From 2006 – 2010 I taught a Quantitative Methods course at ESCP Europe. I enjoyed it immensely and got (relatively) great feedback from students. Since then I’ve continued to gather material but realise that no-one gets to see it. I currently teach QM at Cotrugli Business School, but only a few sessions. So **I wanted to make the full course publicly available**.

The aim of this website is to provide a (mostly) free guide to basic statistics. It should be of use to anyone with an interest in an MBA level education, and I have attempted to supplement my own presentations with links to some exceptional online resources. I say that it is *mostly* free because some of the cases are not available online and some articles require a subscription. If you have any difficulties accessing them, or would like me to recommend alternatives, let me know. I appreciate that Harvard cases and academic journals are expensive (regardless of whether you’re enrolled on a program or a member of the public). But **they are high quality**. Indeed if you are looking for a totally free course then this isn’t for you. The skills you develop in an Analytics course are valuable and important. If you are willing to invest your time in building them, you should also be willing to invest some money. But you can trust my recommendations. Everything below is worth it.

## Before we begin

I hope you find this online course useful, but I am also a fan of the old fashioned way. These materials are intended to tie into the following textbook:

- Curwin, J, and Slater, R., 2013,
*Quantitative Methods for Business Decisions*, Cengage Learning, 7th Edition (££)

In fact, the materials are intended to complement this textbook. It is a very good one: well written, full of examples, and plenty of opportunities to test yourself. You could do a lot worse than simply order it now and then work your way through it.

I’m also intrigued by “Calculus Made Easy“, by Silvanus Thompson. It’s antiquated in format but highly directed toward simplifying concepts and engaging with the reader. Daniel Kunin has a wonderful website called “Seeing Theory“, which allows users to visualise basic concepts in statistics. I’ve integrated links into the course below.

There are also lots of proper online courses to choose from. The only one I have direct experience of is this:

- Quantitative Methods Online Course, Harvard Business School (£££)

If you really need to develop your QM skills then I would recommend you follow the HBS one (instead of mine). However I found it pretty dull and failed to complete it. I’m hoping that by providing a mixture of content you will find mine more enjoyable.

Funnily enough, a few hours after I’d finished this page, a friend of me showed me this website:

- Introductory Statistics, an online course by Andy Field.

It is full of some excellent tutorials that are presented with a unique style. You may prefer his site to mine.

I also love this course: Calling Bullshit in the Age of Big Data.

## Pop analytics

I believe that a good way to prepare for a subject is to read a book that is captivating. Something that stimulates your interest and encourages you to dig deeper. There are lots of bestsellers that have attempted to communicate mathematical ideas to the educated layperson. My favourite 6 are these:

- Mlodinow, L., 2008,
*The Drunkard’s Walk: How Randomness Rules Our Lives*, Pantheon (£) - Taleb, N.N., 2001,
*Fooled by Randomness*, Random House (£) - Bodanis, D., 2001,
*E=MC^2*, Pan Books (£) - Sing, S., 1997,
*Fermat’s Last Theorem,*Fourth Estate (£) - Bernstein, P., 1998,
*Against the Gods*, Wiley (£) - Wheelan, C., 2013,
*Naked Statistics*, Norton (actually, I’ve not read this one yet, but I’ve heard it’s good) (£)

Finally, before you start this course you should read the following:

- Davenport, Thomas H., “Competing on Analytics“, Harvard Business Review, Jan 1st 2006

## 0. Pre-requisite

- If you want to start at the very beginning then take my Numeracy Skills Bootcamp, which covers Fundamentals of Mathematics, some Practice Tests, and a discussion of Gender Differences & Mathematics.

## 1. Statistical Literacy

Prior to the lecture below, you may wish to ask the following question: “How expensive is crude oil?”

**Some basic terminology:**

**Population**: the complete set of objects under study**Sample**: a subset of the objects under study**Census**: gathering data from the population**Survey**: gathering data from the sample

Download the handouts here.

Why data needs theory:

- “Hollaback and Why Everyone Needs Better Research Methods“, The Message
- “Theory vs. fact” (email me for instructions)

Download the handouts here.

Some other great resources:

- “The Use and Misuse of Statistics“, Harvard Management Update, No. U0603C (£)
- “Think like a statistician – without the math“, Flowing data, March 4th 2010
- “How to spot spin and inappropriate use of statistics“, House of Commons Library Standard Note, July 29th 2010
- Bolton, P., and Cracknell, R., “What is a billion? And other units” House of Commons Library Standard Note, January 2009
- How much is a trillion?
- The Monty Hall Problem, BBC News, September 2013
- Strogatz, S., “Why Pi matters“, The New Yorker, March 13, 2015
- Some more stupid charts: here and don’t use 3D pie charts
- Shut up about the y-axis. It shouldn’t always start at zero, Vox

- Bad x axis
- Spurious correlations
- Maybe we should call a bad pie chart a pizza chart

## 2. Descriptive statistics

Download the handouts here.

**Additional readings:**

- Variance: The small schools myth, Alex Tabarrok, Marginal Revolution
- Histograms: How to Read Histograms and Use Them in R
- Annualising data
- Anseau, J., Rounding and significant places, House of Commons Library Standard Note, September 20th 2007

## 3. Probability theory

The lecture below is very heavy. If I were teaching this again I would do the following

- Start off with a group activity: Freemark Abbey Winery (£)
- Collect a
**Problem set**on probability theory, Bayes theorem, permutations, and combinations

Download the handouts here.

