Index

Entries in bold are R functions

• 1 parameter “1” as the intercept
• 1:6 generate a sequence 1 to 6
• = = (“double equals”) logical EQUALS
• != logical NOT EQUAL
  • for barplot
  • influence testing
  • with subsets
• / division
• / nesting of explanatory variables
• %% modulo
• & logical AND
• | conditioning (“given”)
• ( ) arguments to functions
• (a,b] from and including a, up to but not
• including b
• * main effects and interaction terms in a model
• * multiplication
• : generate a sequence; e.g. 1:6
• [[ ]] subscripts for lists
• [ ] subscripts
• [a,b) include b but not a
• \\ double backslash in file paths
• ^ for powers and roots
• { } in defining functions
• in for loops
• <- gets operator
• < less than
• > greater than
• 1st Quartile with summary
• 3rd Quartile with summary
• a intercept in linear regression
• a priori contrasts
• abline function for adding straight lines to a
  • plots
  • after Ancova
  • in Anova
  • with a linear model as its argument
• abline(h = 3) draw a horizontal line
• abline(lm(y ∼ x)) draw a line with a and b
  • estimated from the linear model y ∼ x
• abline(v = 10) draw a vertical line at x =
• absence of evidence
• acceptance null hypothesis
• age effects longitudinal data
• age-at-death data using glm
• aggregation and randomization
• aggregation count data
• AIC Akaike's Information Criterion
• air pollution correlations
• aliasing introduction
• analysis of covariance, see Ancova
• analysis of deviance count data
  • proportion data
• analysis of variance, see Anova
• Ancova
  • contrasts
  • order matters
  • subscripts
  • with binary response
  • with count data
• anova and Anova: anova is an R function for comparing two models, while Anova stands for analysis of variance
• anova analysis of deviance
  • Ancova
  • comparing models
  • function for comparing models
  • model simplification
  • non-linear regression
  • test=“Chi”
  • test=“F”
  • with contrasts
• Anova essence of
  • choice
  • introduction
  • longhand calculations for one-way
  • model formula
  • one-way
• Anova table in regression
  • one-way Anova
  • and non-orthogonal data
• antilogs exp
• ants in trees
• aov function for fitting linear models with categorical explanatory variables
  • analysis of variance models
  • competition example
  • Error for rats example
  • factorial experiments
  • model for analysis of variance
  • multiple error terms using Error
  • with contrasts
• appearance of graphs, improvements
• arcsine transformation of percentage data
• arithmetic mean definition
  • with summary
• array function creating an array specifying its dimensions
• array
• as.character for labels
  • in barplot labels
• as.matrix
• as.numeric
• as.POSIX
• as.vector
  • to estimate proportions
  • with tapply
• assignment, <- not =
• association, contingency tables
• asymptotic exponential in non-linear regression
• attach a dataframe
• autocorrelation random effects
• average of proportions
• averaging speeds
• axis change tic mark locations

