# 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.

## Contents

## 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: