Package 'asbio'

Description

Percent cover of the grass Agrostis variablis at 25 alpine snowbank sites in the Absaroka-Beartooth Mountains.

Usage

data(agrostis)

Format

A data frame with 25 observations on the following 2 variables.

site

Site number

cover

Percent cover

Source

Aho, K. (2006) Alpine and Cliff Ecosystems in the North-Central Rocky Mountains. PhD dissertation, Montana State University, Bozeman, MT.

Description

The veterans administration studied the effect of AZT on AIDS symptoms for 338 HIV-positive military veterans who were just beginning to express AIDS. AZT treatment was withheld on a random component until helper T cells showed even greater depletion while the other group received the drug immediately. The subjects were also classified by race.

Usage

data(aids)

Format

A data frame with 338 observations on the following 3 variables.

race

A factor with levels black, white.

AZT

A factor with levels N, Y.

symptoms

Presence/absence of AIDS symptoms.

Source

Agresti, A. (2012) Categorical Data Analysis, 3rd edition. New York. Wiley.

Description

An experiment was conducted in Iowa in 1944 to see how different varieties of alfalfa responded to the last cutting day of the previous year (Snedecor and Cochran 1967). We know that in the fall alfalfa can either continue to grow, or stop growing and store resources belowground in roots for growth during the following year. Thus, we might expect that later cutting dates inhibits growth for the following year. On the other hand, if plants are cut after they have gone into senescence, there should be little effect on productivity during the following year. There are two factors: 1) variety of alfalfa (three varieties were planted in each of three randomly chosen whole plots), and 2) the date of last cutting (Sept 1, Sept. 20, or Oct. 7). The dates were randomly chosen split plots within the whole plots. Replication was accomplished using six blocks of fields.

Usage

data(alfalfa.split.plot)

Format

The dataframe contains four variables:

yield

Alfalfa yield (tons per acre).

variety

Alfalfa variety. A factor with three levels "L"= Ladak, "C" = Cosack, and "R" = Ranger describing the variety of alfalfa seed used.

cut.time

Time of last cutting. A factor with three levels: "None" = field not cut, "S1" = Sept 1, "S20" = Sept. 20, or "O7" = Oct. 7.

block

The block (whole plot replicate). A factor with six levels: "1", "2", "3", "4", "5", and "6".

Source

Snedecor, G. W. and Cochran, G. C. (1967) Statistical Methods, 6th edition. Iowa State University Press.

Description

Alpha diversity quantifies richness and evenness within a sampling unit (replicate).

The function alpha.div runs Simp.index or SW.index to calculate Simpson's, Inverse Simpson's or Shannon-Weiner diversities.

Simpson's index has a straightforward interpretation. It is the probability of reaching into a plot and simultaneously pulling out two different species. Inverse Simpson's diversity is equivalent to one over the probability that two randomly chosen individuals will be the same species. These measures have been attributed to Simpson (1949). While it does not allow straightforward interpretation of results, the Shannon-Weiner diversity (H') is another commonly used alpha-diversity measure based on the Kullback-Leibler information criterion (Macarthur and Macarthur 1961).

Usage

alpha.div(x,index)
Simp.index(x,inv)
SW.index(x)

Arguments

Value

A single diversity value is returned if x is a vector. A vector of diversities (one for each site) are returned if x is a matrix.

Author(s)

Ken Aho

References

Simpson, E. H. (1949) Measurement of diversity. Nature. 163: 688.

MacArthur, R. H., and MacArthur J. W. (1961) On bird species diversity. Ecology. 42: 594-598.

Examples

data(cliff.sp)
alpha.div(cliff.sp,"simp")

Description

Provides animated depictions of confidence intervals for $\mu$, $\sigma^{2}$, the population median, and the binomial parameter $\pi$.

Usage

anm.ci(parent=expression(rnorm(n)), par.val, conf = 0.95, sigma = NULL,
  par.type = c("mu", "median", "sigma.sq", "p"), n.est = 100,
  n = 50, err.col = 2, par.col = 4, interval = 0.1, ...)

anm.ci.tck()

Arguments

Details

Provides an animated plot showing confidence intervals with respect to a known parameter. Intervals which do not contain the parameter are emphasized with different colors. The function can be run with a tcltk GUI function, anm.ci.tck().

Value

Returns an animated plot.

Author(s)

Ken Aho

See Also

Additional documentation for methods provided in: ci.mu.t, ci.mu.z, ci.median, ci.sigma, and ci.p.

Examples

## Not run: 
parent<-rnorm(100000)
anm.ci(parent, par.val=0, conf =.95, sigma =1, par.type="mu")
anm.ci(parent, par.val=1, conf =.95, par.type="sigma.sq")
anm.ci(parent, par.val=0, conf =.95, par.type="median")
parent<-rbinom(100000,1,p=.65)
anm.ci(parent, par.val=0.65, conf =.95, par.type="p")
##Interactive GUI, requires package 'tcltk'
anm.ci.tck()

## End(Not run)

Description

Creates an animated plot showing the results from coin flips, and the resulting convergence in P(Head) as the number of flips grows large.

Usage

anm.coin(flips = 1000, p.head = 0.5, interval = 0.01, show.coin = TRUE, ...)
anm.coin.tck()

Arguments

Value

If show.coin=TRUE, returns two plots configured as a single graphical object. The first plot shows convergence in estimated P(Head), i.e., number of heads/number of trials, as the number of trials grows large. The second plot shows individual outcomes of coin flips. The second (smaller) plot is not returned if show.coin=TRUE is specified. The function anm.coin() can be run with the tcltk GUI function, anm.coin.tck().

Author(s)

Ken Aho

See Also

rbinom

Examples

## Not run: anm.coin()

Description

A continuous pdf is conceptually a histogram whose bin area sums to one. Infinite, infinitely small bins, however, are required to allow depiction of an infinite number of distinct continuous outcomes.

Usage

anm.cont.pdf(part = "norm", interval = 0.3)

see.pdf.conc.tck()

Arguments

Note

May not work every time, because random values may exceed histogram range.

Author(s)

Ken Aho

Description

Convergence in probability for fair (or loaded) six-sided die.

Usage

anm.die(reps = 300, interval = 0.1, show.die = TRUE, p = c(1/6, 1/6, 1/6, 
1/6, 1/6, 1/6), cl = TRUE)

anm.die.tck()

Arguments

Author(s)

Ken Aho

See Also

anm.coin

Examples

## Not run: 
anm.die()

## End(Not run)

Description

Describes random treatment allocation for fifteen experimental designs.

Usage

anm.ExpDesign(method="all", titles =  TRUE, cex.text = 1, mp.col = NULL, lwda = 1, 
n = 10, EUcol = hcl.colors(n, palette = "Dark 3"), interval = 0.5, iter = 30)


ExpDesign(method="all", titles = TRUE, cex.text = 1, mp.col = NULL, lwda = 1, n = 10, 
EUcol = hcl.colors(n, palette = "Dark 3"),...)

anm.ExpDesign.tck()

Arguments

Details

The function returns a plot or series of plots illustrating the workings of experimental designs. Random apportionment of treatments of experimental units (EUs) is illustrated for each of twelve experimental designs. A character string can be specified in the method argument using a subset of any of the following:
"CRD": a one-way completely randomized design,
"factorial2by2": a 2 x 2 design with four EUs,
"factorial2by2by2": a 2 x 2 x 2 factorial designs with 8 EUs,
"nested": a nested design with two levels of nesting,
"RCBD" a randomized complete block design with two blocks, two treatments and four EUs,
"RIBD": a randomized incomplete block design with three blocks, three treatments, and six EUs,
"split": a split plot design with a whole plot (factor A) and a split plot (factor B),
"split.split": a split split-split plot design,
"SPRB": split plots in randomized blocks,
"strip.split": strip-split plot design,
"latin": a Latin squares design with r = 3, and
"pairs": a matched pairs design.
The function anm.ExpDesign.tck provides an interactive GUI. Details on these designs are given below.

Completely randomized design (CRD)

In a completely randomized design experimental units are each randomly assigned to factor levels without constraints like blocking. This approach can (and should) be implemented in one way ANOVAs, and in more complex formats like factorial and hierarchical designs.

