Fig 1.
Schematic representations of L2 proficiency (vertical axis) declining over AoA (horizontal axis). Only Panels B and C support a potential ‘critical period’, because of the presence of a discontinuity in the AoA function. Figure taken from [36].
Fig 2.
Group differences in multiple aspects of the ERP signal.
An example of how ERP signatures can differ between groups (in this case native speakers, beginning and intermediate L2 learners). We see variation in form, latency and amplitude of parts of the ERP wave across these groups. It is difficult to objectively capture these differences in a traditional analysis, which is often artificially limited to time windows. Figure taken from [23].
Fig 3.
Example of a basis function: a cubic regression spline.
A cubic regression spline is a non-linear curve constructed from sections of cubic polynomials joined together so that the curve is continuous. The cubic regression spline shown (dotted curve) is made up of seven sections of cubic polynomials (solid lines). The points at which they are joined (and the two end points) are known as the ‘knots’ of the spline. Figure taken from [43].
Table 1.
Means (and ranges) of participant characteristics, scores on proficiency measures, and significance of between-group comparisons (Mann-Whitney U test).
Table 2.
Example materials of the EEG experiment.
Fig 4.
Location of the electrodes and ROI.
Approximate location of the EEG recording sites and the central-posterior region of interest used for analysis.
Fig 5.
Accuracy on (behavioral) grammaticality judgments made during the EEG recording session.
Performance in percentage of accurate responses is plotted separately for each level of group (learners, natives), structure (verb, gender) and grammaticality (grammatical, ungrammatical).
Table 3.
Results summary of the mixed-effects logistic regression analysis of the AoA effect in the grammaticality judgments task.
Fig 6.
Waveforms show the ERP signal averaged over the electrodes in the central-posterior region of interest (see Fig 4) for natives and learners. The green lines represent the average response to grammatical targets, the red lines show the response to violations. Underneath the waveform graphs, voltage maps are plotted, which show the scalp topography of the effect in the difference wave (i.e. mean amplitude in ungrammatical minus grammatical condition) in the 0–500, 500–1000 and 1000–1400 ms time window. The scalp topographies are visualized looking down on the head (i.e. the location of the nose is at the top), with positive differences in red, negative differences in blue, and green representing no difference. A traditional group split divides learners into early (7–16) and late (17–36) age of onset of acquisition groups. Both natives and learners show P600 effects for non-finite verb agreement. Only early learners show the same effect for gender agreement, whereas late learners do not show sensitivity for gender violations.
Fig 7.
The effect of AoA on the average ERP signal.
The figure shows the average magnitude of the difference wave per individual (x-axis), against that individual’s AoA (y-axis). This magnitude was calculated by taking the ERP signal per condition, averaged over the electrodes in the central-posterior region of interest (see Fig 4) using the mean amplitude in the 500–1200 ms time window, to calculate the difference between the individual’s response to ungrammatical versus grammatical targets. The plots reveal a weak correlation between AoA and the magnitude of the grammaticality effect in the gender condition (r(64) = -0.32, p = .009), but no effect in the verb condition (r(64) = 0.03, p = .825).
Table 4.
Summary of the results of the GAM model for the effects of time and AoA, for verb and gender violations.
Fig 8.
Visualization of the GAM model for the effects of time and AoA on the difference wave, for the verb (Panel A) and gender (Panel B) condition.
First, the individual smooths and surfaces for the additive effects of time (Panels A1 and B1), AoA (Panels A2 and B2) and their pure interaction (Panels A3 and B3) are plotted separately. These are followed by a plot that summarizes all these effects together (the ‘full effect’ plots, Panels A4 and B4). After taking out the main effect of time, the effect of AoA is not significant on its own, for either verb or gender, but only in interaction with time (see Table 4). These adjustments to the general time pattern match the complexity of the AoA effects on timing, slope and polarity of the ERP components seen in the ‘full effect’ plots: In the verb condition, we see a P600 effect across all AoAs, with only minor adjustments to amplitude, onset and duration of this component for earlier vs. later learners. For gender, there is a diminishing P600 effect for early AoAs and instead a negativity that peaks around 500 ms for later AoAs.
Fig 9.
The effect over time on the ERP signal for learners with an AoA of 10, 20 and 30 for verb and gender violations.
These plots present an alternative visualization of the two-dimensional ‘full effect’ surfaces of Fig 8: AoA values, which were represented on the y-axis in Fig 8 Panels A4 and B4, are now represented by three separate plots for particular AoA values, with microvoltage on the y-axis. The gradual transitions towards different AoAs illustrate the continuity of the effect.