I have made some minor changes to my likelihood ratio slide. The original code was lost somewhere, so I wrote some new code and added documentation. I also changed the orientation of the slide rule so it can be held horizontally and shaded the regions that need to be cut out or away. This program runs in R. I’ve inserted images of the new slide rule on my website:
Here is the code.
#####################
# special functions #
#####################
hline <- function(x1,x2,y0) {segments(x1,y0,x2,y0)}
vline <- function(x0,y1,y2) {segments(x0,y1,x0,y2)}
rectangle <- function(x1,y1,x2,y2) {
x0 <- c(x1,x1,x2,x2)
y0 <- c(y1,y2,y2,y1)
polygon(x=x0,y=y0,density=-1,border=NA,col="gray90")
}
triangle <- function(x1,y1,x2,y2,x3,y3) {
x0 <- c(x1,x2,x3)
y0 <- c(y1,y2,y3)
polygon(x=x0,y=y0,density=-1,border=NA,col="gray90")
}
#####################################
# location of tick marks and labels #
#####################################
# where to draw probability tick marks
pr1 <- c(
0.1,0.2,0.3,0.4,
0.5,0.6,0.7,0.8,0.9,
1,1.5,2,2.5,3,4,
5,6,7,8,9,
10,15,20,25,30,40,
50,60,70,75,80,85,
90,91,92,93,94,
95,96,97,98,99)
# where to print probability labels
pr2 <- c(
0.1,0.2,0.3,
0.5,0.7,
1,2,3,
5,7,
10,20,30,40,
50,60,70,80,
90,93,
95,97,98,99)
# physical location of probability ticks and labels
pr3 <- 60+15*log(pr1/(100-pr1))/log(10)
pr4 <- 60+15*log(pr2/(100-pr2))/log(10)
n1 <- sort(c(1:9,1.5,2.5))
n2 <- c(1:3,5,7)
# where to draw likelihood ratio tick marks
pr5 <- c(n1/100,n1/10,n1,n1*10,100)
# where to print likelihood ratio labels
pr6 <- c(n2/100,n2/10,n2,n2*10,100)
# physical location of likelihood ratio ticks and labels
pr7 <- 50-15*log(pr5)/log(10)
pr8 <- 50-15*log(pr6)/log(10)
# odd and even probability labels
od2 <- paste(pr2[seq(1,length(pr2),by=2)],"%",sep="")
ev2 <- paste(pr2[seq(2,length(pr2),by=2)],"%",sep="")
# odd and even likelihood ratio labels
od4 <- pr4[seq(1,length(pr4),by=2)]
ev4 <- pr4[seq(2,length(pr2),by=2)]
# physical locations of odd/even labels
od6 <- pr6[seq(1,length(pr6),by=2)]
ev6 <- pr6[seq(2,length(pr6),by=2)]
od8 <- pr8[seq(1,length(pr8),by=2)]
ev8 <- pr8[seq(2,length(pr8),by=2)]
draw.frame <- function() {
################################
# outline sleeve of slide rule #
################################
hline( 5, 95, 0)
# bottom edge
hline( 0,100, 20)
# fold line
hline( 0,100, 50)
# fold line
hline( 5, 95, 70)
# top edge
vline( 0, 12, 28)
# left edge
vline( 0, 42, 58)
# left edge
vline(100, 12, 28)
# right edge
vline(100, 42, 58)
# right edge
################
# left notches #
################
vline( 5, 0, 10)
segments( 5, 10, 0, 12)
segments( 0, 28, 5, 30)
vline( 5, 30, 40)
segments( 5, 40, 0, 42)
vline( 5, 60, 70)
segments( 0, 58, 5, 60)
#################
# right notches #
#################
vline( 95, 0, 10)
segments( 95, 10,100, 12)
segments(100, 28, 95, 30)
vline( 95, 30, 40)
segments( 95, 40,100, 42)
vline( 95, 60, 70)
segments(100, 58, 95, 60)
################################
# outline insert of slide rule #
################################
hline( 0,100, 71)
# bottom edge
hline( 0,100,100)
# top edge
vline( 0, 71,100)
# left edge
vline(100, 71,100)
# right edge
####################################
