Chapter 6. Relationships between two quantitative variables

Will your knowledge of statistics improve as you read more and more books on the subject? Is there a relationship between the length of a word and its frequency? Does grammatical proficiency of children depend on the number of lexical items which they have mastered? Does the number of phonemes in a language depend on the number of speakers? All these questions involve correlation between two variables. This chapter explains the principles of correlation analysis and demonstrates how it can be carried out using popular parametric and non-parametric tests. You will also learn how to produce correlograms and scatter plots with a regression line. Some fundamental notions of regression analysis, such as residuals, homo- and heteroscedasticity, will be introduced. The case studies investigate the relationship between word frequency and mean reaction time in a lexical decision task and the correlation between vocabulary size and grammatical proficiency in first language acquisition.