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 “ ”
  • 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 “ ”
  • 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
  • img proof
  • img 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
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