1. Quantitative Analysis: Relationships between variables Sebastian M. Rasinger Quantitative Research in Linguistics. An Introduction 2 nd edition. 2013. London: Bloomsbury S.M.Rasinger. 2013. Quantitative Research in Linguistics. 2e. Bloomsbury.

2. 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. 2013. Quantitative Research in Linguistics. 2e. Bloomsbury.

3. 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. 2013. Quantitative Research in Linguistics. 2e. Bloomsbury.

4. 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. 2013. Quantitative Research in Linguistics. 2e. Bloomsbury.

5. 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. 2013. Quantitative Research in Linguistics. 2e. Bloomsbury.

6. Example: Correlation RespondentScore AScore B A71 B86 C68 D27 E24 F43 G35 H69 I58 J97 Correlation coefficient R=0.133 S.M.Rasinger. 2013. Quantitative Research in Linguistics. 2e. Bloomsbury.

7. Correlation example (2) S.M.Rasinger. 2013. Quantitative Research in Linguistics. 2e. Bloomsbury.

8. 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. 2013. Quantitative Research in Linguistics. 2e. Bloomsbury.