Factorial design

Treatments can be derived by combining factor levels from the multiple factors. This is called a factorial design. In a fully crossed factorial design with two factors, A and B, every level in factor A is contained in every level of factor B.

Randomized block design (RBD)

In a randomized block design a researcher randomly assigns experimental units to treatments separately within units called blocks. If all treatments are assigned exactly once within each block this is known as a randomized complete block design (RCBD)

Latin squares

Latin squares designs are useful when there are two potential blocking variables. These can figuratively or literally be represented by rows and columns. All treatments are assigned to each row and to each column, and for each row and column treatment assignments differ. Of course this stipulation limits the number of ways one can allocate treatments.

Nested design

In a nested design factor levels from one factor will be contained entirely in one factor level from another factor. Consider a design with two factors A and B. When every level of factor A appears with every level of factor B, and vice versa, then we have a fully crossed factorial design (see above). Conversely, when levels of B only occur within a single level of A, then B is nested in A.

Split plot design

A split plot design contains two nested levels of randomization. At the highest level are whole plots which are randomly assigned factor levels from one factor. At a second nested level whole plots are split to form split plots. The split plots are randomly assigned factor levels from a second factor. Split plot designs are replicated in units called blocks. Split-split plot design will have two levels of split plot nesting: C (split-split plots) are split plots within B (split plots), and B are split plots within A (whole plots). We can see obvious and confusing similarities here to nested designs. A split plot randomized block (SPRB) design will have whole plots randomly assigned within blocks, and split plots randomly assigned within the whole plots. Thus, levels of A (whole plot) are assigned randomly to a block, and split plots containing levels of B (split plot) are assigned within a level of A.

Strip plot design

Closely related to split plot designs are strip plots. Strip plots can be used address situations when relatively large experimental units are required for each of two factors in an experiment. A strip plot will have a row and column structure. Let the number of columns equal to the number of levels in factor A, and let the number of rows be equal to the number of levels in factor B. Levels in A are randomly assigned to columns only (across all rows) in a RBD format, and levels in B are assigned to rows only (across all columns). Interestingly, the levels in A serve as split plots in B and vice versa. However, unlike a split plot design assignment of treatments at this level is not entirely random since rows are assigned single levels in A, while columns are assigned single levels in B. Compared to a factorial design strip plots allow for greater precision in the measurement of interaction effects while sacrificing precision in the measurement of main effects. Split-block design discussed by Littell et al. (2006), are indistinguishable from strip plots, described earlier, except that they are placed in the context of blocks. They are also indistinguishable from SPRBs except that the design has an explicit row/column structure (one level of A for each column, one level of B for each row), resulting in larger experimental units for A and B. Conversely, in a SPRB, different levels of A and B can be assigned within columns and rows respectively. A final type of split/strip plot design is known as a strip-split plot. Strip-split plots are three way designs (cf. Hoshmand 2006, Milliken and Johnson 2009). In these models a conventional two factor strip plot is created (factors A and B) and split plots are placed in the resulting cells (levels in factor C). The design is indistinguishable from a split-split plot design except for the fact that "columns" always constitute the same levels in A, while "rows" always constitute the same levels in B, allowing larger experimental units for A and B, and reflecting the strip plot relationship of A and B. Other, even more complex variants of split and strip plots are possible are possible. For instance, Littell et al. (2006) discuss a case study they describe as strip-split-split plot design!

Matched pairs

In a matched pairs design treatments are compared by using the same (or highly similar) experimental units. If treatments are assigned at particular time segments it is assumed that outcomes within an experimental unit are independent, i.e., there is no "carryover" effect from the previous treatment. Violation of this assumption may result in ashpericity and prevent conventional approaches.

Author(s)

Ken Aho

References

Hoshmand, A. R. (2006) Design of Experiments for Agriculture and the Natural Sciences 2nd Edition. CRC Press.

Littell, R. C., Stroup, W. W., and R. J. Fruend (2002) SAS for linear models. Wiley, New York.

Milliken, G. A., and D. E. Johnson (2009) Analysis of messy data: Vol. I. Designed experiments, 2nd edition. CRC.

See Also

samp.design

Examples

ExpDesign()
## Not run: anm.ExpDesign()

Description

Animated depictions of geometric, exponential, and logistic growth.

Usage

anm.geo.growth(n0, lambda, time = seq(0, 20), ylab = "Abundance",
xlab = "Time", interval = 0.1, ...)

anm.exp.growth(n, rmax, time = seq(0, 20), ylab = "Abundance",
xlab = "Time", interval = 0.1, ...)

anm.log.growth(n, rmax, K, time = seq(0, 60), ylab = "Abundance",
xlab = "Time", interval = 0.1, ...)

anm.geo.growth.tck()

anm.exp.growth.tck()

anm.log.growth.tck()

Arguments

Details

Presented here are three famous population growth models from ecology. Geometric, exponential and logistic growth. The first two model growth in the presence of unlimited resources. Geometric growth is exponential growth assuming non-overlapping generations, and is computed as:

$N_t = N_{0}\lambda^t,$

where $N_t$ is the number of individuals at time y, $\lambda$ is the geometric growth rate, and t is time.

Exponential growth allows simultaneous existence of multiple generations, and is computed as:

$\frac{dN}{dt}=r_{max}N,$

where $r_{max}$ is the maximum intrinsic rate of increase, i.e. max(birth rate - death rate), and N is the population size. With logistic growth, exponential growth is slowed as N approaches the carrying capacity. It is computed as:

$\frac{dN}{dt}=r_{max}N\frac{K-N}{K},$

where $r_{max}$ is the maximum rate of intrinsic increase, $N$ is the population size, and $K$ is the carrying capacity

All three functions can be run from tcltk GUIs.

Author(s)

Ken Aho

See Also

anm.LVexp, anm.LVcomp

Examples

## Not run: 
anm.geo.growth(10,2.4)

## End(Not run)

Description

Plots the normal, exponential, Poisson, binomial, and "custom" log-likelihood functions. By definition, likelihoods for parameter estimates are calculated by holding data constant and varying estimates. For the normal distribution a fixed value for the parameter which is not being estimated ($\mu$ or $\sigma^2$) is established using MLEs.

Usage

anm.loglik(X, dist = c("norm", "poi", "bin", "exp", "custom"),
plot.likfunc = TRUE, parameter = NULL, func = NULL, poss = NULL,
plot.density = TRUE, plot.calc = FALSE, xlab = NULL, ylab = NULL,
conv = diff(range(X))/70, anim = TRUE, est.col = 2, density.leg = TRUE,
cex.leg = 0.9, interval = 0.01, ...)

loglik.norm.plot(X, parameter = c("mu", "sigma.sq"), poss = NULL,
plot.likfunc = TRUE, plot.density = TRUE, plot.calc = FALSE,
xlab = NULL, ylab = NULL, conv = 0.01, anim = TRUE, est.col = 2,
density.leg = TRUE, cex.leg = 0.9, interval = 0.01, ...)

loglik.pois.plot(X, poss = NULL, plot.likfunc = TRUE,
plot.density = TRUE, plot.calc = FALSE, xlab = NULL, ylab = NULL,
conv = 0.01, anim = TRUE, interval = 0.01, ...)

loglik.binom.plot(X, poss = NULL, xlab = NULL, ylab = NULL,
plot.likfunc = TRUE, plot.density = TRUE, conv = 0.01, anim = TRUE,
interval = 0.01, ...)

loglik.exp.plot(X, poss = NULL, plot.likfunc = TRUE,
plot.density = TRUE, plot.calc = FALSE, xlab = NULL, ylab = NULL,
conv = 0.01, anim = TRUE, est.col = 2, density.leg = TRUE,
cex.leg = 0.9, interval = 0.01, ...)

loglik.custom.plot(X, func, poss, anim = TRUE, interval = 0.01,
xlab, ylab, ...)

anm.loglik.tck()

Arguments

Details

These plots are helpful in explaining the workings of ML estimation for parameters. Animation is included as an option to further clarify processes. When specifying poss be sure to include the estimate that you "want" the log-likelihood function to maximize in the vector of possibilities, e.g. mean(X) for estimation of $\mu$.

