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

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.

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## 2 Comments

I agree with your statements about instructors who teach the mathematics of statistics without ever understanding or imparting understanding of the real life applications. I teach statistics, but many decades as a practicing statistician in several industries. My approach to teaching is to pull real data that is current, and help my students to understand how the math side of statistics allows us the make sense of data in real life situations. The students appreciate the emphasis on application. In particular, the students who are taking statistics for the second or third time marvel at the difference in approach. Many of my colleagues teach the course entirely by inputs and outputs on a TI calculator. It’s a bit infuriating to me, and a shame for the students, but they don’t have the background to do otherwise. Given that mathematicians are likely to be teaching elementary statistics courses for years to come, it would be great if they were trained in the real life application, maybe by ongoing development courses. It is easy enough to create a course in which data can be generated toward a real goal, all within the classroom setting or even in a lab. I have seen it done.

Thanks for that. In New Zealand teachers are increasing their skills in statistics.