The statistical analysis of
acoustic correlates of speech
rhythm
Denise Duarte*
Universidade Federal de Goiás
and Universidade de São Paulo
Antonio Galves
Universidade de São Paulo
Nancy L. Garcia
Universidade Estadual de Campinas
Ricardo Maronna*
Universidad de La Plata
http://www.ime.usp.br/~tycho
* : authors who presented the paper
1. Introduction
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Data description: two corpora
“20 sentences”: 20 sentences spoken three times
by two female native speakers of BP and EP (
segmented by Flaviane R. Fernandes and Janaisa
M. Viscardi)
“RNM”: 20 sentences of each of : English,
Polish, Dutch, French, Spanish, Catalan, Italian,
Japanese 5 sentences uttered by each of 4 female
speakers
Purposes
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Apply the RNM approach to the enlarged data
set.
Present alternative descriptive statistical measures
Analize the effect of dropping the last vocalic
interval of each sentence.
Introduce a probalility model for duration, which
allows for improved descriptions and hypothesis
testing
Use this model to give statistical support to the
The RNM statistics
For each sentence of the corpus the following are
computed:
∆C, ∆V= standard deviation for vocalic and
consonantal intervals
%V= proportion of time spent on vocalic intervals
Values are averaged for each speaker
%V, ∆C and ∆V for the ten languages
Languages
Polish
English
Dutch
French
Spanish
Italian
Catalan
Japanese
EP
BP
ÇV
ÇC
2.51
4.64
4.23
3.78
3.32
4.00
3.68
4.02
4.33
4.01
%V
5.14
5.35
5.33
4.39
4.74
4.81
4.52
3.56
5.57
4.53
41
40.1
42.3
43.6
43.8
45.2
45.6
53.1
45.3
49.1
%V vs. ∆C for the ten languages
%V and ∆C for individual speakers
en
0.07
0.06
du
EP1
∆C
du
du
po po
po
EP2
it
es
it
en ca
es
BP2
en
it fr ca es frdu
it
ca
es
fr
fr
0.05
po
en
0.04
BP1
ca
ja
ja
ja
ja
0.03
0.35
0.40
0.45
%V
0.50
0.55
∆V vs. ∆C for the ten languages
5.6
EP
Dutch
5.1
Polish
Italian
Spanish
∆C
English
4.6
BP
Catalan
French
4.1
3.6
Japanese
2.5
3.0
3.5
∆V
4.0
4.5
3. Alternative analysis
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3.1 Dropping the last vocalic interval
The last vocalic interval is an important source of
variability.
It was obserded that in BP and EP there is a
stretching in final vocalic intervals.
New data set: omitting the last vocalic interval for
each language, and also the subsequent
consonantal interval, if one exists.
The data without the last vocalic
interval
ep
dut
eng
pol
5.1
sp a
i ta
∆C
4.6
cat
f re
bp
4.1
jap
3.6
40
42
44
46
48
%V
50
52
54
Location of BP and EP speakers in the %V vs. ∆C
Plane – complete sentences
The effect of the last vocalic interval
in BP and EP- individual values
E P sp1
ep
5.5
E P s p 1 - w lv
E P sp2
E P s p 2 - w lv
∆C
e p :w lv
5.0
B P sp2
bp
B P sp1
B P s p 1 - w lv
4.5
b p :w lv
B P s p 2 - w lv
4.0
40
42
44
46
48
%V
50
52
54
3.2 Robust statistics
“Robust”= insensive to extreme values
Simplest robust measure of location: replace the
mean by the median.
To find the median of a set of numbers: sort them
and pick the one in the middle
Simplest robust measure of dispersion: replace the
standard deviation by the median absolute
deviation(MAD).
n +1

x ( m) with m =
if n is odd

2
median( x ) = 
1
n
 ( x (m ) + x ( m+1) ) with m = if n is even
2
2
MAD ( x ) = med xi − med ( x )
Robust statistics
5.5
pol
5.0
dut
esp
eng
DCmad
ita
4.5
cat
ep
4.0
bp
fre
3.5
jap
3.0
40
42
44
46
PVmed
48
50
52
54
4. A probability model for duration
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Former analysis is descriptive
Finding a parametric family of probability
distributions that fits the data closely would have
two advantages:
May yield a better description of data
Allows us to make inference, i. e., to extend
results from the “sample” (the data set) to the
“population” ( the set of all potential setences)
4.1 Histograms show similar
asymmetrical shapes
Histogram: Consonantal intervals - Italian
Histogram: consonantal intervals- Dutch
30
40
25
30
20
15
20
10
10
5
0
0
-0.050 0.005 0.060
0.115
0.170 0.225
time
0.280
0.335
0.390
0.445
0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 0.225 0.250 0.275
time
Several distributions tried: Log-normal, Weibull,
exponential, Gamma
The Gamma was the best fit :quantile-quantile (QQplot)Given a data set and a theoretical, plot the quantiles of the
latter vs those of the empirical distribution
Gamma distribution
It has two parameters:α and β, controlling shape and
size, respectively:
small α: high asymmetry; α = 1 gives the the
exponential distribution;
Large α approximates the normal.
