Difference between revisions of "Statistics"

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This page is currently being build and should be completed for the start of Academic Year 2013/14.
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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 [[media: RedBook.pdf|RedBook]].
  
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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.
 
  
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This page is explicitly designed with MSc Economics (and/or Econometrics) and MA Economics students at The University of Manchester in mind. Below you will be able to identify which topic is expected knowledge for the MSc/MA.
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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 ==
 
== The Basics ==
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These are the basic tools you need when you want to do any statistics.
  
 
{| class="wikitable"
 
{| class="wikitable"
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! scope="col"| Topic
 
! scope="col"| Topic
 
! scope="col"|  
 
! scope="col"|  
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! scope="col"| MA Economics
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! scope="col"| Level 1 (L1)
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! scope="col"| MSc Economics
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! scope="col"| Level 2 (L2)
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|-
 +
|
 +
|
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| MA Economics, <br>MSc Development Economics and Policy
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| MSc Economics, <br>MSc Economics and Econometrics
 
|-
 
|-
 
| [[StatPrelim|Preliminaries and Notation]]
 
| [[StatPrelim|Preliminaries and Notation]]
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|-
 
|-
 
| [[Descriptive|Descriptive Statistics]]
 
| [[Descriptive|Descriptive Statistics]]
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|  
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| [[DesStats_Exercises|Exercises]]
 
| Yes
 
| Yes
 
| Yes
 
| Yes
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| [[Regression_Examples|Exercises]]
 
| [[Regression_Examples|Exercises]]
 
| Correlation only
 
| Correlation only
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| Yes
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|-
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| [[media: OLS_notes.pdf|Extra Regression Notes]]
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| [[media: OLS_ex.pdf|Exercise Questions]] <br> [[media: OLS_ans.pdf|Exercise Answers]]
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|
 
| Yes
 
| Yes
  
 
|}
 
|}
  
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== Probability ==
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== Random Variables and Probability ==
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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.
  
 
{| class="wikitable"
 
{| class="wikitable"
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! scope="col"| Topic
 
! scope="col"| Topic
 
! scope="col"|  
 
! scope="col"|  
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! scope="col"| MA Economics
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! scope="col"| Level 1
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! scope="col"| MSc Economics
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! scope="col"| Level 2
 
|-
 
|-
 
| [[Probability_Intro|Introduction to Probability]]
 
| [[Probability_Intro|Introduction to Probability]]
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|-
 
|-
 
| [[Probability_DiscreteRV|Discrete Random Variables]]
 
| [[Probability_DiscreteRV|Discrete Random Variables]]
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|
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| see Exercises for Cont RV
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| Yes
 
| Yes
 
| Yes
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|-
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| [[Probability_ContRV|Continuous Random Variables]]
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| [[Probability_RV_Exercises|Exercises]]
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| Sections 1-4 only
 
| Yes
 
| Yes
 
|-
 
|-
 
| [[Probability_Norm|Normal Distribution]]
 
| [[Probability_Norm|Normal Distribution]]
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|
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| [[Probability_Norm_Exercises|Exercises]]
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| Yes
 
| Yes
 
| Yes
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|-
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| [[Probability_MomentsExp|Moments and Expectations]]
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| [[Probability_MomentsExp_Exercises|Exercises]]
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| Sections 1-3 only
 
| Yes
 
| Yes
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 +
|}
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== Joint Probability Distributions ==
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 +
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.
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{| class="wikitable"
 
|-
 
|-
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| [[Probability_MomenntsExp|Moments and Expectations]]
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! scope="col"| Topic
−
|
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! scope="col"|
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! scope="col"| Level 1
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! scope="col"| Level 2
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|-
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| [[Joint_Probability_Distributions|Joint Probability Distributions]]
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| see Exercises for Lin Comb of RV
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| Sections 1-4 only
 
| Yes
 
| Yes
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|-
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| [[Linear_Combinations|Linear Combinations of RV]]
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| [[Linear_Combinations_Exercises|Exercises]]
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| Sections 1-2 only
 
| Yes
 
| Yes
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|}
 
|}
  
 
== Statistical Inference ==
 
== Statistical Inference ==
  
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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.
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 +
{| class="wikitable"
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|-
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! scope="col"| Topic
 +
! scope="col"|
 +
! scope="col"| Level 1
 +
! scope="col"| Level 2
 +
|-
 +
| [[Populations_Samples_SampleDistributions|Populations, Samples & Sampling Distributions]]
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|
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| Yes
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| Yes
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|-
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| [[Statistics_SamplingDistributions|Statistics & Sampling Distributions]]
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| see exercises for Point Estimation
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| Yes
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| Yes
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|-
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| [[Point_Estimation|Point Estimation]]
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| [[Point_Estimation_Exercises|Exercises]]
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|
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| Yes
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|-
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| [[Confidence_Intervals|Confidence Intervals]]
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| [[Confidence_Intervals_Exercises|Exercises]]
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|
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| Yes
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|-
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| [[Hypothesis_Testing|Hypothesis Testing]]
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| [[Hypothesis_Testing_Exercises|Exercises]]
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|
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| Yes
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|}
  
 
==<div id="DataSets"></div>Example Data Sets==
 
==<div id="DataSets"></div>Example Data Sets==
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|[http://Gapminder.com]
 
|[http://Gapminder.com]
 
|}
 
|}
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==<div id="DistTables"></div>Distribution Tables==
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{| class="wikitable"
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|-
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! scope="col"| Distribution
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! scope="col"| Standard Normal
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! scope="col"| Chi-Square
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! scope="col"| t-distribution
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! scope="col"| F-distribution
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|-
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|
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| [[media:NormalTable.pdf|NormalTable.pdf]]
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| [[media:ChiSquareTables.pdf|ChiSquareTable.pdf]]
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| [[media:TTable.pdf|TTable.pdf]]
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| [[media:FTables.pdf|FTable.pdf]]
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|}
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== Additional Resuorces ==
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You can find a huge range of freely available resources for Statistics. Here I will list but a few:
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 +
* The Online Stat Book. This is an excellent online resource that contains videos and demonstrations. [http://onlinestatbook.com/2/].
 +
* Wolfram MathWorld. This is a bit like Wikipedia, just specialised on Maths and Stats [http://mathworld.wolfram.com/].

Latest revision as of 20:00, 1 July 2015

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].
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