• b slope in linear regression
• b = SSXY/SSX
• barplot factorial experiments
  • frequencies
  • negative binomial distribution
  • table using tapply
  • two data sets compared
  • with error bars
  • with two sets of bars
• Bernoulli distribution n =
• binary response variable
  • Ancova
  • introduction
• binom.test exact binomial test
• binomial variance/mean ratio
• binomial data introduction
• binomial denominator
• binomial distribution dbinom density
  • function
  • pbinom probabilities
  • qbinom quantiles
  • rbinom random numbers
• binomial errors glm
  • logit link
• binomial test comparing two proportions with prop.test
• binomial trials Bernoulli distribution
• blank plots use type=“n”
• blocks
  • split plot design
  • and paired t-test
• bootstrap confidence interval for mean
  • hypothesis testing with single samples
• bounded count data
• bounded proportion data
• box and whisker plots, see boxplot
• boxplot function
  • garden ozone
  • notch = T for hypothesis testing
• c concatenation function
  • making a vector
• calculator
• cancer with distance example
• canonical link functions glm
• Cartesian coordinates
• categorical variables in data frames
  • use cut to create from continuous
• cbind function to bind columns together
  • in Ancova
  • making contrasts
  • proportion data
  • creating the response variable for proportion data
• ceiling function for “the smallest integer greater than”
• censoring introduction
• central, a function for central tendency
• central limit theorem, introduction
• central tendency central function
  • introduction
• chance and variation
• character mode for variable
• chi squared comparing two distributions
  • test = “Chi”
  • distribution pchisq probabilites qchisq quantiles
• chisq.test Pearson's Chi-squared test
• chi-square contingency tables
• choice of model, usually a compromise
• choose combinatorial function in R
• classical tests
• clear the workspace rm(list = ls())
• clumps, selecting a random individual
• coef extract coefficients from a model object
• coefficients Ancova
  • Anova
  • binary infection
  • coef function
  • extract, as in model$coef
  • factorial experiments
  • gam
  • glm with Gamma errors
  • quadratic regression
  • regression
  • regression with proportion data
  • treatment contrasts
  • with contrasts
• cohort effects in longitudinal data
• col = “red” colour in barplot
• column totals in contingency tables
• columns selecting from an array
  • selecting using subscripts
• columnwise data entry for matrices
• comparing two means
• comparing two proportions
• comparing two variances
• competition experiment
• concatenation function, c
• confidence intervals as error bars
  • introduction
• constant variance glm
  • model checking
• contingency tables dangers of aggregation
  • introduction
  • rather than binary analysis
• continuous variables
  • convert to categorical using cut
  • in data frames
  • using cut to create categorical variables
• contr.treatment treatment contrasts
• contrast coefficients
• contrast conventions compared
• contrast sum of squares example by hand
• contrasts Ancova
  • as factor attribute
  • Helmert
  • introduction
  • sum
  • treatment
• contrasts = c(“contr.treatment”, “contr.poly”)) options
• controls
• Cook's distance plot in model checking
• cor correlation in R
  • paired data
• cor.test scale dependent correlation
  • significance of correlation
• correct=F in chisq.test
• corrected sums of squares Ancova
  • one-way Anova
• correction factor hierarchical designs
• correlation and paired-sample t-test
  • contingency tables
  • introduction
  • partial
  • problems of scale-dependence
  • variance of differences
• correlation coefficient r
• correlation of explanatory variables model checking
  • multiple regression
• correlation structure, random effects
• count data analysis of deviance
  • analysis using contingency tables
  • Fisher's Exact Test
  • introduction
  • negative binomial distribution
  • on proportions
• counting, use table
  • using sum(d > 0)
  • elements of vectors using table function
• counts
• covariance and the variance of a difference
  • introduction
  • paired samples
• critical value and rejection of the null
  • hypothesis
  • F-test
  • rule of thumb for t = 2
  • Student's t
• cross-sectional studies longitudinal data
• cumprod cumulative product function
• current model
• curvature and model simplification
  • in regression
  • model checking
  • multiple regression
• curves on plots, Ancova with Poisson errors
• cut, produce category data from continuous

• d.f., see degrees of freedom
• dangers of contingency tables
• data, fitting models to
• data Ancovacontrasts
  • cases
  • cells
  • clusters
  • compensation
  • competition
  • Daphnia
  • deaths
  • decay
  • f.test.data
  • fisher
  • flowering
  • gardens
  • germination
  • growth
  • hump
  • induced
  • infection
  • isolation
  • jaws
  • light
  • oneway
  • ozone
  • paired
  • pollute
  • productivity
  • rats
  • sexratio
  • sheep
  • skewdata
  • smoothing
  • splityield
  • streams
  • sulphur.dioxide
  • t.test.data
  • tannin
  • two sample
  • worms
  • yvalues
• data dredging using cor
• data editing
• data exploration
• data frame, introduction
• data summary one sample case
• dataframe create using cbind
  • create using read.table
  • name the same as variable name
• dates and times in R
• death data introduction
• deer jaws example
• degree of fit r²
• degrees of freedom checking for
  • pseudoreplication
  • contingency tables
  • definition
  • factorial experiments
  • in a paired t-test
  • in an F test of two variances
  • in Anova
  • in different models
  • in nested designs
  • in the linear predictor
  • model simplification
  • number of parameters
  • one-way Anova
  • spotting pseudoreplication
• deletion tests, steps involved
• density function binomial
  • negative binomial
  • Normal
  • Poisson
• derived variable analysis longitudinal data
• detach a dataframe
• deviations, introduction
• diet supplement example
• diff function generating differences
• differences vs. paired t-test
• differences between means aliasing
  • in Anova model formula
• differences between slopes Ancova
• differences between intercepts Ancova
• difftime
• dim dimensions of an object
• dimensions of a matrix
• dimensions of an array
• dimensions of an object x - 1:12; dim(x) <- c(3,4)
• division /
• dnbinom function for probability density of the negative binomial
• dnorm
  • plot of
  • probability density of the Normal distribution
• dredging through data using cor
• drop elements of an array using negative subscripts
• drop the last element of an array using length
• dt density function of Student's t, plot of
• dummy variables in the Anova model formula
• duration of experiments

