Univariate data analysis (2014)

Class date(s):	13 to 23 January 2014
(PDF)	Course slides
Download video: Link (plays in Google Chrome) [343 M]
Download video: Link (plays in Google Chrome) [327 M]
Download video: Link (plays in Google Chrome) [347 M]
Download video: Link (plays in Google Chrome) [344 M]
Download video: Link (plays in Google Chrome) [262 M]
Download video: Link (plays in Google Chrome) [293 M]
Download video: Link (plays in Google Chrome) [357 M]

Class materials

Date	Class number	Video and audio files		Other materials	Reading (PID)	Slides
13 January	02A	Video (343 M)	Audio (42 M)	R demo file	Chapter 2	Slides for class
15 January	02B	Video (327 M)	Audio (42 M)	See code below
16 January	02C	Video (347 M)	Audio (42 M)	See code below
20 January	03A	Video (347 M)	Audio (42 M)	Using tables of the normal distribution
22 January	03B	Video (262 M)	Audio (42 M)	Using tables of the t-distribution
23 January	03C	Video (293 M)	Audio (41 M)	None
27 January	04A	Video from 2013 (357M)	Audio from 2013 (43M)	See code below
29 January	04B	Video (293 M)	Audio (24 M)	None

Software source code

Please follow the software tutorial to install and run the course software. You should be able to quickly read, understand and use the material in steps 1 to 13.

Class example, 15 Jan

Seeing the Central Limit Theorem in action: rolling dice.

N = 500
m <- t(matrix(seq(1,6), 3, 2))
layout(m)
s1 <- as.integer(runif(N, 1, 7))
s2 <- as.integer(runif(N, 1, 7))
s3 <- as.integer(runif(N, 1, 7))
s4 <- as.integer(runif(N, 1, 7))
s5 <- as.integer(runif(N, 1, 7))
s6 <- as.integer(runif(N, 1, 7))
s7 <- as.integer(runif(N, 1, 7))
s8 <- as.integer(runif(N, 1, 7))
s9 <- as.integer(runif(N, 1, 7))
s10 <- as.integer(runif(N, 1, 7))

hist(s1, main="", xlab="One throw", breaks=seq(0,6)+0.5)
bins = 8
hist((s1+s2)/2, breaks=bins, main="", xlab="Average of two throws")
hist((s1+s2+s3+s4)/4, breaks=bins, main="", xlab="Average of 4 throws")
hist((s1+s2+s3+s4+s5+s6)/6, breaks=bins, main="", xlab="Average of 6 throws")
bins=12
hist((s1+s2+s3+s4+s5+s6+s7+s8)/8,  breaks=bins, main="", xlab="Average of 8 throws")
hist((s1+s2+s3+s4+s5+s6+s7+s8+s9+s10)/10, breaks=bins, main="", xlab="Average of 10 throws")

Class example, 16 Jan

# Read data from a web address
batch <- read.csv('http://datasets.connectmv.com/file/batch-yields.csv')

Code used to illustrate how the q-q plot is constructed:

N <- 10

# What are the quantiles from the theoretical normal distribution?
index <- seq(1, N)
P <- (index - 0.5) / N
theoretical.quantity <- qnorm(P)

# Our sampled data:
yields <- c(86.2, 85.7, 71.9, 95.3, 77.1, 71.4, 68.9, 78.9, 86.9, 78.4)
mean.yield <- mean(yields)       # 80.0
sd.yield <- sd(yields)           # 8.35

# What are the quantiles for the sampled data?
yields.z <- (yields - mean.yield)/sd.yield
yields.z
 
yields.z.sorted <- sort(yields.z)

# Compare the values in text:
yields.z.sorted 
theoretical.quantity  

# Compare them graphically:
plot(theoretical.quantity, yields.z.sorted, asp=1)
abline(a=0, b=1)

# Built-in R function to do all the above for you:
qqnorm(yields)
qqline(yields)

# A better function: see http://learnche.mcmaster.ca/4C3/Software_tutorial/Extending_R_with_packages
library(car)
qqPlot(yields)

Code used to illustrate the central limit theorem's reduction in variance:

# Show the 3 plots side by side
layout(matrix(c(1,2,3), 1, 3))

# Sample the population:
N <- 100
x <- rnorm(N, mean=80, sd=5)
mean(x)
sd(x)

# Plot the raw data
x.range <- range(x)
plot(x, ylim=x.range, main='Raw data')

# Subgroups of 2
subsize <- 2
x.2 <- numeric(N/subsize)
for (i in 1:(N/subsize))
{
    x.2[i] <- mean(x[((i-1)*subsize+1):(i*subsize)])
}
plot(x.2, ylim=x.range, main='Subgroups of 2')

# Subgroups of 4
subsize <- 4
x.4 <- numeric(N/subsize)
for (i in 1:(N/subsize))
{
    x.4[i] <- mean(x[((i-1)*subsize+1):(i*subsize)])
}
plot(x.4, ylim=x.range, main='Subgroups of 4')

Class example, 27 Jan

Test for differences: plotting the raw data.

dilution <- round(rnorm(N, mean=BOD.mean, sd=BOD.sd))
manometric <- round(rnorm(N, mean=BOD.mean*1.6, sd=1.5*BOD.sd))

# Analysis of the data here:
dilution <-   c(11, 26, 18, 16, 20, 12,  8, 26, 12, 17, 14)
manometric <- c(25,  3, 27, 30, 33, 16, 28, 27, 12, 32, 16)

mean(manometric)
mean(dilution)

plot(c(dilution, manometric), ylab="BOD values", xaxt='n')
text(5.5,3, "Dilution")
text(18,3, "Manometric")
abline(v=11.5)

par(mar=c(4.2, 4.2, 0.2, 0.2))  # (bottom, left, top, right); defaults are par(mar=c(5, 4, 4, 2) + 0.1)
plot(dilution, type="p", pch=4, 
    cex=2, cex.lab=1.5, cex.main=1.8, cex.sub=1.8, cex.axis=1.8, 
    ylab="BOD values", xlab="Sample number",
    ylim=c(0,35), xlim=c(0,11.5), col="darkgreen")
lines(manometric, type="p", pch=16, cex=2, col="blue")
lines(rep(0, N), dilution, type="p", pch=4, cex=2, col="darkgreen")
lines(rep(0, N), manometric, type="p", pch=16, cex=2, col="blue")

abline(v=0.5)

legend(8, 5, pch=c(4, 16), c("Dilution", "Manometric"), col=c("darkgreen", "blue"), pt.cex=2)


par(mar=c(4.2, 4.2, 0.2, 0.2))  # (bottom, left, top, right); defaults are par(mar=c(5, 4, 4, 2) + 0.1)
plot(dilution-manometric, type="p", ylab="Dilution - Manometric", xlab="Sample number", 
     cex.lab=1.5, cex.main=1.8, cex.sub=1.8, cex.axis=1.8, cex=2)
abline(h=0, col="grey60")