Value

Three animated plots can be created simultaneously. The first plot shows the normal, Poisson, exponential, binomial, or custom log-likelihood functions. The second plot shows the pdf with ML estimates for parameters. On this graph densities of observations are plotted as pdf parameters are varied. By default these two graphs will be created simultaneously on a single graphics device. By specifying plot.calc = TRUE a third plot can also be created which shows that log-likelihood is the sum of the log-densities. Animation in this third plot will be automatically sped up, using a primitive routine, for large datasets, and slowed for small datasets. The third plot will not be created for the binomial pdf because there will only be a single outcome from the perspective of likelihood (e.g. 10 successes out of 22 trials). The second and third plots will not be created for custom likelihood functions. The function anm.loglik.tck() runs anm.loglik() from a tcltk GUI.

Author(s)

Ken Aho

See Also

dnorm, dpois, dexp, dbinom

Examples

## Not run: 
##Normal log likelihood estimation of mu.
X<-c(11.2,10.8,9.0,12.4,12.1,10.3,10.4,10.6,9.3,11.8)
anm.loglik(X,dist="norm",parameter="mu")

##Add a plot describing log-likelihood calculation.
anm.loglik(X,dist="norm",parameter="mu",plot.calc=TRUE)

##Normal log likelihood estimation of sigma squared.
X<-c(11.2,10.8,9.0,12.4,12.1,10.3,10.4,10.6,9.3,11.8)
anm.loglik(X,dist="norm",parameter="sigma.sq")

##Exponential log likelihood estimation of theta
X<-c(0.82,0.32,0.14,0.41,0.09,0.32,0.74,4.17,0.36,1.80,0.74,0.07,0.45,2.33,0.21,
0.79,0.29,0.75,3.45)
anm.loglik(X,dist="exp")

##Poisson log likelihood estimation of lambda.
X<-c(1,3,4,0,2,3,4,3,5)
anm.loglik(X,dist="poi")

##Binomial log likelihood estimation of p.
X<-c(1,1,0,0,0,1,0,0,0,0)#where 1 = a success
anm.loglik(X,dist="bin",interval=.2)

##Custom log-likelihood function
func<-function(X=NULL,theta)theta^5*(1-theta)^10
anm.loglik(X=NULL,func=func,dist="custom",poss=seq(0,1,0.01),
xlab="Possibilities",ylab="Log-likelihood")

##Interactive GUI, requires package 'tcltk'
anm.loglik.tck()

## End(Not run)

Description

Depicts the process of least squares estimation by plotting the least squares function with respect to a vector of estimate possibilities.

Usage

anm.ls(X, poss=NULL, parameter = "mu", est.lty = 2, est.col = 2,
conv=diff(range(X))/50, anim=TRUE, plot.lsfunc = TRUE, plot.res = TRUE, 
interval=0.01, xlab=expression(paste("Estimates for ", italic(E),
"(",italic(X),")", sep = "")),...)

anm.ls.tck()

Arguments

Value

A plot of the least squares function is returned along with the least squares estimate for E(X) given a set of possibilities. The function anm.ls.tck provides a GUI to run the function.

Author(s)

Ken Aho

See Also

loglik.plot

Examples

## Not run: X<-c(11.2,10.8,9.0,12.4,12.1,10.3,10.4,10.6,9.3,11.8)
anm.ls(X)
## End(Not run)

Description

Depicts the process of least squares estimation of simple linear regression parameters by plotting the least squares function with respect to estimate possibilities for the intercept or slope.

Usage

anm.ls.reg(X, Y, parameter="slope", nmax=50, interval = 0.1, col = "red",...)

anm.ls.reg.tck()

Arguments

Value

An animated plot of the plot possible regression lines is created along with an animated plot of the residual sum of squares. The function anm.ls.reg.tck provides a GUI to run the function.

Author(s)

Ken Aho

See Also

loglik.plot, anm.ls

Examples

## Not run: 
X<-c(11.2,10.8,9.0,12.4,12.1,10.3,10.4,10.6,9.3,11.8)
Y<-log(X)
anm.ls.reg(X, Y, parameter = "slope")
## End(Not run)

Description

Creates animated plots of two famous abundance models from ecology; the Lotka-Volterra competition and exploitation models

Usage

anm.LVcomp(n1, n2, r1, r2, K1, K2, a2.1, a1.2, time = seq(0, 200), ylab =
"Abundance", xlab = "Time", interval = 0.1, ...)

anm.LVexp(nh, np, rh, con, p, d.p, time = seq(0, 200), ylab = "Abundance",
xlab = "Time", interval = 0.1, circle = FALSE, ...)

anm.LVc.tck()

anm.LVe.tck()

Arguments

Details

The Lotka-Volterra competition and exploitation models require simultaneous solutions for two differential equations. These are solved using the function rk4 from odesolve.

The interspecific competition model is based on:

$\frac{dN_1}{dt}=r_{max1}N_1\frac{K_1-N_1-\alpha_{12}}{K_1},$

$\frac{dN_2}{dt}=r_{max2}N_2\frac{K_2-N_2-\alpha_{21}}{K_2},$

where $N_1$ is the number of individuals from species one, $K_1$ is the carrying capacity for species one, $r_{max1}$ is the maximum intrinsic rate of increase of species one, and $\alpha_{12}$ is the interspecific competitive effect of species two on species one.

The exploitation model is based on:

$\frac{dN_h}{dt} = r_hN_h-pN_hN_p,$

$\frac{dN_p}{dt} = cpN_hN_p-d_pN_p,$

where $N_h$ is the number of individuals from the host (prey) species, $N_p$ is the number of individuals from the predator species, $r_h$ is the intrinsic rate of increase for the host (prey) species, $p$ is the rate of predation, $c$ is a conversion factor which describes the rate at which prey are converted to new predators, and $d_p$ is the death rate of the predators.

The term $r_hN_h$ describes exponential growth for the host (prey) species. This will be opposed by deaths due to predation, i.e. the term $pN_hN_p$. The term $cpN_hN_p$ is the rate at which predators destroy prey. This in turn will be opposed by $d_pN_p$, i.e. predator deaths. . The functions anm.LVe.tck() and anm.LVc.tck() allow one to run anm.LVe() and anm.LVc() with tcltk GUIs.

Value

The functions return descriptive animated plots

Author(s)

Ken Aho, based on a concept elucidated by M. Crawley

References

Molles, M. C. (2010) Ecology, Concepts and Applications, 5th edition. McGraw Hill.

Crawley, M. J. (2007) The R Book. Wiley

Examples

## Not run: 

#---------------------- Competition ---------------------#
##Species 2 drives species 1 to extinction
anm.LVcomp(n1=150,n2=50,r1=.7,r2=.8,K1=200,K2=1000,a2.1=.5,a1.2=.7,time=seq(0,200))
##Species coexist with numbers below carrying capacities
anm.LVcomp(n1=150,n2=50,r1=.7,r2=.8,K1=750,K2=1000,a2.1=.5,a1.2=.7,time=seq(0,200))

#----------------------Exploitation----------------------#
#Fast cycles
anm.LVexp(nh=300,np=50,rh=.7,con=.4,p=.006,d.p=.2,time=seq(0,200))
## End(Not run)

Description

The algorithm can use three different variants on MCMC random walks: Gibbs sampling, the Metropolis algorithm, and the Metropolis-Hastings algorithms to move through univariate anm.mc.norm and bivariate normal probability space. The jumping distribution is also bivariate normal with a mean vector at the current bivariate coordinates. The jumping kernel modifies the jumping distribution through multiplying the variance covariance of this distribution by the specified constant.

Usage

anm.mc.bvn(start = c(-4, -4), mu = c(0, 0), sigma = matrix(2, 2, data = c(1, 0,
 0, 1)), length = 1000, sim = "M", jump.kernel = 0.2, xlim = c(-4, 4),
 ylim = c(-4, 4), interval = 0.01, show.leg = TRUE, cex.leg = 1, ...)

anm.mc.norm(start = -4, mu = 0, sigma = 1, length = 2000, sim = "M",
 jump.kernel = 0.2, xlim = c(-4, 4), ylim = c(0, 0.4), interval = 0.01,
 show.leg = TRUE,...)

anm.mc.bvn.tck()

Arguments

Value

The function returns two plots. These are: 1) the proposal bivariate normal distribution in which darker shading indicates higher density, and 2) an animated plot showing the MCMC algorithm walking through the probability space.