Seeing Theory: Basic Probability and Compound Probability

**Additional readings:**

- “How to understand risk in 13 clicks,” BBC News, March 11th 2009
- “Momentous modelling” The Economist, February 3rd 2007
- Conditional probability
- Capen, E.C., 1976 “The Difficulty of Assessing Uncertainty” J Pet Technol 28(8):843-850 would be a great way to teach uncertainty that builds into confidence intervals.

Download the handouts here.

Seeing Theory: Compound Probability

## 4. Game theory

## 5. Inferential statistics

We can make a distinction between:

**Descriptive statistics**= Using group data to describe the group**Inferential statistics**= Using group data to infer about the population

The two main things that we cover in inferential statistics are

**Confidence Intervals**– For estimating a population parameter**Hypothesis/Significance Testing**– To assess the evidence provided by the data regarding some claim about the population

Both methods are based on sampling distributions, with the underlying assumption that the sample data comes from a **randomised** experiment. Any faults of the experiment will impact the validity of the conclusions. Always remember that uncertainty still exists, outside the model

Seeing Theory: Statistical Inference

- Taxi for Professor Evans, December 2012

In The X Files episode “D.P.O” (Season 3 Episode 3, watch it here) five people are seemingly struck by lightning in the same small town. It could be a coincidence. Unlikely events can occur in quick succession for purely random reasons. However Mulder and Scully believe that it is so improbable it isn’t down to chance. Rather, there is something happening that explains these events. This is the essence of conducting probability tests – are the events that we witness the result of chance, or are they evidence that there is an underlying cause? We cannot really ever prove anything, but we can amass evidence that makes it more and more convincing.

Download the handouts here.

**Additional reading**:

- “Measure for Measure: The strange science of Francis Galton“, by Jim Holt, The New Yorker, Jan 24th 2005
- “A Refresher on Statistical Significance” by Amy Gallo, Harvard Business Review, February 16th 2016
- “Statisticians Found One Thing They Can Agree On: It’s Time To Stop Misusing P-Values” by Christy Aschwanden, FiveThirtyEight, March 7th 2016
- “False hope” The Economist, February 21st 2015

Download the handouts here.

## 6. Correlation

Download the handouts here.

Test yourself: http://guessthecorrelation.com/

## 7. Regression analysis

Seeing Theory: Linear Regression

- The Suitcase Case, December 2012

**Additional readings**

- Small numbers
- “Regression Step by Step Using Microsoft Excel“
- Ramcharan, R., 2006, “Regressions: Why Are Economists Obessessed with Them?” Finance and Development, 43(1)
- “Running the numbers” The Economist, October 14th 2000
- “Signifying nothing?” The Economist, January 29th 2004

## 8. Time series

Download the handouts here.

**Further reading:**

- “An Intuitive Guide To Exponential Functions & e“, Better Explained
- “A new fashion in modelling” The Economist, November 24th 2007
- Bolton, P., Index Numbers, House of Commons Library Standard Note, September 20th 2007
- “Demystifying Chain Volume Measures” Australian Bureau of Statistics, March 2003
- A First Course on Time Series Analysis (An open source introductory textbook on time series analysis, free to download)
- “Annualising data“, Dallas Federal Reserve, DataBasics
- “Shifting the base year” MBA Lectures, Jun 19 2010

## 9. Data Presentation

**10. Controversies**

I believe that the best way to internalise the key concepts in this course is to conduct a replication exercise. These have become increasingly common as ways to apply the concepts covered, and test a students knowledge retention. To be honest though I am yet to find any really good examples of statistical tests that companies have utilised, and for which the underlying data set is available.

In their textbook, “Modern Principles: Macroeconomics”, Tyler Cowen and Alex Tabarrok present a good exercise to replicate a Solow Model. My (flawed) attempt to combine two of their problem sets is here:

- Solow 1502.pdf (email me for discussion)

Whilst I continue to look for potential replications, one option is to focus on some controversial statistical debates. These are also good ways to go deeper into the theory, and fully appreciate the link between theory and practice.

- Crime and abortion
- “Crossing continents” BBC Radio 4, December 21st 2006
- Freakonomics video
- Donohue, J.J., and Levitt, S., (2001) “The Impact of Legalised Abortion on Crime”.
*Quarterly Journal of Economics*, Vol. CXVI, Issue 2., pp.379-420 - “Oops-onomics” The Economist, December 1st 2005
- Foote, C.L., and Goetz, C.F., “Testing Economic Hypotheses with State-Level Data: A comment on Donohue and Levitt (2001)”. Federal Reserve Bank of Boston working paper. November 2005
- Levitt, S., “Abortion and crime: who should you believe?” Freakonomics Blog, 15th May 2005

- Sudden Infant Death syndrome
- see Mlodinow, 2008, p118-119
- How Juries are Fooled by Statistics, Peter Donnelly, Ted Global 2005
- Roy Meadow Wikipedia page

- Breast cancer
- “Dodgy numbers“, The Remittance Man, April 14th 2014

- Sovereign debt crises
- “The 90% Question” The Economist, April 20th 2013

## Appendix: Handouts

## Test your knowledge

I know that it is important to test your knowledge but I wanted you be able to explore the information above without a compelling pressure to be surrounded by the architecture of formal education. I wanted you to dip in and out, internalising what you wanted. That said, I did provide 5 quiz questions at the end of each session when I last taught this course, and you can download those questions here:

- Short quiz questions
- Fermat’s Folly (case)

## After party

You should now be a savvy consumer of statistical analysis and passionate about good data management. I recommend that you treat yourself to the following tome:

- Gleick, J., 2012 [2011],
*The Information*, Fourth Estate (£)

Thank you for visiting.

Last updated: March 2016