• E = R x C/G expected frequencies in contingency tables
• each in repeats
• edges, selecting a random individual
• effect size and power
  • factorial experiments
  • fixed effects
  • one-way Anova
• else with the if function
• empty plots use type = “n”
• equals, logical == (“double equals”)
• Error with aov, introduction
  • multiple error terms in aov
• error bars, function for drawing
  • least significant difference
  • on proportions
  • overlap and significance
• error correction
• error structure introduction
  • model criticism
• error sum of squares SSE in regression
• error variance contrast sum of squares
  • in regression
• error.bars function for plotting
• errors Poisson for count data
• eta the linear predictor
• even numbers, %%2 is zero
• everything varies
• exact binomial test binom.test
• Excel dates in R
• exit a function using stop
• exp antilogs (base e) in R
  • predicted value
  • with glm and quasipoisson errors
• expectation of the vector product
• expected frequencies E = R x C / G
  • Fisher's Exact Test
  • negative binomial distribution
• experiment
• experimental design
• explained variation in Anova
  • in regression
• explanatory power of different models
• explanatory variables
  • continuous regression
  • dangers of aggregation
  • specifying, see predict
  • transformation
  • unique values for each binary response
• exponential errors, in survival analysis
• expression, complex text on plots
• extreme value distribution in survival analysis
• extrinsic aliasing
• eye colour, contingency tables
• F as logical False
• F ratio
  • in regression
• F-test, comparing two variances
• factor, numerical factor levels
• factor levels Fisher's Exact Test
  • generate with gl
  • informative
  • in model formula
• factorial, Fisher's Exact Test
• factorial designs, introduction
• factorial experiments introduction
• factor-level reduction in model simplification
• factors categorical variables in Anova
  • in data frames
  • plot
• failure data, introduction
• failures proportion data
• FALSE or F, influence testing
  • logical variable
• falsifiable hypotheses
• family = binomial binary response variable
  • proportion data
• family = poisson for count data
• famous five; sums, sums of squares and sums of products
• file names
• fill colour for legends
  • in barplot legend
• fisher.test Fisher's Exact Test
  • with 2 arguments as factor levels
• Fisher's Exact Test, contingency tables
• Fisher's F-Test, see F-test
• fit of different models
• fitted values definition
• proportion data
• fitting models to data
• fixed effects, introduction
• for loops
  • drawing error bars
  • for plotting residuals
  • negative binomial distribution
  • residuals in Anova
  • with abline and split
• formula, model for Anova
• F-ratio, contrast sum of squares
  • one-way Anova
• frequencies count data
  • using table
• frequency distributions, introduction
• F-test, introduction
• functions written in R
  • error bars
  • exit using stop
  • for a sign test
  • for variance
  • leverage
  • median
  • negative binomial distribution

• gam generalized additive models
  • data exploration
  • introduction
  • library(mgcv)
  • with a binary response
  • y∼s(x)
• Gamma distribution, variance/mean ratio
• Gamma errors glm
  • introduction
• gardenA
• Gaussian distribution in survival analysis
• generalized additive models, see gam
• generalized linear model, see glm
• generate factor levels gl
• geometric mean, definition
• gl generate levels for factors
• glm analysis of deviance
  • Ancova with binomial errors
  • Ancova with poisson errors
  • binary infection
  • binary response variable
  • cancers example
  • Gamma errors
  • proportion data
  • regression with proportion data
  • saturated model with Poisson errors
• gradient, see slope
• graphs, two adjacent, par(mfrow=c(1,2))
• graphs, two by two array, par(mfrow=c(2,2))
• Gregor Mendel effect
• grouping random effects

• h, leverage measure
• hair colour, contingency tables
• harmonic mean
• header = T
• Helmert contrasts Ancova
  • example
• heteroscedasticity introduction
  • model checking
  • multiple regression
• hierarchical designs, correction factor
• hierarchy random effects
  • rats example
• hist function for producing histograms
  • speed
  • values
  • with bootstrap
  • with skew
• histograms,, see hist
• history(Inf) for list of input commands
• honest significant differences TukeyHSD
• horizontal lines on plot abline(h=3)
• how many samples? plot of variance and sample size
• humped relationships significance testing
  • model simplification
  • testing for
  • testing a binary response model
• hypotheses good and bad
• hypotheses testing
  • using chi-square
  • with F

