# Set narrow margins for these graphics:

margins<-c(4,4,2,1)

###############################################################

# Make a normal plot with a biased plot of similar shape just below it:

###############################################################

png(filename="biasednormalplots.png", res=300, bg="white", type="quartz", pointsize=12, width=6, height=6, units="in")

par(new=FALSE)

par(mar=margins)

ub=4

lb=-5

sd=1

xlabel="Value of some parameter X"

ylabel="Likelihood of value X occurring"

mean=0

linecolor="blue"

fillcolor="gray"

x <- seq(lb,ub,length=200)*sd + mean

hx <- dnorm(x,mean,sd)

i <- x >= lb & x <= ub

plot(x, hx, type="n", xlab=xlabel, ylab=ylabel, main=mainlabel, axes=TRUE, col=linecolor)

polygon(c(lb,x[i],ub), c(0,hx[i],0), col=fillcolor)

lines(x,hx, col=linecolor)

# Next (here, biased) normal plot:

par(new=TRUE)

x=seq(-6,4,length=200)

y=dnorm(x, mean=-1, sd=1.2)

polygon(c(-6,x,4),c(0,(y*1),0),col="gray90")

lines(x,(y*1), type="l", lwd=3, col="red")

lb <- -6

ub <- -0.6

x=seq(lb,ub,length=200)

hx=dnorm(x,mean=0,sd=1)

# polygon(c(-6,x,-0.5),c(0,hx,0), col="blue", lty=2)

lines(x,hx,type="l", lty=2,lwd=1,col="blue")

# add text and vertical lines:

abline(v=0,col="blue")

text(0.2,0.3,labels="True avg value of X", srt=90, cex=1.4)

abline(v=-1,col="red")

text(-1.2,0.2,labels="Measured avg value of X", srt=90, cex=1.4)

dev.off()

png(filename="normalsampleplots.png", res=300, bg="white", type="quartz", pointsize=12, width=6, height=6, units="in")

par(new=FALSE)

par(mar=margins)

ub=4

lb=-5

sd=1

xlabel="Value of some parameter X"

ylabel="Likelihood of value X occurring"

mean=0

linecolor="blue"

fillcolor="gray"

x <- seq(lb,ub,length=200)*sd + mean

hx <- dnorm(x,mean,sd)

i <- x >= lb & x <= ub

plot(x, hx, type="n", xlab=xlabel, ylab=ylabel, main=mainlabel, axes=TRUE, col=linecolor)

polygon(c(lb,x[i],ub), c(0,hx[i],0), col=fillcolor)

lines(x,hx, col=linecolor)

# Next (here, biased) normal plot:

par(new=TRUE)

x=seq(-6,4,length=200)

y=dnorm(x, mean=-1, sd=1.2)

polygon(c(-6,x,4),c(0,(y*1),0),col="gray90")

lines(x,(y*1), type="l", lwd=3, col="red")

lb <- -6

ub <- -0.6

x=seq(lb,ub,length=200)

hx=dnorm(x,mean=0,sd=1)

# polygon(c(-6,x,-0.5),c(0,hx,0), col="blue", lty=2)

lines(x,hx,type="l", lty=2,lwd=1,col="blue")

# add text and vertical lines:

abline(v=0,col="blue")

text(0.3,0.2,labels="Avg value of X population", srt=90, cex=1.4)

abline(v=-1,col="red")

text(-1.2,0.2,labels="Sample avg value of X", srt=90, cex=1.4)

dev.off()

png(filename="abnormalsampleplots.png", res=300, bg="white", type="quartz", pointsize=12, width=6, height=6, units="in")

par(new=FALSE)

par(mar=margins)

ub=4

lb=-5

sd=1

xlabel="Value of some parameter X"

ylabel="Likelihood of value X occurring"

mean=0

linecolor="blue"

fillcolor="gray"

x <- seq(lb,ub,length=200)*sd + mean

hx <- dnorm(x,mean,sd)

i <- x >= lb & x <= ub

plot(x, hx, type="n", xlab=xlabel, ylab=ylabel, main=mainlabel, axes=TRUE, col=linecolor)

polygon(c(lb,x[i],ub), c(0,hx[i],0), col=fillcolor)

lines(x,hx, col=linecolor)

# Next (here, biased) normal plot:

par(new=TRUE)

ymult=1

x=seq(-6,2,length=200)

y=dnorm(x, mean=-3, sd=1.3)

polygon(c(-6,x,-3),c(0,(y*ymult),0),col="gray90")

lines(x,(y*ymult), type="l", lwd=3, col="red")

lb <- -6

ub <- -0.6

x=seq(lb,ub,length=200)

hx=dnorm(x,mean=0,sd=1)

# polygon(c(-6,x,-0.5),c(0,hx,0), col="blue", lty=2)

lines(x,hx,type="l", lty=2,lwd=1,col="blue")

# add text and vertical lines:

abline(v=0,col="blue")

text(0.3,0.2,labels="Avg value of X population", srt=90, cex=1.4)

abline(v=-3,col="red")

text(-2.6,0.15,labels="Sample avg value of X", srt=90, cex=1.4)

dev.off()