The current project considers three member (i.e., trigram) sequences of a word as cues and the word as the outcome. For example, Someone pronounced the word “ask” as [æsk], then the lexical outcome is the word “ask”, while its cues are #æs, æsk, sk#, where the “#”s represent word boundaries. Another person might pronounces the word “ask” as [æks], then the lexical outcome is still the word “ask”, but the cues are #æk, æks, ks#.
We have speech data from 100 native English speakers. Most native speakers pronounced “ask” as [æsk], while only a few of them pronunced it as [æks]. In other words, the trigram sk# is more common in native speech in the environment of “ask”, than trigram ks#. The association strength from cue sk# to the outcome is therefore stronger than the association strength from ks# to the outcome.
We used the estimateWeight() function in the ndl package to calculate the association strengths.The function was based on the Dank (2003)’s equilibrium equation.
Table 1 shows the results for “ask” and “her”
| Outcomes | Cues | Association_Strength |
|---|---|---|
| ask | #æk | 0.166 |
| ask | æsk | 0.167 |
| ask | sk# | 0.667 |
| her | #ɚ# | 1.000 |
| her | #hɚ | 0.500 |
| her | hɚ# | 0.500 |
Table 1 shows that “sk#” has a higher association strength than “#æs” or “æsk”. It is understandable given the fact that the selected 100 native American English speakers did not always pronounce the “a” in “ask” as /æ/. They do, however, almost always pronounce the “sk” in “ask” as /sk/. In other words, the pronunciations of “a” is more variable than pronunciations of “sk”.
Given the calculated associated strengths, the association strength from [æsk.ɚ] to the outcome “ask her” is 1.000, which is calculated by summing up association strengths of all the trigram cues (i.e. #æs, æsk, sk#, #ɚ#) and then divide it by the number of words, which is two in this case.
For L2 productions containing cues that are not observed in native speech data, the association strengths for the unobserved cues were defined as 0. For example, L2 production [ask.hɚ] contains cues #as, ask, sk#, #hɚ, hɚ#. Since “#as” and “ask” do not exist in native speech data, their association strengths are therefore considered 0. The association strength from [ask.hɚ] to its outcome “ask her” is therefore
\[(0+0+0.667+0.500+0.500)\div{2} = 0.834\]
The association strength for an L2 production could therefore be intuitively interpreted as how much the L2 production meets the native standard or how much the L2 production resembles its L1 target production. For example, [ask.hɚ] resembles 83.4% of a typical L1 production for “ask her”.
Suppose we have a native speaker who pronounced “ask her” as [æks ɚ]. The trigram cues #æk, æks, ks# do not exist in native data. Their association strengths to the outcome “ask” are therefore 0. Only #ɚ# was observed in native data, whose association strength is 1.00. The association strength from [æks ɚ] to the lexical outcome is only 0.500 \[(0+0+0+1.000)\div{2} = 0.500\]
However, we know that some native speakers do pronounce “ask” as [æks]. Does this mean the calculation failed?
No. I used only 50 native speakers to build the native speaker model. It just so happened that none of the 50 native speakers I picked pronunced “ask” as [æks]. Therefore, we need more native speakers.
For this project, I actually extracted data from 100 native speakers. However, it is not desirable to include all the 100 native speakers in the model, because such treatment will increase the chance of overfitting.
I therefore opted to run the model estimation for 100 times. Each time, a different set of 50 native American English speakers would be randomly chosen to build a slightly different native production model, which would generate a slightly different association strength for each trigram cue. Consequently, the phonological similarity between an L2 production to its L1 target was slightly different each time the model estimation was run. The averaged phonological similarity scores across 100 runs were recorded for further analysis as approximations for dsimilarity.
By running the model estimation 100 times and getting the mean similarity score, we found that the mean similarity score for [æks ɚ] is 0.905, while the similarity score for [ask hɚ] is 0.831. The results indicate that [æks ɚ] is actually more nativelike than [ask hɚ].
You could try the online calculator here !
Thank you for reading through the whole thing! Let me know what you think!