Author(s)

Ken Aho

References

Gelman, A., Carlin, J. B., Stern, H. S., and D. B. Rubin (2003) Bayesian Data Analysis, 2nd edition. Chapman and Hall/CRC.

Description

Animated Comparisons of outcomes from simple random sampling, stratified random sampling and cluster sampling.

Usage

anm.samp.design(n=20, interval = 0.5 ,iter = 30, main = "", lwd = 2, lcol = 2)

samp.design(n = 20, main = "", lwd = 2, lcol = 2)

anm.samp.design.tck()

Arguments

Details

Returns a plot comparing outcomes of random sampling, stratified random sampling and cluster sampling from a population of size 400. For stratified random sampling the population is subdivided into four equally strata of size 100. and n/4 samples are taken within each strata. For cluster sampling the population is subdivided into four equally sized clusters and a census is taken from two clusters (regardless of specification of n). The function anm.samp.design depicts random sampling using animation

Value

A plot is returned with four subplots. (a) shows the population before sampling, (b) shows simple random sampling, (c) shows stratified random sampling, (d) shows cluster sampling. The function anm.samp.design.tck provides interactivity with a tcltk GUI.

Author(s)

Ken Aho

Examples

samp.design(20)

#Animated demonstration
## Not run: anm.samp.design(20)

Description

Schoener (1968) examined the resource partitioning of anolis lizards on the Caribbean island of South Bimini. He cross-classified lizard counts in habitats (branches in trees) with respect to three variables: lizard species A. sargei and A. distichus, branch height (high and low), and branch size (small and large).

Usage

data(anolis)

Format

A data frame with 8 observations on the following 4 variables.

height

Brach height. A factor with levels H, L.

size

Brach size. A factor with levels L, S.

species

Anolis species. A factor with levels distichus, sagrei.

count

Count at the cross classification.

Source

Schoener, T. W. (1968) The Anolis lizards of Bimini: resource partitioning in a complex fauna. Ecology 49(4): 704-726.

Description

A set of four bivariate datasets with the same conditional means, conditional variances, linear regressions, and correlations, but with dramatically different forms of association.

Usage

data(anscombe)

Format

A data frame with 11 observations on the following 8 variables.

x1

The first conditional variable in the first bivariate dataset.

y1

The second conditional variable in the first bivariate dataset.

x2

The first conditional variable in the second bivariate dataset.

y2

The second conditional variable in the second bivariate dataset.

x3

The first conditional variable in the third bivariate dataset.

y3

The second conditional variable in the third bivariate dataset.

x4

The first conditional variable in the fourth bivariate dataset.

y4

The second conditional variable in the fourth bivariate dataset.

Details

Anscombe (1973) used these datasets to demonstrate that summary statistics are inadequate for describing association.

Source

Anscombe, F. J. (1973) Graphs in statistical analysis. American Statistician 27 (1): 17-21.

References

Anscombe, F. J. (1973) Graphs in statistical analysis. American Statistician 27 (1): 17-21.

Examples

# dev.new(height=3.5)
op <- par(mfrow=c(1,4),mar=c (0,0,2,3), oma = c(5, 4.2, 0, 0))
with(anscombe, plot(x1, y1, xlab = "", ylab = "", main = bquote(paste(italic(r),
" = ",.(round(cor(x1, y1),2)))))); abline(3,0.5) 
with(anscombe, plot(x2, y2, xlab = "", ylab = "",, main = bquote(paste(italic(r),
" = ",.(round(cor(x2, y2),2)))))); abline(3,0.5) 
with(anscombe, plot(x3, y3, xlab = "", ylab = "",, main = bquote(paste(italic(r),
" = ",.(round(cor(x3, y3),2)))))); abline(3,0.5) 
with(anscombe, plot(x4, y4, xlab = "", ylab = "",, main = bquote(paste(italic(r),
" = ",.(round(cor(x4, y4),2)))))); abline(3,0.5) 
mtext(expression(italic(y[1])),side=1, outer = TRUE, line = 3)
mtext(expression(italic(y[2])),side=2, outer = TRUE, line = 2.6)
mtext("(a)",side=3, at = -42, line = .5)
mtext("(b)",side=3, at = -26, line = .5)
mtext("(c)",side=3, at = -10.3, line = .5)
mtext("(d)",side=3, at = 5.5, line = .5)
par(op)

Description

Wright et al. (2000) examined behavior of red wood ants (Formica rufa), a species that harvests honeydew in aphids. Worker ants traveled from their nests to nearby trees to forage honeydew from homopterans. Ants descending trees were laden with food and weighed more, given a particular ant head width, then unladen, ascending ants. The authors were interested in comparing regression parameters of the ascending and descending ants to create a predictive model of honeydew foraging load for a given ant size.

Usage

data(ant.dew)

Format

A data frame with 72 observations on the following 3 variables.

head.width

Ant head width in mm

ant.mass

Ant mass in mg

direction

Direction of travel A = ascending, D = descending

Details

Data approximated from Fig. 1 in Wright et al. (2002)

Source

Wright, P. J., Bonser, R., and U. O. Chukwu (2000) The size-distance relationship in the wood ant Formica rufa. Ecological Entomology 25(2): 226-233.

Description

Provides a more powerful alternative to Friedman's test for blocked (dependent) data with a single replicate.

Usage

AP.test(Y)

Arguments

Details

The Agresti-Pendergrast test is more powerful than Friedman's test, given normality, and remains powerful in heavier tailed distributions (Wilcox 2005).

Value

Returns a dataframe showing the numerator and denominator degrees of freedom, F test statistic, and p-value.

Note

code based on Wilcox (2005).

Author(s)

Ken Aho

References

Wilcox, R. R. (2005) Introduction to Robust Estimation and Hypothesis Testing, Second Edition. Elsevier, Burlington, MA.

See Also

friedman.test, MS.test

Examples

temp<-c(2.58,2.63,2.62,2.85,3.01,2.7,2.83,3.15,3.43,3.47,2.78,2.71,3.02,3.14,3.35,
2.36,2.49,2.58,2.86,3.1,2.67,2.96,3.08,3.32,3.41,2.43,2.5,2.85,3.06,3.07)
Y<- matrix(nrow=6,ncol=5,data=temp,byrow=TRUE)
AP.test(Y)

Description

This dataset was used by Littell (2002) to demonstrate repeated measures analyses. The effect of two asthma drugs and a placebo were measured on 24 asthmatic patients. Each patient was randomly given each drug using an approach to minimize carry-over effects. Forced expiratory volume (FEV1), the volume of air that can be expired after taking a deep breath in one second, was measured. FEV1 was measured hourly for eight hours following application of the drug. A baseline measure of FEV1 was also taken 11 hours before application of the treatment.

Usage

data(asthma)

Format

The dataframe has 11 columns:

PATIENT

The subjects (there were 24 patients).

BASEFEV1

A numerical variable; the baseline forced expiratory volume.

FEV11H

Forced expiratory volume at 11 hours.

FEV12H

Forced expiratory volume at 12 hours.

FEV13H

Forced expiratory volume at 13 hours.

FEV14H

Forced expiratory volume at 14 hours.

FEV15H

Forced expiratory volume at 15 hours.

FEV16H

Forced expiratory volume at 16 hours.

FEV17H

Forced expiratory volume at 17 hours.

FEV18H

Forced expiratory volume at 18 hours.

DRUG

A factor with three levels "a" = a standard drug treatment, "c" = the drug under development, and "p" = a placebo.

Source

Littell, R. C., Stroup, W. W., and R. J. Freund (2002) SAS for Linear Models. John Wiley and Associates.

Description

A simple algorithm for calculating AUC.

Usage

auc(obs, fit, plot = FALSE)

Arguments

Author(s)

Ken Aho

References

Agresti, A. (2012) Categorical Data Analysis, 3rd edition. New York. Wiley.