The parameters are related to the mean µ and
standard deviation σ by
µ=αβ
σ2=αβ2
Estimated Gamma parameters
vocalic intervals
Estimated Gamma parameters
consonantal intervals
Mean values for vocalic and
consonantal intervals
Lang
English
Dutc h
P o lis h
EP
F renc h
Spanish
Italian
Catalan
BP
Japanes e
Mean
Consonantal V o c a lic
0.1070
0.07310
0.1000
0.07580
0.1020
0.07110
0.1000
0.07800
0.0950
0.07360
0.0970
0.07430
0.0970
0.07710
0.0890
0.07440
0.0950
0.08580
0.0780
0.08780
5. Hypothesis testing
In view of the close relationship between α and β ,
we may use one of the two, or one function of
both, to represent relevant features.
Based on the RNM results, we choose the model
standard deviation :
â=ÒÑ1/2
Standard deviation of Gamma for the
ten languages – complete sentences
Fre Cat
Jap
Esp
Ita
Dut
0.040
0.045
s tdC
Eng
EP
BP
0.035
Pol
0.050
0.055
Rhythmic class hypothesis
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We represent the rhythmic class hypothesis by the
following statistical model:
1.The syllabic languages ( Italian, Spanish,
French, Catalan , BP) have the same standard
deviation, say, σ1.
2.The accentual ones (Polish, Dutch, English, EP)
share another, say, σ2
3. σ1, σ2and the standard deviation for Japanese
σ3 are different .
Results
To test the model, we first tested (1) and (2) by
means of the Likelihood Ratio Test, which yielded
a p-value of 0.91, which means that the equality of
σ's within rhythmic classes is highly compatible
with the data ( a small p-value indicates rejection).
Then we tested the null hypothesis that some of σ1 ,
σ2, σ3 are equal, which was rejected with a p-value
of 0.0012, thus giving statistical evidence that the
three are different.
Acknowledgments
We want to thank Franck Ramus, Marina
Nespor and Jacques Mehler, who generously
made their unpublished data avalaible to us.
We also thank Janaisa Viscardi and Flaviane
Fernandes for the segmentation of the acoustic
data
The “20 sentences” corpus
The following sentences of the corpus 20 sentences were considered in the statistical
analysis. The choice was based on the quality of acoustic signal and to avoid dubious cases of
labeling.
1. A moderniza o foi satisfatória.
5. A falta de moderniza
o catastrófica.
6. O trabalho da pesquisadora foi publicado.
8. O governador aceitou a moderniza
o.
9. A falta de autoridade foi alarmante.
11. A catalogadora compreendeu o trabalho da pesquisadora.
12. A professora discutiu a gramaticalidade.
15. A procura da gramaticalidade o nosso objetivo.
16. A pesquisadora perdeu autoridade.
18. A autoridade cabe ao governador.
20. A gramaticalidade das frases foi conseguida.
Grants supporting the research
FAPESP grant n. 98/3382-0
(Projeto Temático Rhythmic patterns, parameter setting and
language change )
PRONEX grant 66.2177/1996-6 (Núcleo de Excel ncia Critical
phenomena in probability and stochastic processes)
CNPq grant 465928/2000-5 (Probabilistic tools for pattern
identification applied to linguistics)
Related
papers
and
references
Abercrombie, D. (1967). Elements of general phonetics. Chicago: Aldine.
Grabe, E. and Low, E., L. (2000) Acoustic correlates in rhythmic class. Paper presented at the
7th conference on laboratory phonology, Nijmegen.
Lloyd, J. (1940) Speech signal in telephony. London.
Mehler, J., Jusczyk, P., Dehane-Lambertz, G., Bertoncini, N. And Amiel-Tison, C. (1988) A
percursor of language acquisition in young infants. Cognition 29: 143-178.
Nazzi, T., Bertoncini, N. and Mehler, J. ( 1998) Language discrimination by newborns
towads an understanding of the role of the rhythm. Journal of experimental psychology:
human perception and perfomance 24 (3): 756-766.
Nespor, M. (1990) On the rhythm parameter in phonology. Logical issues in language
acquisition, Iggy Roca , 157-175.
Ramus, F. And Mehler, J. ( 1999). Language acquisition with suprasegmental cues: a study
based on speecch resynthesis. JASA 105: 512-521.
Ramus, F., Nespor, M. and Mehler (1999) Correlates of linguistic rhythm in speech.
Cognition 73: 265-292.
Frota, S. and Vigário, M.(2001) On the correlates of rhythm distinctions: the European/
Brazilian Portuguese case. To be published in Probus.
Appendix: the meaning of a p-value
Consider the situation of testing a statistical hypothesis: To
fix ideas, suppose that we have samples from two
populations, and we want to test the hypothesis that both
have the same (unknown) mean. Of course, even if the
hypothesis is true, the two sample means will be different,
due to sampling variability.
To test the hypothesis, we compute a number T from our
data (the so-called “test statistics”) which measures the
discrepancy between the data and the hypothesis. In our
example T will depend on the differences between the
sample means. If T is very large, we have a statistical
evidence against the hypothesis. What is a rational
definition of “large”?
Suppose our data yields T=3.5; and that we compute
the probability p that, if the hypothesis is true, we
obtain a value of T greater than 3.5. This the socalled “p-value” of the test. If, say, p= 0.002, this
means that, if the means are equal, we would be
observing an exceptionally large value ( since a
larger one is observed only with probability 0.2%);
Thus we would have grounds to reject the
hypothesis.