L3 French Voice-Onset Time at first exposure by Spanish-English bilinguals.

class: center, middle, inverse, title-slide

# L3 French Voice-Onset Time at first exposure by Spanish-English bilinguals.
## Phon & phon at AMU, Fall 2021
### Kyle Parrish
### Rutgers University

---

# Introduction

- Language learning in adulthood is difficult

- It is unclear how native-like an L2 speaker can become.

---

# Introduction

- Much less is known about L3 acquisition (L3A)

- L3 models attempt to predict acquisition patterns when 2 languages are available

- Complicating factors: 
 - Range of L2 ultimate attainment 
 - Language use and dominance 
 - Age effects 
 
- Key questions in L3A:

- Does just 1 language, or do both languages affect L3A? 
 - Are bilinguals better at learning languages than monolinguals?
 
???

The difficulty of learning a new language in adulthood has a well documented history.   
Much less is known about the acquisition of a third language (L3A)

Research in third language acquisition has attempted to model the interplay between L1 and L2 language systems and their cumulative influence in the process of the acquisition of a third.

mong questions asked by third language models is whether the L1 or L2, or a combination of both languages, serves as the basis in L3 acquisition.

This question is complicated in the context of multilingualism due to the widespread diversity in bilingual populations that include wide variation in ultimate attainment in adult L2 learners, and, in the case of phonological acquisition, wide variation in the production patterns of L2 segments

---

Question 1: Does just 1 language, or do both languages affect L3A? 
 
 Question 2: Are bilinguals better at learning languages than monolinguals

L3 models are guided by these questions.

- What do you think?

---

# Models

The **Cumulative Enhancement Model** (Flynn, Foley and Vinnitskaya, 2004)
  - Does just 1 language, or do both languages affect L3A? 
   - Both languages.
  -  Are bilinguals better at learning languages than monolinguals?
   - Yes.
   
--

- Evidence

---

# Models
   
The **L2 Status Factor** (Bardel & Falk, 2007)
  - Does just 1 language, or do both languages affect L3A? 
   - ONLY the L2 affects the L3 in the beginning
  - Are bilinguals better at learning languages than monolinguals?
   - No.

- Evidence

---

# Models   
  
The **Typological Primacy Model** (Rothman, 2011)
  - Does just 1 language, or do both languages affect L3A? 
   - Only 1 language affects the L3 - closest typological match. 
  - Are bilinguals better at learning languages than monolinguals?
   - No.

- Evidence

---

The **Linguistic Proximity Model** (Westergaard et al., 2017)
  - Does just 1 language, or do both languages affect L3A? 
   - Both
  - Are bilinguals better at learning languages than monolinguals?
   - Maybe.

- Evidence

---

# Literature Review

**Broad questions** 
 - How do language systems interact during L3 acquisition?
 
--

- Possible sources of **progressive transfer:** 
  - L1 alone 
  - L2 alone
  - combination of both languages

**Models**
- L3 models: predictions vary. 
 - TPM - closest typological language 
 - L2 Status Factor - L2 by default influences the L3.
 - LPM - either or both language may affect L3 productions.
 
--

**Previous Work**
- Work in L3 VOT production mixed:
  - L2 influence
  - Hybrid values 
  
---

# Literature Review

**Previous Work (cont)**

- A formal model of L3 phonological acquisition has not been proposed 
  - The expansion of L2 Speech models have been proposed 
    - SLM (Flege & Bohn, 2021)
    - PAM (Best & Tyler, 2007)
    - L2LP (van Leussen & Escudero, 2015)
 
- Cross-linguistic similarity of segments is predicted to determine the learnability of segments in a second language.

- In the case of L3 learners, two phonological systems exist to which the L3 segments could be compared.

- It is not well known how assimilation of L3 sounds occur with L1 and L2 categories.

