asbio (version 0.2-1)

samp.dist: Representation of a statistic's sampling distribution

Description

Samples from a parent distribution without replacement with sample size = s.size R times. At each iteration a statistic requested in stat is calculated. Thus a distribution of R statistic estimates is created. This distribution is shown as a relative frequency histogram. Sampling distributions for up to four different statistics utilizing two different parent distributions. Statistic conceptual sampling distributions can be combined in various way by specifying a function in func (see below).

Usage

samp.dist(parent, parent2 = parent, s.size = 1, s.size2 = s.size,R = 1000, 
breaks = 30, stat = mean, stat2 = NULL, stat3 = NULL, stat4 = NULL, 
xlab = expression(bar(X)),ylab="Relative frequency",func=NULL)

Arguments

parent

A vector containing observations from a parental distribution.

parent2

An optional second parental distribution, useful for construction sampling distributions of test statistics

s.size

Sample size to be taken at each of R iterations from the parental distribution.

s.size2

An optional second sample size if a second statistic is to be calculated.

R

The number of samples to be taken.

breaks

Number of breaks in the histogram.

stat

The statistic whose sampling distribution is to be represented. Will work for any statistic with the single argument data.

stat2

An optional second statistic. Useful for conceptualizing sampling distributions of test statistics. Calculated from sampling parent2.

stat3

An optional third statistic. The sampling distribution is created from the same sample data used for stat.

stat4

An optional fourth statistic. The sampling distribution is created from the same sample data used for stat2

xlab

X-axis label.

ylab

Y-axis label.

func

An optional function used to compare the sampling distributions of two statistics. The function must have only sampling dsitributions, i.e. s.dist1, s.dist2, s.dist3, and/or s.dist as non-fixed argument

Value

• Returns a representation of a statistics sampling distribution in the form of a histogram.

Details

Sampling distributions of individual statistics can be created, or the function can be used in more sophisticated ways, e.g. to create sampling distributions of ratios of statistics, i.e. t*, F* etc. (see examples below).

Examples

##Central limit theorem
exp.parent<-rexp(1000000)
par(mfrow=c(2,2),mar=c(4.4,4.5,1,0.5))
samp.dist(parent=exp.parent, s.size=1, R=100) ## n = 1
samp.dist(parent=exp.parent, s.size=5, R=100) ## n = 5
samp.dist(parent=exp.parent, s.size=10, R=100) ## n = 10
samp.dist(parent=exp.parent, s.size=50, R=100) ## n = 50 

##Distribution of t-statistics under valid and invalid assumptions
#valid
parent<-rnorm(100000)
t.star<-function(s.dist1,s.dist2,s.dist3,s.dist4,s.size=6,s.size2=s.size){
MSE<-(((s.size-1)*s.dist3)+((s.size2-1)*s.dist4))/(s.size+s.size2-2)
func.res<-(s.dist1-s.dist2)/(sqrt(MSE)*sqrt((1/s.size)+(1/s.size2)))
func.res}

samp.dist(parent, parent2=parent, s.size=6, R=1000, breaks=35,stat=mean,stat2=mean,
stat3=var,stat4=var,xlab="t*", ylab="Relative frequency",func=t.star)
curve(dt(x,10),from=-6,to=6,add=TRUE,lwd=2)
legend("topleft",lwd=2,col=1,legend="t(10)")

#invalid; same means but different variances and other distributional characteristics.
parent<-runif(100000, min=0,max=2)
parent2<-rexp(100000)

samp.dist(parent, parent2=parent2, s.size=6, R=1000, breaks=35,stat=mean,stat2=mean,
stat3=var,stat4=var,xlab="t*", ylab="Relative frequency",func=t.star)
curve(dt(x,10),from=-6,to=6,add=TRUE,lwd=2)
legend("topleft",lwd=2,col=1,legend="t(10)")