• I “as is” in multiple regression
  • model formulas
• identity link glm
  • Normal errors
• if function
• if with logical subscripts
• incidence functions using logistic regression
• independence
• independence assumption in contingency tables
• independence of errors
  • random effects
• index in one-variable plots
• induced defences example
• infection example
• inference with single samples
• influence introduction
  • model checking
  • one-way Anova
  • testing in multiple regression
• informative factor levels, fixed effects
• initial conditions
• input from keyboard using scan()
• insecticide
• interaction, multiple regression
  • terms with continuous explanatory variables
  • terms model formulae
  • terms in multiple regression
• interaction.plot split plot example
• interactions factorial experiments
  • selecting variables
  • value of tree models
• intercept a
  • calculations longhand
  • differences between intercepts
  • estimate
  • maximum likelihood estimate
  • treatment contrasts
• intercepts Ancova
• interquartile range
  • plots
• intrinsic aliasing
• inverse, and harmonic means

• k of the negative binomial distribution
• key, see , see legend
• kinds of years
• known values in a system of linear equations
• kurtosis definition
  • error structure
  • function for
  • values

• labels changing font size, cex.lab
  • for barplot
• least significant difference (LSD) error bars
  • introduction
• least-squares estimates of slope and intercept in linear regression
• legend barplot with two sets of bars
  • plot function for keys
• length function for determining the length of a vector
  • drop the last element of an array
  • in a sign test function
  • length with tapply
• levels of factors
• levels, generate with gl
• levels introduction
  • model simplification
  • proportion data
  • regression in Ancova
  • with contrasts
• “levels gets” comparing two distributions
  • factor-level reduction
  • with contrasts
• leverage and SSX
• leverage function
  • influence testing
• library ctest for classical tests
  • mgcv for gam
  • nlme for mixed effects models
  • survival for survival analysis
  • tree for tree models
• linear function
• linear mixed effects model lme
• linear predictor introduction
  • logit link
• linear regression example using growth and tannin
• linearizing the logistic
• lines adds lines to a plots (cf. points)
  • binary response variable
  • drawing error bars
  • dt and dnorm
  • exponential decay
  • for errors with proportion data
  • non-linear regression
  • ordered x values
  • over histograms
  • polynomial regression
  • showing residuals
  • type = “response” for proportion data
  • with glm and quasipoisson errors
  • with qt
  • with subscripts
• link, log for count data
• link function complementary log-log
  • logit
• list, in non-linear regression
• lists, subscripts
• liver, rats example
• lm
• lm fit a linear model lm(y∼x)
  • Ancova
  • in regression
  • linear models
  • the predict function
• lme linear mixed effects model
  • handling pseudoreplication
• locator function for determining coordinates on
  • as plot
  • with barplot
• loess local regression non-parametric models
• log exponential decay
• log logarithms (base e) in R
• log link for count data
• log odds, logit
• log transformation in multiple regression
• logarithms and variability
• logical subscripts
• logical tests using subscripts
• logical variables, T or F
  • in data frames
• logistic model, caveats
• logistic S-shaped model for proportion data
  • distribution in survival analysis
• logistic regression, binary response variable
  • example
• logit link binomial errors
  • definition
• log-linear models for count data
• longitudinal data analysis
• loops in R, see for loops
• LSD least significant difference
  • plots
• lty line type (e.g. dotted is lty=2)

• m₃ third moment
• m₄ fourth moment
• marginal totals in contingency tables
• margins in contingency tables
• matrices, columnwise data entry
• matrix function in R
  • with nrow
• matrix multiplication %*%
• maximum. with summary
  • max
• maximum likelihood definition
  • estimates in linear regression
  • estimate of k of the negative binomial
• mean function determining arithmetic mean
• mean, arithmetic
  • geometric
  • harmonic
• mean age at death with censoring
• mean squared deviation, introduction
• means, tapply for tables
  • two-way tables using tapply
• measurement error
• med function for determining medians
• median built-in function
  • with summary
  • writing a function
• mgcv, binomial
• Michelson's light data
• minimal adequate model
  • analysis of deviance
  • multiple regression
• minimum, min, with summary
• mixed effects models
  • library(nlme)
• mode, the most frequent value
• model for Anova
  • contingency tables
  • linear regression
• model checking, introduction
  • in regression
• model criticism, introduction
• model formula for Anova
• model objects, generic functions
• model selection
• model simplification analysis of deviance
  • Ancova
  • caveats
  • factorial experiments
  • factor-level reduction–224
  • multiple regression
  • non-linear regression
  • with contrasts
• model, structure of a linear models using str
• modulo %%
  • for barplot
  • remainder
  • with logical subscripts
• moments of a distribution
• multiple comparisons
• multiple error terms, introduction
• multiple graphs per page, par(mfrow = c(1,2))
• multiple regression, introduction
  • difficulties in
  • minimal adequate model
  • number of parameters
  • quadratic terms
• multiplication, *
• n, sample size
  • and degrees of freedom
  • and power
  • and standard error