---

# Literature Review

### How can the body of work to date be contributed to?

.pull-left[
- Low sample sizes in L3 work 
]

.pull-left[
- Few studies examine first exposure to the L3 
]

.pull-left[
- Proposal: **higher sample size of bilinguals at first exposure**
]
---

# Literature Review

.big[
- Cross-linguistic VOT
 - **Spanish** and **French** - true-voicing languages 
 - **English** - aspirating language 
]

---

# Methods

.pull-left[.big[
- **RQ:** When Spanish-English bilinguals produce French words at first exposure, will their VOT productions be more L1 or L2 like?  
]]

.pull-right[.big[
- **Predictions:** It is possible that hybrid values reported in the literature are due to sampling error or phonological acquisition - it was predicted that **L3 VOT would be practically equivalent to L2 VOT.**
]]

---
# Materials

**VOT measurements**
- French shadowing task

- English elicited Production task

- Spanish elicited Production task

**Language proficiency and background**
- Self-rating on a 1-7 scale

- Language Questionnaire

---

# Materials

.pull-left[
- **Stimuli**
 - Word initial stops of either one or two syllables, with stress on the initial syllable. 
 
 
- **Word lists**
 - *Spanish:* tiro, tema, talla, quiso, queja, cama, piso, pena, pato
 - *English:* tipping, teller, tacky, penny , pass, parrot, kitten, kennel, cabbage
 - *French:* tir, terre, tasse, quitte, quelle, pile, pere, patte
]

.pull-right[
- **Tokens for shadowing task**
 - Produced by a native French speaker
 - Mean relative VOT = 0.064, sd = 0.042
]

---

# Procedure

- The elicited production task and shadowing task were programmed in Labvanced, a browser based software designed for online research.

- All tasks were given in one session.

- Order of the languages was counterbalanced and the stimulus order was randomized.

- Words produced in isolation

---

# Participants

- A total of 76 participants took part in the experiment.

- The data of 37 participants were removed from the final data set, since these bilinguals did not produce distinct Spanish-English VOT values based on a t-test.

- Thus, the data of a total of **39** participants were included in the final analysis.

---

# Participants

- Participants were **L1 Mexican Spanish**, **L2 English** late bilingual speakers recruited from the online platform prolific.co

- **Location:** All participants were born and lived in Mexico at the time of the study.

- **Use:** Assumed to be primarily Spanish

- **Proficiency:** Self-rated + phonetic corroboration

- **Dominance:** Filtering location was intended to find Spanish-dominant speakers

- All participants reported not speaking or having studied a third language.

|Factor      |  Mean|   SD|
|:-----------|-----:|----:|
|AoA         | 11.90| 4.07|
|Current age | 22.74| 3.43|
|Proficiency |  5.26| 0.94|

---

# Data segmentation procedure

- Productions were force aligned using WebMaus and hand-corrected using a PRAAT script.

- VOT was marked at the closest zero-crossing to the onset of visible aspiration and the zero-crossing before before the onset of the vowel.

---

# Statistical Analysis

- All analyses were carried out in `R`

- **Sample size justification**: Power analysis

- **Inclusion and subsetting**: T.tests

- **Quantify the effect of language**: GLMM

- **Determine equivalence**: TOST

---
# Results - all participants

.pull-left[.tiny[
n = 39

![](index_files/figure-html/unnamed-chunk-5-1.png)

|language | Relative VOT|    SD|
|:--------|------------:|-----:|
|english  |        0.134| 0.057|
|french   |        0.090| 0.060|
|spanish  |        0.058| 0.033|
]]

.tiny[.pull-right[
<table style="border-collapse:collapse; border:none;">
<tr>
<th style="border-top: double; text-align:center; font-style:normal; font-weight:bold; padding:0.2cm; text-align:left; ">&nbsp;</th>
<th colspan="3" style="border-top: double; text-align:center; font-style:normal; font-weight:bold; padding:0.2cm; ">relative vot z</th>
</tr>
<tr>
<td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; text-align:left; ">Predictors</td>
<td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; ">Estimates</td>
<td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; ">CI</td>
<td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; ">p</td>
</tr>
<tr>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">(Intercept)</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">1.21</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">0.92&nbsp;&ndash;&nbsp;1.51</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&lt;0.001</td>
</tr>
<tr>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">language [french]</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;0.66</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;0.96&nbsp;&ndash;&nbsp;-0.36</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&lt;0.001</td>
</tr>
<tr>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">language [spanish]</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;1.27</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;1.56&nbsp;&ndash;&nbsp;-0.97</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&lt;0.001</td>
</tr>
<tr>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">text [p]</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;0.95</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;1.25&nbsp;&ndash;&nbsp;-0.65</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&lt;0.001</td>
</tr>
<tr>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">text [t]</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;0.69</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;0.99&nbsp;&ndash;&nbsp;-0.39</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&lt;0.001</td>
</tr>
<tr>
<td colspan="4" style="font-weight:bold; text-align:left; padding-top:.8em;">Random Effects</td>
</tr>