Examples

## Not run: 
obs <-rbinom(30, 1, 0.5)
fit <- rbeta(30, 1, 2)
auc(obs, fit)
## End(Not run)

Description

In general, mammals are able to walk within minutes or hours after birth. Human babies, however, generally don't begin to walk until they are between 10 and 18 months of age. This occurs because, although humans are born with rudimentary reflexes for walking, they are unused, and thus largely disappear by the age of eight weeks. As a result these movements must be relearned by an infant following significant passage of time, through a process of trial and error. Zelazo et al. (1972) performed a series of experiments to determine whether certain exercises could allow infants to maintain their walking reflexes, and allow them to walk at an earlier age. Study subjects were 24 white male infants from middle class families, and were assigned to one of four exercise treatments.

Active exercise (AE): Parents were taught and were told to apply exercises that would strengthen the walking reflexes of their infant. Passive exercise (PE): Parents were taught and told to apply exercises unrelated to walking. Test-only (TO): The investigators did not specify any exercise, but visited and tested the walking reflexes of infants in weeks 1 through 8. Passive and active exercise infants were also tested in this way. Control (C): No exercises were specified, and infants were only tested at weeks one and eight. This group was established to account for the potential effect of the walking reflex tests themselves.

Usage

data(baby.walk)

Format

A data frame with 22 observations on the following 2 variables.

date

Age when baby first started walking (in months)

treatment

A factor with levels AE C PE TO

Source

Ott, R. L., and M. T. Longnecker 2004 A First Course in Statistical Methods. Thompson.

References

Zelazo, P. R., Zelazo, N. A., and S. Kolb. 1972. Walking in the newborn. Science 176: 314-315.

Description

Data from northern myotis bats (Myotis septentrionalis) captured in the field in Vermillion County Indiana in 2000.

Usage

data(bats)

Format

The dataframe has 2 columns:

days

The age of the bats in days.

forearm.length

The length of the forearm in millimeters.

Source

Krochmal, A. R., and D. W. Sparks (2007) Journal of Mammalogy. 88(3): 649-656.

Description

An simple function for for summarizing a Bayesian analysis given discrete or categorical variables and priors.

Usage

Bayes.disc(Likelihood, Prior, data.name = "data", plot = TRUE, 
c.data = seq(1, length(Prior)), ...)

Bayes.disc.tck()

Arguments

Author(s)

Ken Aho

Description

Gelman et al. (2002) describe general methods for Bayesian implementation of simple linear models (e.g. simple and multiple regression and fixed effect one way ANOVA) with standard non-informative priors uniform on $\alpha, \sigma^2$. The function is not yet suited for multifactor or multivariance (random effect) ANOVAs.

Usage

bayes.lm(Y, X, model = "anova", length = 1000, cred = 0.95)

Arguments

Value

Provides the median and central credible intervals for model parameters.

Author(s)

Ken Aho

References

Gelman, A., Carlin, J. B., Stern, H. S., and D. B. Rubin (2003) Bayesian Data Analysis, 2nd edition. Chapman and Hall/CRC.

See Also

mcmc.norm.hier

Examples

## Not run: 
data(Fbird)
X <- with(Fbird, cbind(rep(1, 18), vol))
Y <- Fbird$freq
bayes.lm(Y, X, model = "reg")

## End(Not run)

Description

This dataset, lifted from vegan, contains tree counts in 1-hectare plots in Barro Colorado Island, Panama.

Usage

data(BCI.count)

Format

A data frame with 50 plots (rows) of 1 hectare with counts of trees on each plot with total of 225 species (columns). Full Latin names are used for tree species.

Details

Data give the numbers of trees at least 10 cm in diameter at breast height (1.3 m above the ground) in each one hectare square of forest. Within each one hectare square, all individuals of all species were tallied and are recorded in this table.

The data frame contains only the Barro Colorado Island subset of the original data.

The quadrats are located in a regular grid. See examples for the coordinates.

Source

Condit et al. (2002). Data documentation here follows directly from vegan.

References

Condit, R, Pitman, N, Leigh, E.G., Chave, J., Terborgh, J., Foster, R.B., Nuñez, P., Aguilar, S., Valencia, R., Villa, G., Muller-Landau, H.C., Losos, E. & Hubbell, S.P. (2002). Beta-diversity in tropical forest trees. Science 295, 666–669.

Description

The presence of the tropical trees Alchornea costaricensis and Anacardium excelsum with diameter at breast height equal or larger than 10 cm were recorded on along with environmental factors at Barro Colorado Island in Panama (Kindt and Coe 2005). These data were originally from (Pyke et al. 2001).

Usage

data(BCI.plant)

Format

A data frame with 43 observations on the following 9 variables.

site.no.

A factor with levels C1 C2 C3 C4 p1 p10 p11 p12 p13 p14 p15 p16 p17 p18 p19 p2 p20 p21 p22 p23 p24 p25 p26 p27 p28 p29 p3 p30 p31 p32 p33 p34 p35 p36 p37 p38 p39 p4 p5 p6 p7 p8 p9

UTM.E

UTM easting.

UTM.N

UTM northing.

precip

Precipitation in mm/year.

elev

Elevation in m above sea level.

age

A categorical vector describing age.

geology

A factor describing geology with levels pT Tb Tbo Tc Tcm Tct Tgo Tl Tlc.

Alchornea.costaricensis

Plant presence/absence.

Anacardium.excelsum

Plant presence/absence.

Source

Condit et al. (2002), Kindt et al. (2005).

References

Condit, R, Pitman, N, Leigh, E.G., Chave, J., Terborgh, J., Foster, R.B., Nunez, P., Aguilar, S., Valencia, R., Villa, G., Muller-Landau, H.C., Losos, E. & Hubbell, S.P. (2002). Beta-diversity in tropical forest trees. Science 295, 666–669.

Kindt, R. & Coe, R. (2005) Tree diversity analysis: A manual and software for common statistical methods for ecological and biodiversity studies from the BiodiversityR package.

Pyke CR, Condit R, Aguilar S and Lao S. (2001). Floristic composition across a climatic gradient in a neotropical lowland forest. Journal of Vegetation Science 12: 553-566.

Description

One and two way heteroscedastic rank-based permutation tests. Two way designs are assumed to be factorial, i.e., interactions are tested.

Usage

BDM.test(Y, X)

BDM.2way(Y, X1, X2)

Arguments

Details

A problem with the Kruskal-Wallis test is that, while it does not assume normality for groups, it still assumes homoscedasticity (i.e. the groups have the same distributional shape). As a solution Brunner et al. (1997) proposed a heteroscedastic version of the Kruskal-Wallis test which utilizes the F-distribution. Along with being robust to non-normality and heteroscedasticity, calculations of exact P-values using the Brunner-Dette-Munk method are not made more complex by tied values. This is another obvious advantage over the traditional Kruskal-Wallis approach.

Value

Returns a list with two components

Note

Code based on Wilcox (2005)

Author(s)

Ken Aho

References

Brunner, E., Dette, H., and A. Munk (1997) Box-type approximations in nonparametric factorial designs. Journal of the American Statistical Association. 92: 1494-1502.

Wilcox, R. R. (2005) Introduction to Robust Estimation and Hypothesis Testing, Second Edition. Elsevier, Burlington, MA.

See Also

kruskal.test, trim.test

Examples

rye<-c(50,49.8,52.3,44.5,62.3,74.8,72.5,80.2,47.6,39.5,47.7,50.7)
nutrient<-factor(c(rep(1,4),rep(2,4),rep(3,4)))
BDM.test(Y=rye,X=nutrient)

Description

Counts of grizzly bear (Ursus arctos) litter sizes from the Greater Yellowstone Ecosystem from 1973-2010.

Usage

data(bear)

Format

A data frame with 38 observations on the following 5 variables.

Year

Year.

X1.cub

The number of litters with one cub.

X2.cub

The number of litters with two cubs.

X3.cub

The number of litters with three cubs.

X4.cub

The number of litters with four cubs.

Source

Haroldson, M. A (2010) Assessing trend and estimating population size from counts of unduplicated females. Pgs 10-15 in Schwartz, C. C., Haroldson, M. A., and K. West editors. Yellowstone grizzly bear investigations: annual report of the Interagency grizzly bear study team, 2010. U. S. Geological Survey, Bozeman, MT.

Description

Saint Germain et al. (2007) modeled the presence absence of a saprophytic wood boring beetle (Anthophylax attenuatus) as a function of the wood density of twenty-four decaying aspen trees (Populus tremuloides) in Western Quebec Canada.

