Much of statistics relies on being able to evaluate expectations of random variables, and finding quantiles of distributions.

There have been a number of important issues that have dominated research and debate in SLA for many years without researchers reaching a consensus of resolution. We have touched on these issues throughout the book, but in this final chapter we are going to revisit some of them, review the research, give our opinion and suggest possible applications to practice.

As of this writing, there are more than 3000 objects in the R base packages, and more than 15,000 other packages available on CRAN, most containing dozens of objects of their own. This represents a huge amount of functionality, and nobody could be expected to remember it all. The best we can hope for is that people should be able to discover it, using the help system and other resources, as well as judicious guesses about where to look. Guessing is made easier when consistent principles are followed as code is written. For example, names should reflect the purpose of packages and functions. Guessing is made harder by inconsistency, for example when names are poorly chosen, or conventions for forming names are inconsistent.

the Environment of Evolutionary Adaptation (EEA) • proximate and ultimate levels of explanation • heritable variability • differential reproductive success • particulate inheritance • eugenics • the Great Chain of Being (scala naturae) • sociobiology • gene–culture co-evolution/dual-inheritance theory • naturalistic fallacy • moralistic fallacy

Programming involves writing relatively complex systems of instructions. There are two broad styles of programming: the imperative style (used in R, for example) involves stringing together instructions telling the computer what to do. The declarative style (used in HTML in web pages, for example, and to some extent in ggplot2, as described in Section 3.4) involves writing a description of the end result, without giving the details about how to get there. Within each of these broad styles, there are many subdivisions, and a given program may involve aspects of several of them. For example, R programs may be procedural (describing what steps to take to achieve a task), modular (broken up into self-contained packages), object-oriented (organized to describe operations on complex objects), and/or functional (organized as a collection of functions which do specific calculations without having external side-effects), among other possibilities. In this book we will concentrate on the procedural aspects of programming.

evolutionary psychopathology • Darwinian medicine • pathogen • aetiology • pathogenesis • trait variation • immune system • verification module • smoke detector principle • affective disorders • social competition hypothesis • schizophrenia • personality disorders •seasonal affective disorder • FSD model

We have decided to finish our book by providing a brief summary of the main points and recommendations we have made. But first we would like to stress the most obvious application of generally accepted theories of SLA. This would be to stop planning for, preparing for and delivering transmission approaches to the teaching of languages, and to start encouraging planners, curriculum and materials developers, teacher trainers, assessors and teachers to work together to promote experiential approaches to language learning in which learners are active agents of their own learning, benefiting from the exposure to language in use, from the opportunities for language use and from the opportunities for discovery they help to create.

Having installed the R and RStudio systems, you are now ready to begin to learn the art of statistical programming. The first step is to learn the syntax of the language that you will be programming in; you need to know the rules of the language. This chapter will give you an introduction to the syntax of R. Most of what we discuss here relates to what you would type into the R console or into the RStudio script window.

sexual strategies theory • mate guarding • male provisioning hypothesis • last common ancestor • male parental investment • cryptic oestrus • sexual dimorphism • polygyny • polyandry • reproductive value • sperm competition • sexy sons • Coolidge effect