<tr>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; padding-top:0.1cm; padding-bottom:0.1cm;">&sigma;2</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left;" colspan="3">0.35</td>

<tr>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; padding-top:0.1cm; padding-bottom:0.1cm;">&tau;00 participant</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left;" colspan="3">0.14</td>

<tr>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; padding-top:0.1cm; padding-bottom:0.1cm;">N participant</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left;" colspan="3">39</td>

<tr>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; padding-top:0.1cm; padding-bottom:0.1cm;">N word</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left;" colspan="3">26</td>
<tr>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; padding-top:0.1cm; padding-bottom:0.1cm; border-top:1px solid;">Observations</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left; border-top:1px solid;" colspan="3">949</td>
</tr>
<tr>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; padding-top:0.1cm; padding-bottom:0.1cm;">Marginal R2 / Conditional R2</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left;" colspan="3">0.424 / 0.650</td>
</tr>

</table>
]]

---

# Averages per segment full dataset

|language |text | Relative VOT|    SD|
|:--------|:----|------------:|-----:|
|english  |k    |        0.160| 0.055|
|french   |k    |        0.148| 0.055|
|spanish  |k    |        0.086| 0.034|

|language |text | Relative VOT|    SD|
|:--------|:----|------------:|-----:|
|english  |t    |        0.134| 0.046|
|french   |t    |        0.078| 0.053|
|spanish  |t    |        0.046| 0.021|

|language |text | Relative VOT|    SD|
|:--------|:----|------------:|-----:|
|english  |p    |        0.109| 0.058|
|french   |p    |        0.063| 0.042|
|spanish  |p    |        0.041| 0.022|

---

# Results: L2 subset

.pull-left[.tiny[

Subsetting procedure: inconclusive French-English t.tests

**Hybrid values**  n = 23

![](index_files/figure-html/fig1-1.png)

|language | Relative VOT|     SD|
|:--------|------------:|------:|
|english  |       0.1304| 0.0559|
|french   |       0.1059| 0.0636|
|spanish  |       0.0585| 0.0341|
]]

.tiny[.pull-right[
<table style="border-collapse:collapse; border:none;">
<tr>
<th style="border-top: double; text-align:center; font-style:normal; font-weight:bold; padding:0.2cm; text-align:left; ">&nbsp;</th>
<th colspan="3" style="border-top: double; text-align:center; font-style:normal; font-weight:bold; padding:0.2cm; ">relative vot z</th>
</tr>
<tr>
<td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; text-align:left; ">Predictors</td>
<td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; ">Estimates</td>
<td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; ">CI</td>
<td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; ">p</td>
</tr>
<tr>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">(Intercept)</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">1.14</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">0.81&nbsp;&ndash;&nbsp;1.48</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&lt;0.001</td>
</tr>
<tr>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">language [french]</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;0.34</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;0.67&nbsp;&ndash;&nbsp;-0.02</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">0.038</td>
</tr>
<tr>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">language [spanish]</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;1.19</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;1.50&nbsp;&ndash;&nbsp;-0.87</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&lt;0.001</td>
</tr>
<tr>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">text [p]</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;0.96</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;1.28&nbsp;&ndash;&nbsp;-0.63</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&lt;0.001</td>
</tr>
<tr>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">text [t]</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;0.68</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;1.01&nbsp;&ndash;&nbsp;-0.36</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&lt;0.001</td>
</tr>
<tr>
<td colspan="4" style="font-weight:bold; text-align:left; padding-top:.8em;">Random Effects</td>
</tr>

<tr>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; padding-top:0.1cm; padding-bottom:0.1cm;">N word</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left;" colspan="3">26</td>
<tr>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; padding-top:0.1cm; padding-bottom:0.1cm; border-top:1px solid;">Observations</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left; border-top:1px solid;" colspan="3">561</td>
</tr>
<tr>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; padding-top:0.1cm; padding-bottom:0.1cm;">Marginal R2 / Conditional R2</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left;" colspan="3">0.398 / 0.659</td>
</tr>

</table>
]]

