Quantitative Analysis: Relationships between variables Sebastian M. Rasinger Quantitative Research in Linguistics. An Introduction 2 nd edition. 2013.

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Quantitative Analysis: Relationships between variables Sebastian M. Rasinger Quantitative Research in Linguistics. An Introduction 2 nd edition London: Bloomsbury S.M.Rasinger Quantitative Research in Linguistics. 2e. Bloomsbury.

Relationships between variables Are the two variables X and Y related in any way? Is learner’s age related to their language learning? Are younger learners better learners? S.M.Rasinger Quantitative Research in Linguistics. 2e. Bloomsbury.

Causal relationships Causal relationships must fulfil 3 criteria: 1.X and Y must correlate 2.There is a chronological order between X and Y, e.g. Y follows X or X follows Y 3.The relationship between X and Y does not disappear when controlling for third variables S.M.Rasinger Quantitative Research in Linguistics. 2e. Bloomsbury.

Causal relationships (2) Example: Age-effect on learner’s L2 attainment – possible 3 rd variables – Lengths of residence – Exposure, integration/assimilation – Motivation – (general cognitive abilities) S.M.Rasinger Quantitative Research in Linguistics. 2e. Bloomsbury.

Pearson Correlation Statistical instrument to see whether 2 variables correlate NO information about causality!!!! EXCEL: =correl(array1, array2) -1 ≤ 0 ≤ 1 1 = perfect positive correlation: with every unit increase of X, 1 unit increase of Y -1: perfect negative correlation. With every increase in X, 1 unit decrease in Y S.M.Rasinger Quantitative Research in Linguistics. 2e. Bloomsbury.

Example: Correlation RespondentScore AScore B A71 B86 C68 D27 E24 F43 G35 H69 I58 J97 Correlation coefficient R=0.133 S.M.Rasinger Quantitative Research in Linguistics. 2e. Bloomsbury.

Correlation example (2) S.M.Rasinger Quantitative Research in Linguistics. 2e. Bloomsbury.

For non-parametric data Spearman rank correlation: – -1<rho<1 – Uses ranks instead of actual values – Loss of detail Kendall’s tau – -1<tau<1 – Good for very small data sets S.M.Rasinger Quantitative Research in Linguistics. 2e. Bloomsbury.