To students of statistics
Most of my posts are directed at teachers and how to teach statistics. The blog this week and next is devoted to students. I present principles that will help you to learn statistics. I’m turning them into a poster, which I will make available for you to printing later. I’d love to hear from other teachers as I add to my list of principles.
1. Statistics is learned by doing
One of the best predictors of success in any subject is how much time you spent on it. If you want to learn statistics, you need to put in time. It is good to read the notes and the textbook, and to look up things on the internet and even to watch Youtube videos if they are good ones. But the most important way to learn statistics is by doing. You need to practise at the skills that are needed by a statistician, which include logical thinking, interpretation, judgment and writing. Your teacher should provide you with worthwhile practice activities, and helpful timely feedback. Good textbooks have good practice exercises. On-line materials have many practice exercises.
Given a choice, do the exercises that have answers available. It is very important that you check what you are doing, as it is detrimental to practise something in the wrong way. Or if you are using an on-line resource, make sure you check your answers as you go, so that you gain from the feedback and avoid developing bad habits.
So really the first principle should really be “statistics is learned by doing correctly”.
2. Understanding comes with application, not before.
Do not wait until you understand what you are doing before you get started. The understanding comes as you do the work. When we learn to speak, we do not wait until we understand grammatical structure before saying anything. We use what we have to speak and to listen, and as we do so we gain an understanding of how language works. I have found that students who spent a lot of time working through the process of calculating conditional probabilities for screening tests grew to understand the “why” as well as the “how” of the process. Repeated application of using Excel to fit a line to bivariate data and explaining what it meant, enabled students to understand and internalise what a line means. As I have taught statistics for two decades, my own understanding has continued to grow.
There is a proviso. You need to think about what you are doing, and you need to do worthwhile exercises. For example, mechanically calculating the standard deviation of a set of numbers devoid of context will not help you understand standard deviation. Looking at graphs and trying to guess what the standard deviation is, would be a better exercise. Then applying the value to the context is better still.
Applying statistical principles to a wide variety of contexts helps us to discern what is specific to a problem and what is general for all problems. This brings us to the next principle.
3. Spend time exploring the context.
In a statistical analysis, context is vital, and often very interesting. You need to understand the problem that gave rise to the investigation and collection of the data. The context is what makes each statistical investigation different. Statisticians often work alongside other researchers in areas such as medicine, psychology, biology and geology, who provide the contextual background to the problem. This provides a wonderful opportunity for the statistician to learn about a whole range of different subjects. The interplay between the data and context mean that every investigation is different.
In a classroom setting you will not have the subject expert available, but you do need to understand the story behind the data. These days, finding out is possible with a click of a Google or Wikipedia button. Knowing the background to the data helps you to make more sensible judgments – and it makes it more interesting.
In mathematics, particularly pure mathematics, context is stripped away in order to reveal the inner pure truth of numbers and logic. There are applied areas involving mathematics, which are more like statistics, such as operations research and engineering. At school level, one of the things that characterises the study of maths is right and wrong answers, with a minimum of ambiguity. That is what I loved about mathematics – being able to apply an algorithm and get a correct answer. In statistics, however, things are seldom black-and-white. In statistics you will need to interpret data from the perspective of the real world, and often the answer is not clear. Some people find the lack of certainty in statistics disturbing. There is considerable room for discussion in statistics. Some aspects of statistics are fuzzy, such as what to do with messy data, or which is the “best” model to fit a time series. There is a greater need for the ability to write in statistics, which makes if more challenging for students for whom English is not their native language.
5. Technology is essential
With computers and calculators, all sorts of activities are available to help learn statistics. Graphs and graphics enable exploration that was not possible when graphs had to be drawn by hand. You can have a multivariate data set and explore all the possible relationships with a few clicks. You should always look at the data in a graphical form before setting out to analyse.
Sometimes I would set optional exercises for students to explore the relationship between data, graphs and summary measures. Very few students did so, but when I led them through the same examples one at a time I could see the lights go on. When you are given opportunities to use computing power to explore and learn – do it!
But wait…there’s more
Here we have the first five principles for students learning statistics. Watch this space next week for some more. And do add some in the comments and I will try to incorporate your ideas as well.