Inferential statistics

No obvious differences in durations are noted between genders, as they show almost the same pattern of vowel durations (for inferential statistics, see the next section). The results in Figure 5.3 show great consistency for the vowel sequence based on duration. Moreover, all PA participants kept the lax/short and tense/long vowels clearly separated, as the lax vowels were produced with obviously shorter durations than tense vowels, as the AE natives would do, especially for the PA female participants.

This can be expected given that Arabic has a short-long contrast in the vowel inventory.

Similar findings, however, have been reported in other EFL studies with L1s that do not have a length contrast in their vowel systems (e.g., Perwitasari, 2019 for Sundanese and Javanese learners of American English).

types × 3 tokens), which yields too small a sample of speakers for a sufficiently powerful statistical analysis. Empty cells in the data matrix were therefore reduced by aggregating (i.e., averaging over) the nominally two /hVd/ tokens. This decreased the nominal number of datapoints by one-third, i.e., to 440 /hVd/ (6 missing data points, or 1%) and an equal number of /CVd/ points (19 missing, or 4%). The 25 remaining missing data points (= 3%) were restored by noniterative two-dimensional imputation. I computed the marginal means for rows (=

speakers) and columns (= vowels), separately for the two contexts (/CVd/ keywords, /hVd/

targets) in the data matrix, skipping the cells with missing values. I then determined per speaker, per vowel, and per context how much the marginals deviated from the grand mean and then replaced the empty cell by the grand mean plus the deviation in the three dimensions. The imputed values were thus equal to what would be predicted by linear addition of the speaker effect, the vowel, and the context effect with no adjustment for possible interactions. Through this imputation, the mean values of speakers, vowels and contexts are the same in the original dataset with missing values and in the restored dataset. In the remaining statistical analyses, the restored dataset will be used. The analyses will be graphically illustrated with interaction diagrams. Full numerical data underlying the breakdowns in the graphs can be found in Appendix 5.4. Table 5.3 summarizes the RM-ANOVAs for F1 frequency (after conversion to Bark), F2 frequency (in Bark), and Vowel duration.

Table 5.3. Summary of RM-ANOVA. The dependent variables are F1, F2, and vowel duration. Within-participant factors are Vowel type and Context (/hVd/, /CVd/). The between-Within-participant factor is Gender of speaker. All main effects and interactions are listed. Nominal degrees of freedom are reported, but p-values were

computed after Greenhouse-Geiser correction (ɛ correction coefficient is specified). Significant effects and interactions (α = .050) are in highlighted cells. When the effect size pη² ≥ .100, the cell entry is also bolded.

Tests of Within-Subjects Effects First formant Second formant Duration

Effect/Interaction df1, 2 F p pη² F p pη² F p pη²

Vowel 10, 380 274.5 < .001 .878 599.5 < .001 .940 79.1 < .001 .675

ɛ = .630 ɛ = .423 ɛ = .464

Vowel * Gender 10, 380 4.1 < .001 .098 1.9 .103 .048 1.2 .294 .032

ɛ = .654 ɛ = .659 ɛ = .324

Context 1, 38 .1 .775 .002 17.5 < .001 .315 29.9 < .001 .440 Context * Gender 1, 38 .3 .573 .008 .7 .418 .017 13.9 .001 .268 Vowel * Context 10, 380 8.6 < .001 .185 9.8 < .001 .205 3.5 .016 .084 Vowel * Context * Gender 10, 380 1.5 .176 .038 .6 .771 .015 1.3 .275 .033 Tests of Between-Subjects Effect

Gender 1, 38 75.2 < .001 .664 200.0 < .001 .840 .7 .419 .017 Table 5.3 specifies all possible main effects and interactions, separately for the within -speaker and between--speaker terms. In none of the three analyses was the condition of sphericity met, so I used the Greenhouse–Geisser correction of degrees of freedom as a safety

precaution. In the table, however, I list the nominal degrees of freedom (for the sake of clarity);

the p-values listed were computed after GG-correction. Except for one, all factors in the RM-ANOVA are dichotomies, which require no post-hoc analyses for multiple contrasts. Vowel type, however, has 11 levels, which were tested pairwise by post-hoc t-tests with Bonferroni correction for multiple comparisons. My criterion for significance is α = .050; however, to avoid having to factor in small effects, I made the additional requirement that the effect or interaction should have an effect size of partial eta squared (pη²) of at least .100. All significant effects/interactions are highlighted in the table; they are additionally bolded if the pη² requirement is met.

First formant (F1). The effect of Vowel is significant. Bonferroni post-hoc tests indicate that the four (half-)close vowels /i, ɪ, u, ʊ/ have the same F1; so do the semi-diphthongs /e, o/, and the pair /ɑ, ʌ/. The F1 of /ɛ/ and /æ/ differ significantly from one another as well as from any other vowel.

Context has no effect on F1 and does not interact with Gender. However, Context interacts with Vowel. The third-order interaction between Vowel, Context, and Gender is insignificant.

Female speakers have higher F1 values than males because they have smaller/shorter resonance cavities, so the Gender effect is predictably significant. Additionally, the Vowel-by-Gender interaction is significant but does not reach the pη² ≥ .100 criterion, so that this interaction will be ignored. Figure 5.4 plots the F1 center frequency for the 11 vowels broken down by Gender (row panels) and by Context (column panels). The vowels are ordered from left to right in descending order of F2 frequency as they were found in the AE control data (i.e., I used the same axis layout as in Figure 5.5, which plots F2).

