Elena Babatsouli
1, David Ingram
2, Dimitrios Sotiropoulos
3[email protected], [email protected], [email protected]
1Institute of Monolingual and Bilingual Speech, 2Arizona State University, 3Technical University of Crete Abstract. Phonological word proximity, PWP, was introduced by Ingram and Ingram (2001) and Ingram (2002) to evaluate performance in child speech per word by weighing correctly produced in context consonants twice as much as produced vowels and substituted consonants. Babatsouli, Ingram, and Sotiropoulos (2011, 2014) obtained an explicit formula for PWP cumulatively for all words in a speech sample, in terms of the proportion of consonants correct (PCC), the proportion of phonemes deleted (PPD), and the proportion of targeted consonants (PC). In the present study, the relative weight of phones is taken as an arbitrary number n, in order to compare the advantages and disadvantages of such a PWP to Babatsouli et al.’s (2011, 2014) PWP of n=2, in assessing child speech. The derived expression for PWP is similar to Babatsouli et al.’s (2011, 2014);
however, the weights of PCC and PPD are now dependent on n as well as on PV. As the product nPC increases, the weight of PCC increases and that of PPD decreases; when n is greater than 2, the weight of PCC is greater than that of PPD; for n=2 the weights are equal, while for n smaller than 2, the weight of PPD is larger. However, the difference between PCC (or PPD) weights of different n’s, which generally increases for increasing PC, remains effectively constant for PC larger than 40%. These results have implications on how to compute phonological word proximity (PWP) for assessment purposes. Smaller relative weights of phones guarantee larger phonological word proximities when the proportion of vowels produced is larger than the proportion of consonants correct, which is generally the case. In comparing phonological word proximity between two such samples with their difference in the proportion of phonemes deleted (PPD) being larger than their difference in the proportion of consonants correct (PCC), it is advantageous to use smaller relative weights of phones if larger differences in PWP are sought. When, however, changes in PCC are larger than changes in PPD, phonological word proximity (PWP) becomes more sensitive for larger relative weights of phones. Last, independent of the relative weight of phones, phonological word proximity is more sensitive than PCC when changes in PPD are larger than changes in PCC; otherwise, it is not. These results may guide the establishment of speech performance norms for normal children, as well as assessing children with speech sound disorders (SSP) whose PCC values vary little across categories of word complexity, such as across monosyllabic or multisyllabic words with singleton consonants and monosyllabic or multisyllabic words with consonant clusters.
Keywords: phonological word proximity, measure, assessment, child, normal speech, disordered
Introduction
The proportion of consonants correct (PCC) (e.g., Shriberg, Austin, Lewis, McSweeney, & Wilson (1997)) has been widely used in the literature since the mid-1980s, and in practice for assessing typical and atypical children’s speech in development, as well as children’s disordered speech in terms of consonants productions. However, it was not until the early 2000s that a phonological measure was proposed to evaluate whole word productions. Ingram and Ingram (2001) and Ingram (2002) introduced the phonological mean length of utterance (PMLU) as the arithmetic mean of the PMLU of individual words, which is defined as the sum of the produced vowels and the substituted consonants plus twice the correctly produced (as targeted) consonants. Furthermore, the same authors introduced the proportion of word proximity (PWP) per word, hereon referred to as phonological word proximity, as the proportion of the produced PMLU to the targeted PMLU, with the PWP for a number of words in a speech sample being the arithmetic average of the PWP of individual words.
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Since the introduction of PMLU and PWP, researchers have used these measures to evaluate speech performance in monolingual and bilingual child speech. Taelman, Durieux, and Gillis (2005) discussed how to use CLAN (MacWhinney, 2000) to compute PMLU and PWP using large speech data. Bunta, Fabiano-Smith, Goldstein, & Ingram (2009) compared 3-year old Spanish-English bilingual children to their monolingual peers to compute, among other quantities, PWP and the proportion of consonants correct, PCC. They found that while PWP and PCC differ in general, bilinguals only differ on PCC from their monolingual peers in Spanish and that when comparing the Spanish and English of the bilingual participants, PCC was significantly different but PWP was similar. Burrows and Goldstein (2010) compared PWP and PCC accuracy in Spanish-English bilinguals with SSD to age-matched monolingual peers. Macleod, Laukys, & Rvachew (2011) compared the change in PWP to that in PCC for two samples of twenty children each, both taken at the age of 18 months and at 36 months. One of the samples involved monolingual English children while the other involved bilingual French-English children. Their results showed that the PWP change was larger than the PCC change.
Babatsouli, Ingram, and Sotiropoulos (2011, 2014) took another look at the proportion of phonological word proximity (PWP). Instead of defining PWP per word, they defined it cumulatively for all the words in a speech sample. This enabled them to express PWP for the whole speech sample analytically in terms of the proportion of consonants correct (PCC), the proportion of consonants deleted (PCD) and the proportion of vowels (PV) in the targeted speech, and obtain upper and lower PWP bounds in general.
In the present paper, yet another look is taken at PWP in order to question why the correctly produced (as targeted) consonants should weigh twice as much as vowels and substituted consonants. This weighing factor, 2, was decided arbitrarily by Ingram and Ingram (2001) and Ingram (2002) and the effect of its choice on the sensitivity of PWP to changes of PCC and PCD has not been examined to date. The analytical expression derived by Babatsouli et al. (2011, 2014) provides the starting point for such an examination which will be done in the present paper.