Usage

data(beetle)

Format

A data frame with 24 observations on the following 4 variables.

Snag

Snag identifier

Yrs.since.death

The number of years since death, determined using dendrochronological methods.

Wood.density

The density of the decaying wood (dry weight/volume) in units of g cm$-3$.

ANAT

Beetle presence/absence (1/0)

Source

Saint-Germain, M., Drapeau, P., and C. Buddle (2007) Occurrence patterns of aspen- feeding wood-borers (Coleoptera: Cerambycidae) along the wood decay gradient: active selection for specific host types or neutral mechanisms? Ecological Entomology 32: 712-721.

Description

Distinct classifications will have class labels that may prevent straightforward comparisons. This algorithm considers all possible permutations of class labels to find a configuration that maximizes agreement on the diagonal of a contingency table comparing two classifications. Classifications need not have the same number of classes.

Usage

best.agreement(class1, class2, test = FALSE, rperm = 100)

Arguments

Details

Class assignments are fixed in class1, all possible permutations of class labels in class2 are considered to find a configuration that maximizes agreement in the two classifications. If test=TRUE, a permutation test is run for the null hypothesis that maximum agreement between classifications is no better than random. This is done by sampling without replacement rperm times from class2, finding maximum agreement between class1 and the randomly permuted classifications, and dividing one plus the number of times that maximum agreement between the random classifications and class1 was greater than the maximum agreement observed for class1 and class2. Testing can be slow because it will be based on nested loops with $p x c!$ steps, where p is nperm and c! is the number of combinatorial permutations possible for categories in class2.

Value

A object of class max_agree.

Author(s)

Ken Aho. The internal permutations algorithm for obtaining all possible permutations was provided by Benjamin Christoffersen on stackoverflow.

See Also

cutree, hclust

Examples

# Example comparing a 4 cluster average-linkage solution 
# and a 5 cluster Ward-linakage solution 

avg <- hclust(dist(USArrests), "ave")
avg.4 <- as.matrix(cutree(avg, k = 4))
war <- hclust(dist(USArrests), "ward.D")
war.5 <- as.matrix(cutree(war, k = 5))

ba <- best.agreement(avg.4, war.5, test = TRUE)
ba

Description

The function bin2dec Converts binary representations to digital numbers (e.g., 10101011 = 171). Fractions, (e.g., 0.11101) will be evaluated to the number of bits provided. The function will not handle codification of whole numbers with fractional parts. The function dec2bin Converts decimal representations to binary and can handle whole numbers, fractional, and numbers with both whole and fractional parts.

Usage

bin2dec(digits, round = 4)

dec2bin(num, max.bits = 10, max.rep0 = 6)

Arguments

Details

If a decimal number with fractional, or both whole and fractional parts is provided to dec2bin, a vector with seperate binary expressions for each of these components is returned.

Author(s)

Ken Aho

Examples

bin2dec(1011001101) #=717
dec2bin(717)

Description

To investigate how pollen removal varied with reproductive caste in bemblebees (Bombus sp.) Harder and Thompson (1989) recorded the proportion of pollen removed by thirty five bumblebee queens and twelve worker bees.

Usage

data(bombus)

Format

This data frame contains the following columns:

pollen

A numeric vector indicating the proportion of pollen removed.

caste

A character string vector indicating whether a bee was a worker "W" or a queen "Q".

Source

Harder, L. D. and Thompson, J. D. 1989. Evolutionary options for maximizing pollen dispersal in animal pollinated plants. American Naturalist 133: 323-344.

Description

Neter et al. (1996) described an experiment in which researchers investigated the confounding effect of gender and bone development on growth hormone therapy for prepubescent children. Gender had two levels: "M" and "F". The bone development factor had three levels indicating the severity of growth impediment before therapy: 1 = severely depressed, 2 = moderately depressed, and 3 = mildly depressed. At the start of the experiment 3 children were assigned to each of the six treatment combinations. However 4 of the children were unable to complete the experiment, resulting in an unbalanced design.

Usage

data(bone)

Format

A data frame with 14 observations on the following 3 variables.

gender

A factor with levels F M

devel

A factor with levels 1 2 3

growth

A numeric vector descibing the growth difference before and after hormone therapy

Source

Neter, J., Kutner, M. H., Nachtsheim, C. J., and Wasserman, W (1996) Applied Linear Statistical Models. McGraw-Hill, Boston MA, USA.

Description

Provides a pulldown GUI menus to allow access to asbio statistical and biological graphical demos, e.g. anm.ci, samp.dist, anm.loglik, etc. The function demos is deprecated. The function book.menu currently provides links to over 100 distinct GUIs (many of these are slaves to other GUIs), which in turn provide distinct graphical demonstrations. The GUIs work best with an SDI R interface.

Usage

book.menu()

Author(s)

Ken Aho and Roy Hill (Roy created the book.menu GUI)

See Also

anm.coin, anm.ci, anm.die, anm.exp.growth, anm.geo.growth, anm.log.growth, anm.loglik, anm.LVcomp, anm.LVexp, anm.ls, anm.ls.reg, anm.transM, see.lmu.tck, samp.dist, see.HW, see.logic, see.M, see.move, see.nlm, see.norm.tck, see.power, see.regression.tck, see.typeI_II, selftest.se.tck1, shade.norm, Venn

Examples

## Not run: 
book.menu()

## End(Not run)

Description

Creates a bootstrap confidence interval for location differences for two samples. The default location estimator is the Huber one-step estimator, although any estimator can be used. The function is based on a function written by Wilcox (2005). Note, importantly, that P-values may be in conflict with the confidence interval bounds.

Usage

boot.ci.M(X1, X2, alpha = 0.05, est = huber.one.step, R = 1000)

Arguments

Value

Returns a list with one component, a dataframe containing summary information from the analysis:

Author(s)

Ken Aho and R. R. Wilcox from whom I stole liberally from code in the function m2ci on R-forge

References

Manly, B. F. J. (1997) Randomization and Monte Carlo methods in Biology, 2nd edition. Chapman and Hall, London.

Wilcox, R. R. (2005) Introduction to Robust Estimation and Hypothesis Testing, 2nd edition. Elsevier, Burlington, MA.

See Also

bootstrap, ci.boot

Examples

## Not run: 
X1<-rnorm(100,2,2.5)
X2<-rnorm(100,3,3)
boot.ci.M(X1,X2)

## End(Not run)

Description

The function serves as a simplified alternative to the function boot from the library boot.

Usage

bootstrap(data, statistic, R = 1000, prob = NULL, matrix = FALSE)

Arguments

Details

With bootstrapping we sample with replacement from a dataset of size n with n samples R times. At each of the R iterations a statistical summary can be created resulting in a bootstrap distribution of statistics.

Value

Returns a list. The utility function asbio:::print.bootstrap returns summary output. Invisible items include the resampling distribution of the statistic, the data, the statistic, and the bootstrap samples.

Author(s)

Ken Aho

References

Manly, B. F. J. (1997) Randomization and Monte Carlo Methods in Biology, 2nd edition. Chapman and Hall, London.

See Also

boot, ci.boot

Examples

data(vs)
# A partial set of observations from a single plot for a Scandinavian 
# moss/vascular plant/lichen survey.
site18<-t(vs[1,])

#Shannon-Weiner diversity
SW<-function(data){
d<-data[data!=0]
p<-d/sum(d)
-1*sum(p*log(p))
}

bootstrap(site18[,1],SW,R=1000,matrix=FALSE)

Description

The function calculates the angle of azimuth from a Cartesian coordination given in X and Y to a nearest neighbor coordinate given by nX and nY. The nearest neighbor coordinates can be obtained using the function near.bound.

Usage

bound.angle(X, Y, nX, nY)

Arguments

Details

The function returns the nearest neighbor angles (in degrees) with respect to a four coordinate system ala ARC-GIS Near(Analysis). Output angles range from $-180^{\circ}$ to $180^{\circ}$: $0^{\circ}$ to the East, $90^{\circ}$ to the North, $180^{\circ}$ (or $-180^{\circ}$) to the West, and $-90^{\circ}$ to the South.

Value

Returns a vector of nearest neighbor angles.