Figure 5.4. Center frequency of F1 (Bark) for 11 American English monophthongs pronounced by 20 male and 20 female Palestinian Arabic learners of English as a foreign language. Error bars are the 95% confidence intervals of the speaker means. Tokens were produced in /CVd/ everyday keywords (panel A) or in /hVd/

context (panel B). Vowels are ordered by descending F2 as determined for a control sample of 20 native speakers of American English.

Post-hoc tests with Bonferroni correction for multiple comparisons (α = .050) show that 4 subsets should be distinguished within which vowels do not differ from each other in terms of F1 (in ascending order of F1): /i, u¹, ʊ^1,2, ɪ^1,2,3, ɛ^2,3, e^2,3, o³, ɔ⁴, ɑ⁴, ʌ, æ/. Vowels with the same superscript number do not differ significantly from one another. Subsets may overlap, e.g., /ɪ/

is a member of three partially overlapping subsets: {u, ʊ, ɪ}, {ʊ, ɪ, ɛ, e}, {ɪ, ɛ, e, o}. The vowels /i, ʌ, æ/ differ significantly from each other and from all other vowels.

The effect of Context is very small visually and can be seen only for the open vowels /æ, ɑ, ʌ/, whose somewhat discrepant F1 in the two contexts would explain the significant Vowel-by-Context interaction.

Second formant (F2). Figure 5.5 plots the F2 center frequency for the 11 vowels broken down by Gender and Context. The vowels are ordered from left to right in descending magnitude of F2 as found in the AE control data.

Figure 5.5. Center frequency of F2 (Barks) for 11 English monophthongs pronounced in /hVd/ words and in rhyming everyday keywords (/CVd/) by Palestinian Arabic EFL learners, broken down by Gender and by Context. Error bars include the 95% confidence interval of the speaker means. Vowels are ordered from left to

right by descending F2 as found for American control data.

The effect of Vowel is very strong. Post-hoc comparisons show that all vowels differ significantly from each other in terms of F2, with the exception of two nonoverlapping subsets, {ʊ, ʌ, ɑ} and {ɔ, u, o}, within which the members do not differ from one another (listed here in descending order of F2): /i, e, ɪ, ɛ, æ, ʊ¹, ʌ¹, ɑ¹, ɔ², u², o²/. Gender is a predictably significant effect (see above). Additionally, the Vowel × Gender interaction reaches significance. Context exerts a small (but significant) effect on F2. Finally, the Vowel × Context interaction reaches significance. No other effects or interactions were found to be significant. Interactions between the main effects (even when significant) are hardly noticeable. There are only two effects that are of importance: the effect of Vowel and the effect of Gender. The Vowel effect is what I am interested in. The effect of Gender will be neutralized in subsequent analyses through

z-transformation within speakers (Lobanov normalization). The effect of Context (11.56 Bk for /hVd/ vs 11.66 Bk for /CVd/), even though significant, is indeed very small (± .05 Bark). The automatic classification in the next section will be performed on the /hVd/ tokens only, since this is the only context for which I have native control data (Wang & Van Heuven, 2006). Note that, in contradistinction to the American native control speakers, the PA EFL learners produce a small but significant F2 difference between the vowels /ɑ, ɔ/.

Duration. The effect of Vowel was highly significant. Bonferroni post-hoc pairwise comparisons bear out that in the ascending order of duration /ɪ, ɛ¹, ʌ¹, ʊ, i², ɑ², u², o^2,3, æ³, e⁴, ɔ⁴/ there are four subsets within which the vowels do not differ significantly in duration. It should be highlighted that each of the four lax vowels is significantly shorter than any of the phonetically tense vowels. This finding suggests that duration is used by the EFL learners to differentiate lax /ɪ, ɛ, ʌ, ʊ/ from their spectrally nearest (overlapping, see Figure 5.4) tense competitors /e, ɑ, o/.

Vowel durations do not differ significantly between male and female speakers. There is no interaction between Gender and Vowel, nor is there interaction between Gender and any other factor. Target vowels are pronounced longer in everyday keywords (103 ms) than in /hVd/ items (93 ms). Moreover, the Context interacts with the Vowel type. Figure 5.6 shows the interaction.

Although there is no second-order interaction between Gender and Vowel duration, there is a remarkable third-order interaction by which the female speakers produce longer vowel durations for the tense vowels (and the males’ shorter durations) in the everyday keywords (/CVd/ context) than in the /hVd/ targets (in the latter context, male and female speakers produce equally long durations for each vowel type). This interaction fails to reach significance (see Table 5.3), probably because the second-order interaction between Context and Gender explains the variance, while the male and female tense vowel durations have overlapping confidence intervals even though they differ by some 20 ms. The breakdown of vowel duration by Vowel type, Gender of speaker and Context is shown in Figure 5.6.

Figure 5.6. Vowel duration (ms) for eleven American English monophthongs produced by male and female Palestinian Arabic learners of English as a foreign language. The vowels are arranged in ascending order of

diration as found for 20 American native control speakers. See Figure 5.5 for more information.