# An Introduction to R: Notes on R: A Programming Environment by William N. Venables, David M. Smith, R Development Core Team By William N. Venables, David M. Smith, R Development Core Team

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The function is defined as follows: > twosam <- function(y1, y2) { n1 <- length(y1); n2 <- length(y2) yb1 <- mean(y1); yb2 <- mean(y2) s1 <- var(y1); s2 <- var(y2) s <- ((n1-1)*s1 + (n2-1)*s2)/(n1+n2-2) tst <- (yb1 - yb2)/sqrt(s*(1/n1 + 1/n2)) tst } With this function defined, you could perform two sample t-tests using a call such as > tstat <- twosam(data\$male, data\$female); tstat As a second example, consider a function to emulate directly the Matlab backslash command, which returns the coefficients of the orthogonal projection of the vector y onto the column space of the matrix, X.

The stimulus variables influence the distribution of y through a single linear function, only. This linear function is called the linear predictor, and is usually written η = β1 x1 + β2 x2 + · · · + βp xp , hence xi has no influence on the distribution of y if and only if βi = 0. • The distribution of y is of the form fY (y; µ, ϕ) = exp A {yλ(µ) − γ (λ(µ))} + τ (y, ϕ) ϕ where ϕ is a scale parameter (possibly known), and is constant for all observations, A represents a prior weight, assumed known but possibly varying with the observations, and µ is the mean of y.

Off() cat(paste(date(),"\nAdios\n")) } # a small safety measure. # Is it time for lunch? 9 Classes, generic functions and object orientation The class of an object determines how it will be treated by what are known as generic functions. Put the other way round, a generic function performs a task or action on its arguments specific to the class of the argument itself. If the argument lacks any class attribute, or has a class not catered for specifically by the generic function in question, there is always a default action provided.