Author(s)

Ken Aho

See Also

near.bound, prp

Examples

bX<-seq(0,49)/46
bY<-c(4.89000,4.88200,4.87400,4.87300,4.88000,4.87900,4.87900,4.90100,4.90800,
4.91000,4.93300,4.94000,4.91100,4.90000,4.91700,4.93000,4.93500,4.93700,
4.93300,4.94500,4.95900,4.95400,4.95100,4.95800,4.95810,4.95811,4.95810,
4.96100,4.96200,4.96300,4.96500,4.96500,4.96600,4.96700,4.96540,4.96400,
4.97600,4.97900,4.98000,4.98000,4.98100,4.97900,4.98000,4.97800,4.97600,
4.97700,4.97400,4.97300,4.97100,4.97000)

X<-c(0.004166667,0.108333333,0.316666667,0.525000000,0.483333333,0.608333333,
0.662500000,0.683333333,0.900000000,1.070833333)
Y<-c(4.67,4.25,4.26,4.50,4.90,4.10,4.70,4.40,4.20,4.30)
nn<-near.bound(X,Y,bX,bY)

bound.angle(X,Y,nn[,1],nn[,2])

Description

Creates barplots for displaying statistical summaries by treatment (e.g. means, medians, M-estimates of location, standard deviation, variance, etc.) and their error estimates by treatment (i.e. standard errors, confidence intervals, IQRs, IQR confidence intervals, and MAD intervals). Custom intervals can also be created. The function can also be used to display letters indicating if comparisons of locations are significant after adjustment for simultaneous inference (see pairw.anova, pairw.kw, and/or pairw.fried).

Usage

bplot(y, x, bar.col = "gray", loc.meas = mean, sort = FALSE, order = NULL, int = "SE",
 conf = 0.95, uiw = NULL, liw = NULL, sfrac = 0.1, slty = 1, scol = 1,
 slwd = 1, exp.fact = 1.5, simlett = FALSE, lett.side = 3, lett = NULL,
 cex.lett = 1, names.arg = NULL, ylim = NULL, horiz = FALSE, xpd = FALSE, 
 print.summary = TRUE, ...)

Arguments

Details

It is often desirable to display the results of a pairwise comparison procedure using sample measures of location and error bars. This functions allows these sorts of plots to be made. The function is essentially a wrapper for the function barplot.

Value

A plot is returned. Bar centers (ala barplot) are returned invisibly.

Author(s)

Ken Aho

References

Chambers, J. M., Cleveland, W. S., Kleiner, B. and Tukey, P. A. (1983) Graphical Methods for Data Analysis. Wadsworth & Brooks/Cole.

McGill, R., Tukey, J. W. and Larsen, W. A. (1978) Variations of box plots. The American Statistician 32, 12-16.

See Also

mad, barplot, pairw.anova, pairw.kw, pairw.fried

Examples

eggs<-c(11,17,16,14,15,12,10,15,19,11,23,20,18,17,27,33,22,26,28)
trt<-c(1,1,1,1,1,2,2,2,2,2,3,3,3,3,4,4,4,4,4)
bplot(y=eggs, x=factor(trt),int="SE",xlab="Treatment",ylab="Mean number of eggs",
simlett=TRUE, lett=c("b","b","b","a"))

Description

Cheatgrass (Bromus tectorum) is an introduced annual graminoid that has invaded vast areas of sagebrush steppe in the intermountain west. Because it completes its vegetative growth stage relatively early in the summer, it leaves behind senescent biomass that burns easily. As a result areas with cheatgrass often experience a greater frequency of summer fires. A number of dominant shrub species in sagebrush steppe are poorly adapted to fire. As a result, frequent fires can change a community formerly dominated by shrubs to one dominated by cheatgrass. Nitrogen can also have a strong net positive effect on the cheatgrass biomass. A study was conducted at the Barton Road Long Term Experimental Research site (LTER) in Pocatello Idaho to simultaneously examine the effect of shrub removal and nitrogen addition on graminoid productivity.

Usage

data(bromus)

Format

The dataframe has 3 columns:

Plot

Plot number.

Biomass

Grass biomass in grams per meter squared.

Trt

Treatment. C = Control, LN = Low nitrogen, HN = High Nitrogen, SR = Shrub removal.

Description

Creates diagnostic bivariate quelplot ellipses (bivariate boxplots) using the method of Goldberg and Iglewicz (1992). The output can be used to check assumptions of bivariate normality and to identify multivariate outliers. The default robust=TRUE option relies on on a biweight correlation estimator function written by Everitt (2006). Quelplots, are potentially asymmetric, although the method currently employed here uses a single "fence" definition and creates symmetric ellipses.

Usage

bv.boxplot(X, Y, robust = TRUE, D = 7, xlab = "X", ylab="Y", pch = 21, 
pch.out = NULL, bg = "gray", bg.out = NULL, hinge.col = 1, fence.col = 1, 
hinge.lty = 2, fence.lty = 3, xlim = NULL, ylim = NULL, names = 1:length(X), 
ID.out = FALSE, cex.ID.out = 0.7, uni.CI = FALSE, uni.conf = 0.95, 
uni.CI.col = 1, uni.CI.lty = 1, uni.CI.lwd = 2, show.points = TRUE, ...)

Arguments

Details

Two ellipses are drawn. The inner is the "hinge" which contains 50 percent of the data. The outer is the "fence". Observations outside of the "fence" constitute possible troublesome outliers. The function bivariate from Everitt (2004) is used to calculate robust biweight measures of correlation, scale, and location if robust = TRUE (the default). We have the following form to the quelplot model:

$E_i = \sqrt{\frac{X^2_{si} + Y^2_{si} - 2R^*X_{si}Y_{si}}{1-R^{*2}}}.$

where $X_{si} = (X_i - T^*_X)/S^*_X$, and $Y_{si} = (Y_i - T^*_X)/S^*_Y$ are standardized values for $X_i$ and $Y_i$, respectively, $T^*_X$ and $T^*_Y$ are location estimators for X and Y, $S^*_X$ and $S^*_Y$ are scale estimators for X and Y, and $R^*$ is a correlation estimator for X and Y. We have:

$E_m = median\{E_i:i=1,2,...,n\},$

and

$E_{max} = max\{E_i: E_i^2 < DE^2_m\}.$

where $D$ is a constant that regulates the distance of the "fence" and "hinge".

To draw the "hinge" we have:

$R_1 = E_m\sqrt{\frac{1 + R^*}{2}},$

$R_2 = E_m\sqrt{\frac{1 - R^*}{2}}.$

To draw the "fence" we have:

$R_1 = E_{max}\sqrt{\frac{1 + R^*}{2}},$

$R_2 = E_{max}\sqrt{\frac{1 - R^*}{2}}.$

For $\theta$ = 0 to 360, let:

$\Theta_1 = R_1cos(\theta),$

$\Theta_2 = R_2sin(\theta).$

The Cartesian coordinates of the "hinge" and "fence" are:

$X=T^*_X=(\Theta_1+\Theta_2)S^*_X,$

$Y=T^*_Y=(\Theta_1-\Theta_2)S^*_Y.$

Quelplots, are potentially asymmetric, although the current (and only) method used here defines a single value for $E_{max}$ and hence creates symmetric ellipses. Under this implementation at least one point will define $E_{max}$, and lie on the "fence".

Value

A diagnostic plot is returned. Invisible objects from the function include location, scale and correlation estimates for $X$ and $Y$, estimates for $E_m$ and $E_{max}$, and a list of outliers (that exceed $E_{max}$).

Author(s)

Ken Aho, the function relies on an Everitt (2006) function for robust M-estimation.

References

Everitt, B. (2006) An R and S-plus Companion to Multivariate Analysis. Springer.

Goldberg, K. M., and B. Ingelwicz (1992) Bivariate extensions of the boxplot. Technometrics 34: 307-320.

