An introduction to third language acquisition

class: center, middle, inverse, title-slide

# An introduction to third language acquisition
## One Mind Two Languages: Fall 2021
### Kyle Parrish
### Rutgers UniversityFall 2021Last update: 2021-11-22

---

# Introduction

.big[
- **Third Language Acquistion** is the process of learning a language by someone who already knows 2 languages. 
]

.big[
- 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 
 
???

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

---

# Questions

.big[
 **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? 
 
 - Take a few moments to write down your hypotheses to both queations.

---

# Models

.big[
The **Cumulative Enhancement Model** (Flynn, Foley and Vinnitskaya, 2004)
]

.pull-left[
L3 learners will can draw on **both languages** they know during L3A.

Both languages are helpful.

**Q1:** Does just 1 language, or do both languages affect L3A? 
   
   Both languages.
  
**Q2:** Are bilinguals better at learning languages than monolinguals?

Yes.
]

.pull-right[
## Evidence:

L3 English influenced by **L2** (L1 Kazakh-L2 Russian) Flynn et al. (2004)

L3 English influenced by **L1** (Hungarian L1-German L2) Berkés and Flynn (2012) 
]

---

# Models

.big[
The **L2 Status Factor** (Bardel & Falk, 2007)
]

.pull-left[
L2 will influence the L3

**Q1:** Does just 1 language, or do both languages affect L3A?

ONLY the L2 affects the L3 in the beginning.

**Q2:** Are bilinguals better at learning languages than monolinguals?

No
]

.pull-right[
## Evidence (Bardel and Falk, 2007)

Word order in the L3

**Group 1:** L1 Non-Germanic L2 Germanic L3 Germanic

**Group 2:** L1 Germanic L2 Non-Germanic L3 Germanic

Groups behaved **differently** - Group 1 outperformed group 2 
 - Group 1: target like L3 word order 
 - Group 2: L2 and non-target like L3 word order 
]

---

# Models   
  
.big[  
The **Typological Primacy Model** (Rothman, 2011)
]

.pull-left[
Similarity between languages determines influence

One language influences the L3 holistically

**Q1:** Does just 1 language, or do both languages affect L3A?

Only 1 language affects the L3 - closest typological match. 
   
**Q2:** Are bilinguals better at learning languages than monolinguals?

No.
]

.pull-right[
## Evidence (Rothman, 2011)

Similar adjective placement in two groups

L1 Italian-L2 English-L3 Spanish

L1 English-L2 Spanish-L3 Brazilian Portuguese (BP)
]

---

# Models

.big[
The **Linguistic Proximity Model** (Westergaard et al., 2017)
]

.pull-left[
Activation of **both languages** causes the L3 values to fall between L1 and L2 values.

**Q1:** Does just 1 language, or do both languages affect L3A?

Both

**Q2:** Are bilinguals better at learning languages than monolinguals?

Maybe.
]

.pull-right[
## Evidence (Westergaard et al., 2017)

Word order in L3 English

Norwegian-Russian bilinguals with L3 English

L1 Norwegian L2 English

L1 Russian L2 English

Accuracy: 1st L1 Russian L2 English

2nd Norwegian-Russian bilinguals 
            
3rd L1 Norwegian L2 English
]

---

# VOT Study

.big[
- I conducted a study to test how Spanish-English bilinguals pronounce French words at first exposure.  
]

.big[
- Specifically, they pronounced words beginning in /p/, /t/ or /k/ in all three languages.

- I measured Voice-onset time to compare productions between languages.
]

.med[
- Voice-onset time (VOT) is a phonetic measure of duration in milliseconds that distinguishes consonants (such as /p/ from /b/) in many of the world's languages 
]

.med[
- Cross-linguistic VOT
 - **Spanish** and **French** - similar production of /ptk/
 - **English** - longer VOT and aspiration of /ptk/
]

---

# 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

.big[
**VOT measurements**
- French shadowing task

- English word reading task

- Spanish word reading task 
]

---

# Procedure

---

# Participants

.big[
39 participants were **L1 Mexican Spanish**, **L2 English** late bilinguals
]

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

---

# Results - all participants

.pull-left[.tiny[
n = 39

![](talk_slides_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

![](talk_slides_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[
![](talk_slides_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

![](talk_slides_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

![](talk_slides_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[
![](talk_slides_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

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

---

# Discussion and Conclusions

.big[
- Participants are primarily influenced by one of their source languages but to different degrees
]

.big[
 - L1 influence, L3 VOT ~ L1 values, 
 - L2 influence, L3 VOT values fell between L1 and L2 values
]

---

# Discussion and Conclusions

.big[.pull-left[
- Which model do these results support?

- Are the conclusions different for the group level and the individual level?

- Have your answers to question 1 and question 2 changed? 
]]

.big[.pull-right[
**Q1:** Does just 1 language, or do both languages affect L3A?

**Q2:** Are bilinguals better at learning languages than monolinguals?
]]