Statistics

The purpose of these pages is to give prospective and current postgraduate students in Economics at The University of Manchester an opportunity to understand what Statistics knowledge they are expected to have and, of course, a source of revision information. The material presented here is largely based on material written by our colleagues Len Gill, Denise Osborn and Chris Orme at The University of Manchester. Most of this material is presented in this pdf file RedBook.

This page is explicitly designed with MSc Economics (and/or Econometrics), MA Economics and MSc Development Economics and Policy students at The University of Manchester in mind. Below you will be able to identify which topic is expected entry knowledge for the respective programmes.

The Basics

These are the basic tools you need when you want to do any statistics.

Topic		Level 1 (L1)	Level 2 (L2)
		MA Economics, MSc Development Economics and Policy	MSc Economics, MSc Economics and Econometrics
Preliminaries and Notation		Yes	Yes
Data types		Yes	Yes
Graphical Representation		Yes	Yes
Descriptive Statistics	Exercises	Yes	Yes
Correlation & Regression	Exercises	Correlation only	Yes
Extra Regression Notes	Exercise Questions Exercise Answers		Yes

Random Variables and Probability

In Statistics we are dealing with uncertainty. The tool to handle uncertainty is to treat outcomes of variables as random. We then assign probabilities to the possible outcomes to these random variables. These are the tools to deal with these constructs.

Topic		Level 1	Level 2
Introduction to Probability		Yes	Yes
Conditional Probability	Exercises	Yes	Yes
Discrete Random Variables	see Exercises for Cont RV	Yes	Yes
Continuous Random Variables	Exercises	Sections 1-4 only	Yes
Normal Distribution	Exercises	Yes	Yes
Moments and Expectations	Exercises	Sections 1-3 only	Yes

Joint Probability Distributions

In Economics (and indeed many other disciplines) we are often interested in the relationships between two (or even more) random variables. Therefore we need to introduce the concept of joint probability distributions and need to understand how they combine.

Topic		Level 1	Level 2
Joint Probability Distributions	see Exercises for Lin Comb of RV	Sections 1-4 only	Yes
Linear Combinations of RV	Exercises	Sections 1-2 only	Yes

Statistical Inference

The core problem in statistics is that we want to know things about populations, but usually only have sample evidence. How is that done, how can we possibly use information from 1000 people to predict the outcome of an election? This is what statistical inference is about.

Topic		Level 1	Level 2
Populations, Samples & Sampling Distributions		Yes	Yes
Statistics & Sampling Distributions	see exercises for Point Estimation	Yes	Yes
Point Estimation	Exercises		Yes
Confidence Intervals	Exercises		Yes
Hypothesis Testing	Exercises		Yes

Example Data Sets

Throughout these pages a few example datasets will be used.

Description	Organisation	Data File	Source
Data used to calculate a quality of Life Index	OECD (collecting data from various sources)	BetterLifeIndex.xls	[1]
Exchange Rate USD/UKP	Board of Governors of the Federal reserve System	USDUKP.xlsx	[2]
UK Gross Domestic Product	Office of national Statistics	UK_GDP_INF.xlsx	[3]
Passengers on the Titanic		Titanic.xlsx	[4]
CO2 and GDP	Gapminder.com	GDP_CO2.xlsx	[5]

Distribution Tables

Distribution	Standard Normal	Chi-Square	t-distribution	F-distribution
	NormalTable.pdf	ChiSquareTable.pdf	TTable.pdf	FTable.pdf

Additional Resuorces

You can find a huge range of freely available resources for Statistics. Here I will list but a few:

• The Online Stat Book. This is an excellent online resource that contains videos and demonstrations. [6].
• Wolfram MathWorld. This is a bit like Wikipedia, just specialised on Maths and Stats [7].