See Also

boxplot

Examples

Y1<-rnorm(100, 17, 3)
Y2<-rnorm(100, 13, 2)
bv.boxplot(Y1, Y2)

X <- c(-0.24, 2.53, -0.3, -0.26, 0.021, 0.81, -0.85, -0.95, 1.0, 0.89, 0.59, 
0.61, -1.79, 0.60, -0.05, 0.39, -0.94, -0.89, -0.37, 0.18)
Y <- c(-0.83, -1.44, 0.33, -0.41, -1.0, 0.53, -0.72, 0.33,  0.27, -0.99, 0.15, 
-1.17, -0.61, 0.37, -0.96, 0.21, -1.29, 1.40, -0.21, 0.39)
b <- bv.boxplot(X, Y, ID.out = TRUE, bg.out = "red")
b

Description

The function uses functions from lattice and mvtnorm to make wireframe plots of bivariate normal distributions. Remember that the covariance must be less than the product of the marginal standard deviations (square roots of the diagonal elements).

Usage

bvn.plot(mu = c(0, 0), cv = 0, vr = c(1, 1), res = 0.3, xlab = expression(y[1]),
ylab = expression(y[2]), zlab = expression(paste("f(", y[1], ",", y[2], ")")), ...)

Arguments

Author(s)

Ken Aho

Description

Atmospheric $\delta ^{14}$C (per mille) and CO$_2$ (ppm) measurements for La Jolla Pier, California. Latitude: 32.9 Degrees N, Longitude: 117.3 Degrees W, Elevation: 10m; $\delta$ $^{14}$C derived from flask air samples

Usage

data(C.isotope)

Format

A data frame with 280 observations on the following 5 variables.

Date

a factor with levels 01-Apr-96 01-Jul-92 01-Jul-93 02-Apr-01 02-Feb-96 02-Nov-94 02-Oct-92 03-Aug-06 03-Aug-92 03-Jan-95 03-Jan-97 03-Jul-95 03-Mar-93 03-May-05 03-May-96 03-Nov-05 04-Apr-94 04-Jun-01 04-Jun-03 04-Mar-03 04-May-01 04-May-07 04-Sep-96 05-Aug-96 05-Jul-05 05-Jun-00 05-Sep-00 06-Aug-02 06-Oct-06 06-Sep-01 06-Sep-07 07-Apr-05 07-Apr-95 07-Aug-07 07-Dec-07 07-Feb-01 07-Feb-03 07-Feb-05 07-Jun-07 07-Mar-01 07-Sep-05 08-Feb-94 08-Feb-95 08-Feb-99 08-Jan-01 08-Jun-95 08-Sep-99 09-Dec-01 09-Feb-93 09-Jan-02 09-Jun-04 09-Nov-00 09-Nov-02 09-Nov-06 09-Sep-02 09-Sep-03 09-Sep-92 10-Apr-03 10-Aug-01 10-Aug-97 10-Aug-99 10-Jan-98 10-Jun-02 10-Nov-95 10-Oct-00 10-Oct-04 10-Oct-97 11-Dec-92 11-Feb-00 11-Jan-07 11-Jan-93 11-Mar-94 11-Mar-96 11-Nov-93 11-Oct-02 12-Apr-93 12-Apr-99 12-Aug-93 12-Jul-02 12-Jun-06 12-Oct-07 13-Feb-98 13-Jan-98 13-Jun-01 13-Mar-95 13-May-02 13-Sep-06 14-Apr-00 14-Aug-00 14-Dec-98 14-Feb-03 14-Jul-00 14-Sep-04 15-Dec-93 15-Feb-06 15-Feb-95 15-May-95 15-Oct-99 16-Apr-96 16-Jul-01 16-Jun-00 16-Nov-03 16-Nov-99 16-Oct-95 17-Dec-02 17-Feb-02 17-Feb-97 17-Jul-06 17-Jul-07 17-Mar-06 17-May-94 17-Nov-99 18-Aug-00 18-Dec-92 18-Jul-97 18-Jun-05 18-Mar-03 18-May-93 18-Nov-94 19-Apr-05 20-Apr-04 20-Mar-00 21-Apr-06 21-Aug-95 21-Dec-04 21-Jan-00 21-Jul-99 21-Jun-02 21-Jun-93 22-Apr-97 22-Feb-00 22-Feb-96 22-Jan-96 22-Jun-94 22-Mar-02 22-May-06 22-May-98 23-Apr-98 23-Feb-07 23-Jul-92 23-Jun-97 23-Mar-01 23-Mar-05 24-Apr-03 24-Aug-94 24-Feb-93 24-Jul-01 24-Jul-02 24-Jun-03 24-Mar-04 25-Apr-02 25-Aug-98 25-Jan-06 25-Oct-96 26-Aug-04 26-Dec-03 26-Feb-04 26-Jan-05 26-Jan-99 26-Jun-96 26-Mar-04 26-May-00 26-May-04 26-Sep-95 27-Jul-04 27-Mar-07 27-Nov-96 27-Oct-05 28-Jul-04 28-Jul-05 29-Aug-03 29-Dec-02 29-Jul-98 29-Jun-98 29-Oct-92 29-Oct-98 30-Jun-97 30-Nov-93 31-Dec-99 31-Jan-04 31-Oct-01 31-Oct-03

Decimal.date

A numeric vector

CO2

CO$_2$ concentration (in ppm)

D14C

$\delta$ $^{14}$C (in per mille)

D14C.uncertainty

measurement uncertainty for D14C(in per mille)

Source

H. D. Graven, R. F. Keeling, A. F. Bollenbacher Scripps CO$_2$ Program Scripps Institution of Oceanography (SIO) University of California, La Jolla, California USA 92093-0244 and

T. P. Guilderson Center for Accelerator Mass Spectrometry (CAMS) Lawrence Livermore National Laboratory (LLNL) Livermore, California USA 94550

References

H. D. Graven, T. P. Guilderson and R. F. Keeling, Observations of radiocarbon in CO$_2$ at La Jolla, California, USA 1992-2007: Analysis of the long-term trend. Journal of Geophysical Research.

Description

Stratified random sampling was used to estimate the size of the Nelchina herd of Alaskan caribou (Rangifer tarandus) in February 1962 (Siniff and Skoog 1964). The total population of sample units (for which responses would be counts of caribou) consisted of 699 four mile$^2$ areas. This population was divided into six strata, and each of these was randomly sampled.

Usage

data(caribou)

Format

A data frame with 6 observations on the following 5 variables.

stratum

Strata; a factor with levels A B C D E F

N.h

Strata population size

n.h

Strata sample size

x.bar.h

Strata means

var.h

Strata variances

Source

Siniff, D. B., and R. O. Skoog (1964) Aerial censusing of caribou using stratified random sampling. Journal of Wildlife Management 28: 391-401.

Description

These data were used by Ramsey and Schaefer (1997) to demonstrate multiple regression. The dataset was originally collected by Sacher and Stafeldt (1974) and provided (for varying sample sizes) average values of brain weight, body weight, gestation period and litter size for 96 placental mammal species.

Usage

data("case0902")

Format

A data frame with 96 observations on the following 5 variables.

Xs

A factor defining common names for mammal species under examination.

Y

Brain weight (in grams).

Xb

Body weight (in kilograms).

Xg

Gestation period length (in days).

Xl

Litter size.

Source

Ramsey, F., and Schafer, D. (1997). The statistical sleuth: a course in methods of data analysis. Cengage Learning.

References

Sacher, G. A., and Staffeldt, E. F. (1974). Relation of gestation time to brain weight for placental mammals: implications for the theory of vertebrate growth. The American Naturalist, 108(963), 593-615.

Examples

data(case0902)

Description

Ramsey and Schafer (1997) used this dataset to illustrate considerations in model selection. The data describe attributes of 61 female and 32 male clerical employees hired between 1965 and 1975 by a bank sued for sexual harassment.

Usage

data("case1202")

Format

A data frame with 93 observations on the following 7 variables.

Yhire

Annual salary upon hire (US dollars).

Y77

Annual salary in 1977 (US dollars).

Xsex

Sex; a factor with the levels FEMALE and MALE.

Xsen

Seniority (months since first hired).

Xage

Age (in months).

Xed

Education (in years).

Xexp

Experience previous to being hired by the bank (in months).

Source

Ramsey, F., and Schafer, D. (1997). The statistical sleuth: a course in methods of data analysis. Cengage Learning.

Examples

data(case1202)

Description

Chi-plots (Fisher and Switzer 1983, 2001) provide a method to diagnose multivariate non-independence among Y variables.

Usage

chi.plot(Y1, Y2, ...)

Arguments