Statistics for all

Let’s start with a question. Please answer it now before you read any further!

Statistics, like Operations Research, is a mathematical science. However people can be intelligent consumers of statistical analysis without having to use mathematics. The statement in the box above is false.
Often statistics is taught by mathematics teachers, who understand the mathematical aspects of statistics, but may never have dirtied their hands with real data. They teach the mechanics of calculating the values of standard deviations and confidence intervals, intending that this will lead to understanding. Unfortunately many of their pupils do not gain understanding from the application of formulas. A high school maths teacher in a Masters in Education course I taught was excited to understand at last what a confidence interval was. He had taught his students how to calculate one, and the textbook interpretation, but he hadn’t really “got it” until then.

Statistics is not just mathematics with context. Statistics is magical and exciting, like a treasure hunt or a detective story. You start with an idea, and collect some data and then explore the data for its secrets. You uncover relationships and effects, and have to decide whether they constitute real evidence for your ideas. You then need to work out how to express your findings in sentences and in graphs in ways that your audience will understand.
Statistical analysis is needed for most research. Research in areas such as psychology, marketing, sociology, astronomy, medicine, political science, forensics and education, all rely on statistical analysis.
My belief is that there are a few main concepts behind statistics, and if you can understand them, most analysis will be comprehensible.
The key ideas are:

• variability,
• sampling and
• the p-value (inference).

The aim of this blog is to help people learn statistics and the allied discipline, operations research. It also aims to provide ideas and insights to teachers of statistics and operations research. Each of the key ideas will be addressed, and techniques explained.
I hope that people will sometimes disagree with what I say, and let me know. Debate without rancour leads to improved thinking. There is also room for contributions from other teachers of statistics and operations research.