Univariate data analysis (2013)

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Class date(s): 15 to 29 January 2013
Nuvola mimetypes pdf.png (PDF) Course slides
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Course notes and slides

Software source code

Please follow the software tutorial to install and run the course software. Here was the example used in class:

# Read data from a web address
batch <- read.csv('http://openmv.net/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.sorted <- sort(yields.z)

# Compare the values in text:

# 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:

# A better function: see http://learnche.mcmaster.ca/4C3/Software_tutorial/Extending_R_with_packages

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)

# 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')

Code to show how to superimpose plots

data <- read.csv('http://openmv.net/file/raw-material-properties.csv')

# Single plot

# Connect the dots
plot(data$density1, type='b')

# Another variable
plot(data$density2, type='b', col="red")

# Superimpose them?
plot(data$density1, type='b', col="blue")
lines(data$density2, type='b', col="red")  # where's density2 ?

# Superimpose them: limits
plot(data$density1, type='b', col="blue", ylim=c(10, 45))
lines(data$density2, type='b', col="red")  # now density2 shows up

Code to show how to deal with missing values:

data <- read.csv('http://openmv.net/file/raw-material-properties.csv')
summary(data)  # notice the NAs in the columns: these refer to missing value (Not Available)

sd(data$density1)  # why NA as the answer?
sd(data$density1, na.rm=TRUE)  # no NA answer anymore!

help(IQR)  # etc: all these functions accept and na.rm input