Univariate data analysis (2014)
Jump to navigation
Jump to search
Class date(s): | 13 to 23 January 2014 | ||||
(PDF) | Course slides | ||||
| |||||
| |||||
| |||||
| |||||
| |||||
| |||||
| |||||
| |||||
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 (180 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. Run this code in your browser (no need to install/run in R)
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:
Run this code in your browser (no need to install/run in R)
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:
Run this code in your browser (no need to install/run in R)
# 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.
Run this code in a web-browser
# 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")