• names in barplot
• names of variables in a dataframe
• natural experiments
• negative binomial distribution definition
  • dnbinom density function
• negative correlation in contingency tables
• negative skew
• negative subscripts to drop elements of an array
• nested Anova, model formulae
• nesting model formulae
  • of explanatory variables, %in%
• new line of output using “\n”
• nice numbers in model simplification
• nlme library for mixed effects models
  • non-linear mixed effects model
• nls non-linear least squares models
• non-constant variance count data
  • model criticism
  • proportion data
• non-linear least squares, see nls
• non-linear mixed effects model, see nlme
• non-linear regression introduction
• non-linear terms in model formulae
  • use of nls
• non-linearity in regression
• non-Normal errors introduction
  • count data
  • model checking
  • model criticism
  • proportion data
• non-orthogonal data observational studies
  • order matters
• non-parametric smoothers gam
  • pairs
  • with a binary response
• Normal and Student's t distributions compared
• Normal calculations using z
• Normal curve, drawing the
• Normal distribution, introduction
  • dnorm density function
  • pnorm probabilities
  • qnorm quantiles
  • rnorm random numbers
• Normal errors identity link
  • model checking
• Normal q-q plot in model checking
• normality, tests of
• not equal, !=
• notch=T in boxplot for significance testing
  • plots for Anova
  • with boxplot
• nrow, number of rows in a matrix
• n-shaped humped relationships
• nuisance variables, marginal totals in contingency tables
• null hypotheses
  • rejection and critical values
  • with F-tests
• null model y ∼ 1
• numbers as factor levels
• numeric, definition of the mode of a variable

• observational data
• observed frequencies in contingency tables
• Occam's Razor
  • and choice of test
  • contingency tables
• odd numbers, %%2 is one
• odds, p/q, definition
• one-sample t-test
• one-way Anova introduction
• options contrasts = c(“contr.helmert”, “contr.poly”))
  • contrasts = c(“contr.sum”, “contr.poly”))
  • contrasts = c(“contr.treatment”, “contr.poly”))
• order function
  • in sorting dataframes
  • with scatter plots
  • with subscripts
• order matters Ancova
  • non-orthogonal data
• ordering, introduction
• orthogonal contrasts
• orthogonal designs
  • Anova tables
• outliers definition
  • in box and whisker plots
  • new line using “\n”
• overdispersion and transformation of explanatory variables
  • no such thing with binary data
  • proportion data
  • use quasibinomial for proportion data
  • use quasipoisson for count data
• over-parameterization in multiple regression
• ozone and lettuce growth in gardens

• Π Greek Pi, meaning the product of
• p number of parameters
  • and influence
  • in the linear predictor
  • estimated parameters in the model
• p values
  • compared for t-test and Wilcoxon Rank Sum Test
• paired samples t-test
• pairs mutli-panel scatterplots
• panel.smooth in pairs
• par graphics parameters
• par(mfrow=c(1,1)) single graph per page
• par(mfrow=c(1,2)) two graphs side by side
• par(mfrow=c(2,2)) four plots in a 2×2 array
• parallel lines in Ancova
• parameter estimation in non-linear regression
• parameters 2-parameter model
  • in multiple regression
• parsimony
• partial correlation, introduction
• paste to concatenate text
• path analysis
• path name for files
• pch with split
• pch = 35
  • solid circle plotting symbols
  • with split
• pchisq cumulative probability of chi squared distribution
• Pearson's chi-squared definition
  • for comparing two distributions
• Pearson's Product-Moment Correlation
  • cor.test
• percentage data and the arcsine transformation
  • from counts
• percentiles
  • plots
  • in box and whisker plots
  • with summary
• pf cumulative probability from the F
  • distribution
  • in F-tests
  • in regression
  • one-way Anova
• piece-wise regression, with a binary response
• Pivot Table in Excel
• plot 5
  • abline for adding straight lines
  • adding points to a plot
  • binary response variable
  • box and whisker
  • compensation example
  • correlation
  • count data
  • growth and tannin
  • in Anova
  • in error checking
  • las=1 for vertical axis labels
  • multiple using pairs
  • multiple using par(mfrow = c(1,2))
  • non-linear scatterplot
  • proportion data
  • regression with proportion data
  • scale dependent correlation
  • the locator function for determining coordinates
  • type = “n” for blank plotting area
  • with index
  • with split
• plot(model) introduction
  • for gam
  • and transformation of explanatory variables
  • for tree models
  • glm with Gamma errors
  • model checking
  • multiple regression
  • one-way Anova
• plot.gam with a binary response
• plots, box and whisker
  • pairs for many scatterplots
  • for binary response example
• plotting symblols pch in plot
• pnorm probabilities from the Normal
  • distribution
  • probabilities of z values
• points adding points to a plot (cf. lines)
  • with gam plot
  • with split
  • with subscripts
• Poisson distribution definition
  • dpois density function
  • rpois random number generator
• poisson errors count data
  • glm for count data
• pollution, example of multiple regression
• polygon function for shading complex shapes
• polynomial regression, introduction
• population growth, simulation model
• positive correlation, and paired-sample t-test
  • contingency tables
• POSIX
• power, probability of rejecting a false null hypothesis
  • functions for estimating sample size
  • power.t.test
• powers ^
• p/q, see odds
• predict, function to predict values from a model for specified values of the explanatory variables
  • binary response variable
  • non-linear regression
  • polynomial regression
  • type = “response” for proportion data
  • with glm and quasipoisson errors
• predicted value, standard error of ^y
• predictions
• probabilities, contingency tables
• probability density, binomial distribution
  • Normal
  • negative binomial distribution
  • Poisson distribution
• products, cumprod function for cumulative products
• prop.test binomial test for comparing two proportions
• proportion, transformation from logit
• proportion data introduction
  • analysis of deviance
  • Ancova
  • binomial errors
  • rather than binary analysis
• proportions from tapply with as.vector
• pseudoreplication
  • analysis with
  • checking degrees of freedom
  • removing it
  • split plots
• pt cumulative probabilities of Student's t distribution
  • garden ozone
  • test for skew