The present study is motivated by the need to provide a proper measure for practitioners to evaluate children’s speech performance, as far as a phonological word measure is concerned. Ingram (2015) points out that when comparing typically developing children to children with SSD, PCC changes are dramatically different across categories of word complexity: monosyllabic words without consonant clusters, monosyllabic words with at least one consonant cluster, multisyllabic words without consonant clusters, multisyllabic words with at least one consonant cluster. For example, for children with SSD, PCC will likely remain unchanged when comparing performance between words without consonant clusters and words with consonant clusters. While for typically developing children or children with speech delay, this is not the case.
This and other cases will be examined here, in general, in light of how to compute PWP with respect to the value of the relative weight between correct consonants on the one hand and vowels and substituted consonants on the other hand. Therefore, the results of the present paper will provide guidelines for assessing speech performance not only for all the words in a speech sample but also for different categories of word complexity in the sample. The results obtained here are applicable to
samples of running speech as well as to speech samples obtained from picture naming tests.
Phonological word proximity (PWP) for general weight of correct consonants
Ingram and Ingram (2001) and Ingram (2002) introduced the phonological word proximity (PWP) per word as follows:
PWP = (CCP + PH)/(2CCT+VT) (1)
where CCP is the number of correctly produced (as targeted) consonants, PH is the number of consonants and vowels produced whether correctly or not (vowels are assumed to be produced correctly as targeted), CCT is the number of targeted consonants in the word, and VT is the number of
Proceedings ISMBS 2015
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targeted vowels in the word. Therefore, in computing PWP per word using equation (1), correctly produced (as targeted) consonants (CCP) are weighed twice as much as substituted consonants and produced vowels. PWP for a number of words in a speech sample was subsequently obtained as the arithmetic average of the PWPs per word. However, such a cumulative PWP could not be analyzed in general.
Babatsouli et al. (2011, 2014) expressed the PWP in (1) in terms of the proportion of correctly produced (as targeted) consonants to the targeted consonants (PCC), the proportion of deleted segments to the targeted segments (PPD), and the proportion of targeted vowels to all targeted segments (PV), as follows:
PWP = pPCC + (1-p) (1-PPD), p = (1-PV)/(2-PV) (2) Then, by taking the weighted average of the PWPs per word given by (2), Babatsouli et al. (2011,
2014) obtained a cumulative PWP for all the words in exactly the same form as (2), with the three phonological parameter components PCC, PPD, and PV now computed as the weighted averages of their corresponding values per word. For example, the cumulative PCC is now the proportion of correctly produced (as targeted) consonants in the whole speech sample to the targeted consonants in the whole speech sample as well. The cumulative PWP as expressed by equation (2), made it possible to obtain, in general, its upper and lower bounds.
Here, in order to analyze the effect of the weighing factor for correctly produced (as targeted) consonants on the cumulative PWP, a general weight equal to n+1 is considered, where n is any real number greater than zero, as it would be senseless not to weigh correctly produced (as targeted) consonants more than substituted consonants. The weight which was taken by Ingram and Ingram (2001) and Ingram (2002) and adopted by Babatsouli et al. (2011, 2014) as equal to 2 (n=1), is a special case of the general n>0 considered here. Following a similar derivation as in Babatsouli et al.
(2011, 2014), the cumulative PWP for a general n>0 now becomes
PWP = pPCC + (1-p) (1-PPD), p = nPC/(1+ nPC) (3) where PC=1-PV is the proportion of consonants to all segments (consonants and vowels) in the targeted speech sample. It is seen that when n=1, (3) reduces to (2). Further, the weight of PCC, p, is an increasing function of nPC while the weight of PPD, 1-p, is a decreasing function of nPC. The numerical values of the two weights are depicted in Figure 1 for different values of nPC. It is seen that the weight of PCC is smaller than the weight of PPD for nPC values smaller than 1, the two weights are equal for nPC equal to 1, while the weight of PCC is larger than the weight of PPD for nPC values larger than 1. In Ingram’s proposition, n is equal to 1 and, therefore, the weight of PCC is always smaller than the weight of PPD, independent of the speech sample, as the proportion of targeted consonants, PC, to all targeted segments is smaller than 1.
Now, p, the weight of PCC, will be compared to the weight of the proportion of consonants deleted to the targeted consonants, for different values of n. To do this, PPD is written in terms of its two components, the proportion of consonants deleted to the targeted consonants, PCD, and the proportion of vowels deleted to the targeted vowels, PVD, as the sum of the following two products:
PPD = PCD (PC) + PVD (PV) (4)
Comparing the weight of PCC, p, to the weight of PCD, (1-p)PC, gives:
(1-p)PC/p = 1/n (5)
so that the weight of PCC is larger than the weight of PCD for any n larger than 1, it is equal to it for n equal to 1 (Ingram’s proposition), and it is smaller than it for any n smaller than 1. Therefore, the value of n affects the relative contributions of PCC and PCD in PWP as given by (5).
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0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
The weights in PWP
n PC