---

# L2 subset - Test of Equivalence

.pull-left[
![](index_files/figure-html/unnamed-chunk-13-1.png)

```
## TOST results:
## t-value lower bound: -0.0271 	p-value lower bound: 0.511
## t-value upper bound: -2.74 	p-value upper bound: 0.004
## degrees of freedom : 43.29
## 
## Equivalence bounds (Cohen's d):
## low eqbound: -0.4 
## high eqbound: 0.4
## 
## Equivalence bounds (raw scores):
## low eqbound: -0.024 
## high eqbound: 0.024
## 
## TOST confidence interval:
## lower bound 90% CI: -0.054
## upper bound 90% CI:  0.005
## 
## NHST confidence interval:
## lower bound 95% CI: -0.06
## upper bound 95% CI:  0.011
## 
## Equivalence Test Result:
## The equivalence test was non-significant, t(43.29) = -0.0271, p = 0.511, given equivalence bounds of -0.024 and 0.024 (on a raw scale) and an alpha of 0.05.
## Null Hypothesis Test Result:
## The null hypothesis test was non-significant, t(43.29) = -1.384, p = 0.174, given an alpha of 0.05.
## Based on the equivalence test and the null-hypothesis test combined, we can conclude that the observed effect is statistically not different from zero and statistically not equivalent to zero.
```
]

---

# Individual differences - L2 subset

![](index_files/figure-html/unnamed-chunk-14-1.png)

---

# Results: L1 subset

.pull-left[.tiny[

Subsetting procedure: p < .05 French-English t.tests

**Heavy L1 influence** n = 16

![](index_files/figure-html/fig2-1.png)

|language | Relative VOT|    SD|
|:--------|------------:|-----:|
|english  |        0.140| 0.058|
|french   |        0.066| 0.046|
|spanish  |        0.057| 0.032|
]]

.tiny[.pull-right[
<table style="border-collapse:collapse; border:none;">
<tr>
<th style="border-top: double; text-align:center; font-style:normal; font-weight:bold; padding:0.2cm; text-align:left; ">&nbsp;</th>
<th colspan="3" style="border-top: double; text-align:center; font-style:normal; font-weight:bold; padding:0.2cm; ">relative vot z</th>
</tr>
<tr>
<td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; text-align:left; ">Predictors</td>
<td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; ">Estimates</td>
<td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; ">CI</td>
<td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; ">p</td>
</tr>
<tr>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">(Intercept)</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">1.31</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">0.96&nbsp;&ndash;&nbsp;1.66</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&lt;0.001</td>
</tr>
<tr>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">language [french]</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;1.13</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;1.43&nbsp;&ndash;&nbsp;-0.82</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&lt;0.001</td>
</tr>
<tr>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">language [spanish]</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;1.39</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;1.71&nbsp;&ndash;&nbsp;-1.07</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&lt;0.001</td>
</tr>
<tr>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">text [p]</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;0.94</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;1.23&nbsp;&ndash;&nbsp;-0.65</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&lt;0.001</td>
</tr>
<tr>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">text [t]</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;0.70</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;0.99&nbsp;&ndash;&nbsp;-0.41</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&lt;0.001</td>
</tr>
<tr>
<td colspan="4" style="font-weight:bold; text-align:left; padding-top:.8em;">Random Effects</td>
</tr>

<tr>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; padding-top:0.1cm; padding-bottom:0.1cm;">&tau;11 participant.languagefrench</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left;" colspan="3">0.04</td>

<tr>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; padding-top:0.1cm; padding-bottom:0.1cm;">&tau;11 participant.languagespanish</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left;" colspan="3">0.10</td>

<tr>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; padding-top:0.1cm; padding-bottom:0.1cm;">&rho;01 participant.languagefrench</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left;" colspan="3">-1.00</td>

<tr>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; padding-top:0.1cm; padding-bottom:0.1cm;">&rho;01 participant.languagespanish</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left;" colspan="3">-1.00</td>

<tr>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; padding-top:0.1cm; padding-bottom:0.1cm;">N word</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left;" colspan="3">26</td>
<tr>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; padding-top:0.1cm; padding-bottom:0.1cm; border-top:1px solid;">Observations</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left; border-top:1px solid;" colspan="3">388</td>
</tr>
<tr>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; padding-top:0.1cm; padding-bottom:0.1cm;">Marginal R2 / Conditional R2</td>
<td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left;" colspan="3">0.657 / NA</td>
</tr>