• qchisq quantiles of the chi-square distribution
• qf quantiles of the F distribution
  • contrast sum of squares
  • in regression
  • one-way Anova
• qnorm quantiles of the Normal distribution
• qqline introduction
• qqnorm introduction
  • in regression
• qt quantiles of the t distribution
  • confidence interval for mean
  • critical value of Student's t
• quadratic regression. introduction
  • multiple regression
  • in a binary response model
  • model formulae
• quantile function in R
  • of the chi-square distribution using qchisq
  • of the F distribution usibng qf
  • of the Normal distribution using qnorm
  • of the t distribution usibng qt
• quartile plots
  • with summary
• quasibinomial analysis of deviance
  • family for overdispersed proportion data
• quasipoisson analysis of deviance
  • family for overdispersed count data
• r correlation coefficient
  • in terms of covariance
  • in terms of SSXY
• R downloadi
• R language
• r² as a measure of explanatory power of a model
  • definition
  • r² = SSR/SSY
• random effects introduction
  • longitudinal data
  • uninformative factor levels
• random numbers from the normal distribution
  • rnorm
  • from the Poisson distribution, rpois
  • from the uniform distribution, runif
• randomization in sampling and experimental design
• randomizing variable selection
• range function returning maximum and minimum
• rank function in R
• read.table introduction
• reading data from a file
• reciprocal link with Gamma errors
• reciprocals
• regression introduction
  • anova table
  • at different factor levels Ancova
  • binary response variable
  • by eye
  • calculations longhand
  • choice
  • exponential decay
  • linear
  • logistic
  • non-linear
  • parameter estimation in non-linear
  • piece-wise
  • polynomial
  • predict in non-linear
  • quadratic
  • summary in non-linear
  • testing for humped relationships
  • testing for non-linearity
• rejection critical values
  • null hypothesis
  • using F-tests
• relative growth rate with percentage data
• removing variables with rm
• rep function for generating repeats
  • error bars
  • for subject identities
  • LSD bars
  • repeat function
  • text
• repeated measures
  • random effects
• repeats, generating repeats, see rep
• replace = T sampling with replacement
• replication 7
  • checking with table
• residual deviance in proportion data
• residual errors
• residual plots in model checking
• residuals definition
  • extract residuals from a model object
  • in Anova
  • model checking
  • pattern and heteroscedasticity
• response, predict with type = “response”
• response variable and the choice of model
  • regression
  • types of
• rev with order in sorting dataframes
• rev(sort(y)) sort into reverse order
• rm removing variables from the work space
• rm(list = ls()) clear everything
• rnorm random normally distributed numbers
• roots, ^(fraction)
  • in calculating geometric mean
• row names in data frames
• row totals contingency tables
• row.names in read.table
• rows selecting from an array
  • selecting using subscripts
• rules of thumb
  • parameters in multiple regression p/3
  • power 80% requires n > = 16 s²/d²
  • t >2 is significant
• runif uniform random numbers
• Σ Greek Sigma, meaning summation
• S language, background
• s(x) smoother in gam
• proof
• proof
• sample, function for sampling at random from a vector
  • with replacement, replace = T
  • selecting variables
  • for shuffling, replace = F
• sample size and degrees of freedom
• sampling with replacement; sample with replace = T
• saturated model
  • contingency tables
• saving your work from an R session
• scale location plot, used in model checking
• scale parameter, overdispersion
• scale-dependent correlation
• scan() input from keyboard
• scatter, measuring degree of fit with r²
• scatterplot, graphic for regression
• sd standard deviation function in R
• seed production compensation example
• selecting a random individual
• selecting certain columns of an array
• selecting certain rows of an array
• selection of models, introduction
• self-starting functions in non-linear regression
• seq generate a series
  • values for x axis in predict
• sequence generation, see seq
• serial correlation
  • random effects
• sex discrimination, test of proportions
• shuffling using sample
• sign test definition
  • garden ozone
• significance
  • in boxplots using notch = T
  • of correlation using cor.test
  • overlap of error bars
• significant differences in contingency tables
• simplicity, see Occam's Razor
• simplification, see model simplification
• simulation experiment on the central limit theorem
• single sample tests
• skew definition
  • asymmetric confidence intervals
  • function for
  • in histograms
  • negative
  • values
• slope b
  • calculations longhand
  • definition
  • differences between slopes
  • maximum likelihood estimate
  • standard error
• slopes Ancova
  • removal in model simplification
• smoothing gam
  • model formulae
  • panel.smooth in pairs
• sort function for sorting a vector
  • rev(sort(y)) for reverse order
• sorting a dataframe
• sorting, introduction
• spaces in variable names or factor levels
• spatial autocorrelation random effects
• spatial correlation and paired t-test
• spatial pseudoreplication
• Spearman's Rank Correlation
• split for species data
  • proportion data
  • separate on the basis of factor levels
• split-plots Error terms
  • introduction
  • different plotting symbols
• spreadsheets and data frames
• sqrt square root function in R
• square root function, see sqrt
• SSA explained variation in Anova
  • one-way Anova
  • shortcut formula
• SSC contrast sum of squares
• SSE error sum of squares
  • in Ancova
  • in Anova
  • in regression
  • one-way Anova
  • the sum of the squares of the residuals
• S-shaped curve logistic
• SSR Ancova
  • in regression
  • regression sum of squares
• SSX corrected sum of squares of x
  • calculations longhand
• SSXY corrected sum of products
  • Ancova
  • calculations longhand
  • shortcut formula
• SSY total sum of squares defined
  • calculations longhand
  • in Anova
  • null model
  • one-way Anova
• SSY = SSR+SSE
• standard deviation, sd function in R
  • and skew
  • in calculating z
• standard error
  • as error bars
  • difference between two means
  • Helmert contrasts
  • mean
  • of kurtosis
  • of skew
  • of slope and intercept in linear regression
• standard normal deviate, see z
• start, initial parameter values in nls
• statistical modelling, introduction
• status with censoring
• step automated model simplification
• str, the structure of an R object
• straight line
• strong inference
• strptime, in R
• Student's t-distribution introduction
  • pt probabilities
  • qt quantiles
• Student's t-test statistic
  • normal errors and constant variance
• subjects, random effects
• subscripts [ ] introduction
  • barplot with two sets of bars
  • data selection
  • factor-level reduction
  • for computing subsets of data
  • in data frames
  • in lists [[ ]]
  • in calculations for Anova
  • influence testing
  • lm for Ancova
  • residuals in Anova
  • with order
  • using the which function
• subset in model checking
  • influence testing
  • multiple regression
• subsets of data using logical subscripts
• substitute, complex text on plots
  • in plot labels
• successes, proportion data
• sulphur dioxide, multiple regression
• sum function for calculating totals
• sum contrasts
• sum of squares introduction
  • computation
  • contrast sum of squares
  • shortcut formula
• summary introduction
  • analysis of deviance
  • Ancova
  • Ancova with poisson errors
  • factorial experiments
  • glm with Gamma errors
  • glm with poisson errors
  • in regression
  • non-linear regression
  • of a vector
  • regression with proportion data
  • speed
  • split plot aov
  • with data frames
  • with quasipoisson errors
• summary(model)
  • gam
  • piece-wise regression
  • with survreg
• summary.aov
  • Ancova
  • in regression
  • one-way Anova
• summary.lm
  • Ancova
  • effect sizes in Anova
  • factorial experiments
  • Helmert contrasts
  • in Anova
  • two-way Anova
  • with contrasts
• sums of squares in hierarchical designs
• suppress axis labelling xaxt = “n”
• survfit plot survivorship curves
• survival analysis introduction
  • library(survival)
• survivorship curves, plot(surfit)
• survreg analysis of deviance
• symbols in model formulae
• symbols on plots complex text on plots
  • different symbols
• Sys.time

