Next:
Introduction
Up:
course
Previous:
course
Contents
Introduction
Purpose of this course
Brief history of statistics
What exactly is statistics ?
Some fundamental concepts
Statistical software
Further reading for this course
Descriptive statistics
Tabulation and the data matrix
Descriptive statistics for univariate data
Key attributes of sample data
Resistant statistics
Empirical quantiles
Example: Summary statistics for the height data
Graphical representation
Transformation of data
Further reading
Basic probability concepts
Motivation
Events and event space
Random variables
How is probability defined?
Definition 1: Number of symmetric ways
Definition 2: Relative frequency of repeated event
Definition 3: Non-frequentist subjective approach
Definition 4: The axiomatic approach
Joint and conditional probabilities
Odds
Expectation, (co-)variance, and correlation
Summary of statistical notation
Further reading
Probability distributions
Motivation
Distributions of discrete variables
Definition
Empirical estimates
Theoretical discrete distributions
Distributions of continuous variables
Definition
Empirical estimates
Theoretical continuous distributions
Further reading
Parameter estimation
Motivation
Sampling distributions
Sampling errors
Confidence intervals
Example 1: Confidence Interval for population mean
Example 2: Confidence Interval for sample proportion
Example 3: Confidence Interval for sample variance
Choice of estimator
Accuracy and bias of estimators
Example 1: The sample mean
Example 2: The sample variance
Further reading
Statistical hypothesis testing
Motivation
The basic approach
A legal example
Getting rid of straw men
Decision procedure
Alternative hypotheses
Examples of bad practice
One sample tests in environmental science
Z-test on a mean with known variance
T-test on a mean with unknown variance
Z-test for non-zero correlation
Two sample tests
T-test on unpaired means with unknown variance
T-test on paired means with unknown variance
F-test for equal variances
Z-test for unpaired equal correlations
Further reading
Basic Linear Regression
A few words on modelling strategy ...
Linear regression
ANalysis Of VAriance (ANOVA) table
Model fit validation using residual diagnostics
Weighted and robust regression
Further sources of information
Multiple and nonlinear regression
Multiple regression
Multivariate regression
Non-linear response
Parametric and non-parametric regression
Further sources of information
Introduction to time series
Introduction
Time series components
Filtering and smoothing
Serial correlation
ARIMA(p,d,q) time series models
Further sources of information
Bibliography
David Stephenson 2005-09-30