</table>
]]
---

# L1 subset - Test of Equivalence

.pull-left[
![](index_files/figure-html/unnamed-chunk-17-1.png)

```
## TOST results:
## t-value lower bound: 1.77 	p-value lower bound: 0.044
## t-value upper bound: -0.496 	p-value upper bound: 0.312
## degrees of freedom : 26.6
## 
## Equivalence bounds (Cohen's d):
## low eqbound: -0.4 
## high eqbound: 0.4
## 
## Equivalence bounds (raw scores):
## low eqbound: -0.0159 
## high eqbound: 0.0159
## 
## TOST confidence interval:
## lower bound 90% CI: -0.015
## upper bound 90% CI:  0.033
## 
## NHST confidence interval:
## lower bound 95% CI: -0.02
## upper bound 95% CI:  0.038
## 
## Equivalence Test Result:
## The equivalence test was non-significant, t(26.6) = -0.496, p = 0.312, given equivalence bounds of -0.0159 and 0.0159 (on a raw scale) and an alpha of 0.05.
## Null Hypothesis Test Result:
## The null hypothesis test was non-significant, t(26.6) = 0.635, p = 0.531, given an alpha of 0.05.
## Based on the equivalence test and the null-hypothesis test combined, we can conclude that the observed effect is statistically not different from zero and statistically not equivalent to zero.
```
]

---
# Individual Differences - L1 subset

![](index_files/figure-html/unnamed-chunk-18-1.png)

---

# Post-hoc analyses

Table: Effect sizes of each subset per language pairing

|  X| t.test| eff_size| ci_low|  ci_hi|pair            |set          |
|--:|------:|--------:|------:|------:|:---------------|:------------|
|  1|  0.000|    3.360|  2.308|  4.412|English-Spanish |L1 subset    |
|  2|  0.000|    2.888|  1.919|  3.856|English-French  |L1 subset    |
|  3|  0.160|   -0.479| -1.166|  0.208|French-Spanish  |L1 subset    |
|  4|  0.000|    2.480|  1.855|  3.105|English-Spanish |L2 subset    |
|  5|  0.002|    0.769|  0.282|  1.257|English-French  |L2 subset    |
|  6|  0.000|   -1.788| -2.344| -1.232|French-Spanish  |L2 subset    |
|  7|  0.000|    2.739|  2.208|  3.270|English-Spanish |full dataset |
|  8|  0.000|    1.236|  0.820|  1.652|English-French  |full dataset |
|  9|  0.000|   -1.258| -1.675| -0.840|French-Spanish  |full dataset |
---

# Post-hoc analyses

![](index_files/figure-html/unnamed-chunk-20-1.png)

---

# Limitations

.big[
- A rich background questionnaire was not taken.

- Subset results may be sampling error.

- These individual differences could be explored in future research.
]

---

# Discussion and Conclusions

- Participants are primarily influenced by one of their source languages but to different degrees

- L1 influence, L3 VOT ~ L1 values, 
 - L2 influence, L3 VOT values fell between L1 and L2 values
 
--

Table: Post-hoc power anlyses

| power|subset      |pairing         |
|-----:|:-----------|:---------------|
|   100|L1 subset   |English-Spanish |
|   100|L2 subset   |English-Spanish |
|   100|Full subset |English-Spanish |
|    18|L1 subset   |French-Spanish  |
|   100|L2 subset   |French-Spanish  |
|    80|Full subset |French-Spanish  |
|   100|L1 subset   |French-English  |
|    45|L2 subset   |French-English  |
|    91|Full subset |French-English  |

---

# Discussion and Conclusions

- Statistical power > .8

- First exposure bilinguals allow for the teasing apart of facilitative influence of a previously known language and phonological acquisition.

- **Future project:** 
 - Perception task - PAM phoneme categorization task.
 - Same group, but an aspirated L2, such as German.

---

# Future directions and questions

- If the L3 stimulus were more L2-like

- Detailed case studies
 
---

# Future directions and questions

- Phonetics or language influence?

.pull-left[
![](index_files/figure-html/unnamed-chunk-22-1.png)
]

.pull-right[
![](index_files/figure-html/unnamed-chunk-23-1.png)
]