• T logical True
• t distribution, see Student's t distribution
• t.test garden ozone
  • one sample
  • paired = T
• table, function for counting elements in vectors
  • binary response variable
  • checking replication
  • counting frequencies
  • counting values in a vector
  • determining frequency distribution
  • with cut
• tables of means introduction
  • tapply on proportions
• tails of the Normal distribution
• tails of the Normal and Student's t compared
• tapply for tables of means
  • for proportions
  • function in R
  • mean age at death
  • mean age at death with censoring
  • reducing vector lengths
  • table of totals, with sum
  • table of variances, with var
  • two-way tables of means
  • with contrasts
  • with count data
  • with cut
  • with length
• temporal autocorrelation random effects
• temporal pseudoreplication
• test statistic for Student's t
• test = “Chi” contingency table
• test = “F” anova
• tests of hypotheses
• tests of normality
  • text(model) for tree models
• theory
• three-way Anova, model formulae
• thresholds in piece-wise regression
• ties, problems in Wilcoxon Rank Sum Test
• tilde ∼ means “is modelled as a function of” in lm or aov
• model formulae
• time and date in R
• time at death
• time series, random effects
• time series
• time-at-death data, introduction
• transformation
  • arcsine for percentage data
  • count data
  • explanatory variables
  • from logit to p
  • linear models
  • logistic
  • model criticism
  • model formulae
  • the linear predictor
• transpose, using concatenate, c
• transpose function for a matrix, t
• treatment contrasts introduction
• treatment totals, contrast sum of squares
  • in Anova
• tree models
  • advantages of
  • data exploration
  • ozone example
• trees, selecting a random individual
• Tribolium
  • logical variable
• t-test definition
  • paired samples
  • rule of thumb for t = 9
• TukeyHSD, Tukey's Honest significant differences
• two sample problems
  • t-test with paired data
• two-parameter model, linear regression
• two-tailed tests
  • Fisher's Exact Test
• two-way Anova, model formulae
• Type I Errors
• Type II Errors
• type = “b” both points and lines
• type = “l” line rather than points in plot
• type = “n” for blank plots
  • proportion data
• type = “response”, model output on back-transformed scale
  • Ancova with poisson errors
  • with binary data
  • with proportion data

