Abstract
This chapter presents the third of seven studies examining lexical facility as a second language vocabulary construct. Study 3 examines the sensitivity of the lexical facility measures (VKsize, mnRT, and CV) to score differences across five adjacent IELTS bands (5–7). The data were obtained from students in an Australian university foundation-year program.
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Notes
- 1.
The original number of participants was 371. However, 27 of these had false-alarm rates exceeding 50%, including several around 75%. These cases, mostly from the 5 and 5.5 bands, were removed from the analysis, leaving a total sample of N = 344.
- 2.
The false-alarm data depart markedly from a normal distribution, given that some participants had few-to-none false alarms. A Kruskal–Wallis test was run to test for the equality of the group false-alarm means. There was a significant difference (at p < .001) between the groups, χ 2 = 36.89, p < .001, η 2 = .07 (Lenhard and Lenhard 2014). A follow-up Mann–Whitney test of the pairs showed that the 5, 5.5, and 6 bands were not significantly different. Bands 6 and 6.5 were significantly different, U = 871, p < .001, d = .53, as were bands 6 and 7+, U = 459, p < .001, d = 1.05. Bands 6.5 and 7 were not significantly different.
- 3.
Statistical significance is set at the conventional p < .05, and strength of the difference is reported in effect size measures. The effect size for the omnibus ANOVAs is eta-squared (η 2). The ‘real-world’ interpretation of η 2 is based on Plonsky and Oswald (2014, p. 889), with .06 considered small, .16 medium, and .36 large. The effect size for the post hoc comparisons is Cohen’s d. It is interpreted as .40 being small, .70 medium, and 1.0 large.
- 4.
The first assumption for hierarchical regression is that the criterion variable is continuous. The criterion here is the five IELTS band-score levels. In the analysis, they are treated as continuous scores, though the small range of five levels might make this a questionable assumption for some. The data met the other assumptions for the use of the regression procedure. There was independence of residuals, as assessed by a Durbin–Watson statistic of 1.64. Scatterplot analyses indicated that a linear relationship exists between the three predictor variables collectively and individually. A visual inspection of the P–P plot showed the standardized residuals to be approximately normally distributed, while the residual plots indicated that the data met the homoscedasticity assumption. Tolerance values of around .9 showed no problem with multicollinearity.
References
Lenhard, W., & Lenhard, A. (2014). Calculation of effect sizes. Retrieved November 29, 2014, from http://www.psychometrica.de/effect_size.html
Plonsky, L., & Oswald, F. L. (2014). How big is “big”? Interpreting effect sizes in L2 research. Language Learning, 64, 878–912. doi:10.1111/lang. 12079.
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Harrington, M. (2018). Lexical Facility and IELTS Performance. In: Lexical Facility. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-137-37262-8_8
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DOI: https://doi.org/10.1057/978-1-137-37262-8_8
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