In jr-packages/jrModellingBio: Statistical Modelling with R for Biologists

library(formatR)

set.seed(1)
z = rnorm(10)
m = t.test(z)
m_stats = signif(c(m$statistic, m$parameter, m$p.value, m$conf.int), 3)
options(width = 58)

Introduction

Many of the standard statistical functions that we use in R return a collection of model diagnostics that does not fit naturally into a single data frame. For example, suppose we carry out a simple one-sided $t$-test

t.test(z)

\noindent The R output returns:

• the test statistic: m_stats[1]
• the degrees of freedom: r m_stats[2]
• the $p$-value: r m_stats[3]
• the confidence interval: (r m_stats[4], r m_stats[5]).

When performing $\chi^2$ tests, amongst other things, the output contains expected and observed values. In this chapter, we will investigate how to programmatically access these objects.

An R list

An R list is an object consisting of an ordered collection of (possibly different) objects known as its components. For example, a list could consist of a numeric vector and a data frame. To create a list, we use the list function

lst = list(course = "modelling", no_of_partipants = 3,
    first_names = c("Rod", "Hull", "Emu"))

\noindent Components are always numbered. In the lst object above, we can access individual components using the double bracket notation. For example to select the third element from the list, we have

lst[[3]]

\noindent So to access the first element of the third component we do^[The third component is first_names.]

lst[[3]][1]

\noindent The length() function gives the number of top level components:

length(lst)

\noindent Components of lists may also be named. If this is the case, then we can also access the element using its name:

lst[["course"]]
lst$course

\noindent A useful function for interrogating an object is str().^[str is short for structure.] Using the lst object as an example, we have

str(lst)

Example: $t$-test

Lets go back to the $t$-test example in Section \@ref(sec:S3-1). Rather than print the function output to the screen, we will store the output in the variable rst:

rst = t.test(z)

\noindent The rst object has r length(rst) elements

length(rst)

\noindent with the following names

names(rst)

\noindent Using the str() function, we can interogate the rst object further

str(rst)

\noindent We can see that the $t$-function returns a list of nine elements. We can access these elements in the usual way

rst$statistic
rst[[2]]

\noindent Being able to extract the output from functions will be very useful when we look at more advanced statistical routines.

votes = data.frame(Labour = c(762, 484),
  Cons = c(327, 239),
  LibDem = c(468, 477))
rownames(votes) = c("M", "F")
xsq = chisq.test(votes)

Example: $

Let's now return to the $\chi^2$ example from the notes. As before, we can extract the names of individuals list components, using the names() function\sidenote{I would also use the str() function, but to save space in the notes, I've omitted the output.}

names(xsq)

\noindent Each component of the list contains some information from the statistical analysis. For example, to get the $p$-value we use

xsq$p.value

\noindent to retrieve the expected number of counts under the null hypothesis

xsq$expected

\noindent If we were interested in which cells differed the most, we could look at the standardised residuals

xsq$stdres

\noindent This table helps to explain why we rejected the null hypotheis of no association between gender and voting preference. It appears that more males voted Labour and fewer voted Liberal Democrat than would have been expected if the null hypothesis was true.

jr-packages/jrModellingBio documentation built on Dec. 11, 2019, 9:41 a.m.