• unexplained variation
  • in Anova
  • in regression
• uniform random numbers with runif function
• uninformative factor levels
  • rats example
• unlist
• unplanned comparisons, a posteriori contrasts
• unreliability, estimation of
  • intercept
  • predicted value
  • slope
• update in model simplification
  • after step
  • analysis of deviance
  • contingency table
  • multiple regression
• using variance to estimate unreliability
  • testing hypotheses

• var variance function in R
• var(x,y) function for covariance
• var.test F-test in R
  • for garden ozone
• variable names in dataframes
• variance, definition and derivation
  • and corrected sums of squares
  • and power
  • and sample size
  • and standard error
  • constancy in a glm
  • count data
  • data on time-at-death
  • F-test to compare two variances
  • formula
  • gamma distribution
  • in Anova
  • minimizing estimators
  • of a difference
  • of the binomial distribution
  • plot against sample size
  • random effects
  • sum of squares / degrees of freedom
  • var function in R
  • VCA, variance components analysis
• variance components analysis
  • rats example
• variance constancy model checking
• variance function, random effects
• variance/mean ratio
  • aggregation in count data
  • examples
• variation
  • using logs in graphics
• variety and split
• VCA, see variance components analysis
• vector functions in R
• weak inference
• web address of this book, xii
  • proportion data
• Welch Two Sample t-test
• which, R function to find subscripts
• whiskers in box and whisker plots
• wilcox.test Wilcoxon Rank Sum Test
• Wilcoxon Rank Sum Test
  • non-normal errors
• worms dataframe
• writing functions in R, see functions

• x, continuous explanatory variable in regression
• xlab labels for the x axis
  • in Anova

• y response variable in regression
• y ∼ 1 null model
• y ∼ x-1 removing the intercept
• Yates’ correction Pearson's Chi-squared test
• yaxt = “n” suppress axis labelling
• yield experiment, split plot example
• ylab labels for the y axis
  • in Anova
• ylim controlling the scale of the y axis in plots
  • in Anova

• z of the Normal distribution
  • approximation in Wilcoxon Rank Sum Test
• zero term negative binomial distribution
  • Poisson distribution