# cut-out for pre-test probability #
####################################
h <- 29
hline( 17, 83,h+0)
# bottom edge
hline( 17, 83,h+7)
# top edge
vline( 17,h+0,h+7)
# left edge
vline( 83,h+0,h+7)
# right edge
#####################################
# cut-out for post-test probability #
#####################################
h <- 46
v <- 50
hline(v-3,v+3,h+0)
# top edge
hline(v-3,v+3,h-6)
# bottom edge
vline(v-3,h+0,h-6)
# left edge
vline(v+3,h+0,h-6)
# right edge
vline(v+0,h+0,h+1)
# top tick
vline(v+0,h-6,h-7)
# bottom tick
}
draw.ticks <- function() {
####################
# Likelihood ratio #
####################
h <- 29
segments(pr7,h+0,pr7,h-1)
# all ticks
segments(od8,h-2,od8,h-1)
# extend odd ticks
segments(ev8,h-4,ev8,h-1)
# extend even ticks
text(od8,h-3,od6)
# label odd ticks
text(ev8,h-5,ev6)
# label even ticks
########################
# Pre-test probability #
########################
h <- 79
segments(pr3,h-1,pr3,h+1)
# all ticks
segments(od4,h+2,od4,h+1)
# extend odd ticks
segments(ev4,h+4,ev4,h+1)
# extend even ticks
text(od4,h+3,od2)
# label odd ticks
text(ev4,h+5,ev2)
# label even ticks
#########################
# Post-test probability #
#########################
h <- 97
segments(pr3,h+1,pr3,h-1)
# all ticks
segments(od4,h-2,od4,h-1)
# extend odd ticks
segments(ev4,h-4,ev4,h-1)
# extend even ticks
text(od4,h-3,od2)
# label odd ticks
text(ev4,h-5,ev2)
# label even ticks
}
draw.shade <- function() {
xlo <- -999
ylo <- -999
xhi <- 999
yhi <- 999
#########################
# shade extreme regions #
#########################
rectangle(xlo,ylo,xhi, 0)
# bottom
rectangle(xlo,100,xhi,yhi)
# top
rectangle(xlo,ylo, 0,yhi)
# left
rectangle(100,ylo,xhi,yhi)
# right
rectangle( 0, 70,100, 71)
# between sleeve and insert
################
# left notches #
################
rectangle( 0, 0, 5, 10)
triangle ( 0, 10, 5, 10, 0, 12)
triangle ( 0, 30, 5, 30, 0, 28)
rectangle( 0, 30, 5, 40)
triangle ( 0, 40, 5, 40, 0, 42)
triangle ( 0, 60, 5, 60, 0, 58)
rectangle( 0, 60, 5, 70)
#################
# right notches #
#################
rectangle(100, 0, 95, 10)
triangle (100, 10, 95, 10,100, 12)
triangle (100, 40, 95, 40,100, 42)
rectangle(100, 30, 95, 40)
triangle (100, 30, 95, 30,100, 28)
triangle (100, 60, 95, 60,100, 58)
rectangle(100, 60, 95, 70)
########################
# Pre-test probability #
########################
h <- 29
rectangle( 17,h+0, 83,h+7)
#########################
# Post-test probability #
#########################
h <- 46
v <- 50
rectangle(v-3,h-6,v+3,h+0)
}
draw.notes <- function() {
m0 <- paste(
"Line up the pre-test probability",
"with the likelihood ratio, and read",
"the post-test probability here.", sep="\n")
m1 <- paste(
"(C) The Children's Mercy Hospital.",
"For more information, please go to",
"www.childrensmercy.org/sliderule.asp", sep="\n")
text(45,43,m0,adj=1)
text(55,43,m1,adj=0)
text(15,33,"Pre-test\nprobability",adj=1)
text(15,25,"Likelihood\nratio",adj=1)
}
pdf(file="sliderule.pdf",width=8,height=10)
par(mar=rep(0.1,4),cex=0.75,adj=0.5)
plot(c(0,100),c(0,100),axes=F,type="n",xlab=" ",ylab=" ")
draw.notes()
draw.shade()
draw.frame()
draw.ticks()
dev.off()## png
## 2You can find an earlier version of this page on my old website.