Statistics without Mathematics

A little personal history

When I first learned statistics as a student of psychology, I had to run statistical tests by hand. The process was long, laborious and definitely arithmetical! Later, I broke the formulae down into groups of small, simple calculations and automated them by putting them on a spreadsheet.

My intention was to speed things up, but there was an unexpected side-effect. The more I ran the calculations, the more I found that the formulae became irrelevant to what I was doing. The purpose of any given test emerged, blinking in the light of day, rather than the preoccupation of getting my sums right!

A little statistical history

Many of the more complicated statistical tests were theoretically possible in pre-computing days, but were impractical to run. It is only in the day of electronic statistical software - what traditionalists refer to as 'canned statistics' - that various sophisticated tests came to be used. Indeed, Bayesian statistics, created and developed in the 18th and early 19th centuries, are so demanding in terms of calculation that they did not come into favour until the early 21st century, with the advent of today's tremendously fast personal computers.

The disconnect between the machine and its parts

The typical automobile driver these days knows little of its engine or its parts. It isn't necessary. Apart from basic maintenance, the skill is in planning the journey and remembering why you drove there in the first place (ok, and getting there safely).

Similarly, given the context of your studies, choosing the most relevant test and interpreting its results are the key to applied statistics. If, for example, I think that the consumption of stronger cannabis tends to be related to poorer examination results, then if the data I have to hand seems to indicate this, I can run a test to see whether or not the effect is likely to be a matter of chance, or if I have reason to reject the idea of it being a chance phenomenon.

Testing, testing

My main considerations are threefold:

• The type of test needed for the research design
• Which of the available tests is most suited to the data
• How to interpret the results of the test

The one thing I don't worry about is the formula; let the computer compute!

But isn't statistics mathematics?

The developers of statistical tests certainly knew their mathematics. And if you want to create a statistical test, or adapt one for a specific purpose, then you will need to understand the necessary calculations. No question.

Applied statistics is different, as I have already indicated, and the discipline of statistics as a whole is not united in this matter. There are of course traditionalists, who appear to ignore the historical paradox I outlined earlier about the impossibility of doing many of the tests without fast computers, and may believe that statistics will lose respectability.

I take more seriously those who claim that formulae are 'more expressive' or that they represent a 'deeper learning'. This depends upon who you are. If you are a mathematically inclined person, then the first argument is almost certainly true.

I am less convinced about the second argument. When I write, I do not ignore statistical concepts. It is important to understand what statistical tests do, but I believe that actual formulae are unnecessary for understanding statistics.

Statisticians against mathematics!

There are statisticians who take a similarly radical approach:

" Statisticians are convinced that statistics, while a mathematical science, is not a subfield of mathematics. Like economics and physics, it makes heavy use of mathematics, yet has its own territory to explore and its own core concepts to guide the exploration. Given those convictions, we would naturally prefer that beginning statistics be taught as statistics." Cobb and Moore (1997) *

Briggs (2013) † considers mathematics to be one way, not necessarily the best one, of understanding statistics. And he does not see statistics as a branch of mathematics.

" Statistics rightly belongs to epistemology, the philosophy of how we know what we know. Probability and statistics can even be called quantitative epistemology."

Statistics as decision-making

Simplifying Briggs' point, we can refer to applied statistics as a form of logic, a decision-making science if you like. For our purposes in the Statistics without Mathematics series, this pursuit - which I hope will become an interesting one - is one of making a range of decisions, dependent on research design and the data available. We are not 'doing mathematics'!

Should you be anxious about statistics?

There is a fair amount of rather conflicting research on the subject of 'statistics anxiety'. Without going into too much detail, I would say two major contributing elements are attitude and perceived relevance.

What I would say in general terms is that your attitude to statistics is of particular importance. If you don't spend your time thinking that statistics is largely about mathematics, then you will be less daunted. Similarly, don't feel the need to study formal logic. Applied statistics is about decision-making.

Statistical analysis is both a fundamental tradition of your discipline and a current requirement. If you recognise the need to evaluate relevant evidence, you will see the relevance of statistics to your studies. It is of course quite understandable that you came to study your academic discipline because of its implicit interest to you or its usefulness in the outside world, and that therefore statistics seems rather beside the point. This is a perfectly rational way of thinking, but if you allow your lack of interest in 'stats' to take over, you may throw out the baby with the bathwater.

I hope that you will become engaged in what is an interesting part of your studies. Here is a typical response to my books:

" I .. find your style of writing easy to teach and the students don't get lost in arcane trivia about click a radio button to change the font in the graphs and other nonsense. Clear writing that gets the point across to them without me looking back at a class of blank faces. [A] rare quality in a statistics book. " (A personal communication, 2018.)

More detail

* Briggs W.M. (2013) Statistics is Not Math. http://wmbriggs.com/post/3169/

† Cobb G.W. and Moore D.S. (1997) Mathematics, Statistics and Teaching. The American Mathematical Monthly, 104, 801-823

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