.
(Sometimes also known as standard score)
• In z-score data, µ = 0,  = 1
• Sensitivity score
d’ = z(H) - z(FA)
See Excel worksheet
sensitivity.xls
Quantifying Differences
(Näätänen et al. 1997)
(Aoshima et al. 2004)
(Maye et al. 2002)
Normal Distribution
Dispersion
around mean
Standard Deviation
A measure of dispersion
around the mean.
Mean (µ)
√(
∑(x - µ)2
n
)
The Empirical Rule
1 s.d. from mean: 68% of data
2 s.d. from mean: 95% of data
3 s.d. from mean: 99.7% of data
• If we observe 1 individual, how likely is it that
his score is at least 2 s.d. from the mean?
• Put differently, if we observe somebody
whose score is 2 s.d. or more from the
population mean, how likely is it that the
person is drawn from that population?
• If we observe 2 people, how likely is it
that they both fall 2 s.d. or more from
the mean?
• …and if we observe 10 people, how
likely is it that their mean score is 2 s.d.
from the group mean?
• If we do find such a group, they’re
probably from a different population

• Standard Error
is the Standard Deviation of sample
means.

n
• If we observe a group whose mean
differs from the population mean by 2
s.e., how likely is it that this group was
drawn from the same population?
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