With a name like mine, it was easy when I was growing up to love reading Alice in Wonderland and Alice through the Looking Glass by Lewis Carroll. In that second book Alice encounters Humpty Dumpty and the conversation goes like this:

“ ‘When I use a word,’ Humpty Dumpty said in rather a scornful tone, ‘it means just what I choose it to mean — neither more nor less.’

’The question is,’ said Alice, ‘whether you can make words mean so many different things.’

’The question is,’ said Humpty Dumpty, ‘which is to be master — that’s all.’ ”

Which brings me to the concept of lexical ambiguity – the notion that, as Alice says, you can make words mean so many different things.

This is never more true than in English. I’m thinking words such as “mean” itself, “normal” and most slippery of all, “significant.”

The thing is, a word like “normal” can have one meaning in general English, the English of general conversation, and quite another in mathematical or even statistical English. In general English normal can mean usual, typical, or expected. We talk about things like a “normal” range for a cholesterol level, for example, when that level is what is expected for a healthy person. In mathematical English, the term “normal” refers to a line which is at right angles to a point on a curve. You may remember learning about this line in high schools maths, along with its slightly better known companion, the tangent. Somehow going off at a tangent is a phrase that has made it into general English while going off at a normal is not so common! And in statistical English, the word “normal” refers to a distribution which is symmetric and kind of bell-shaped, indeed a shape sometimes known as a bell curve.

“Mean” behaves in a similar way. In general English mean can refer to the character of a person, heartless or cruel. It can also refer to the definition of something, as in “To procrastinate means to put off doing a task until later”. And in statistical English, “mean” refers to a measure of the centre or location of a set of data, calculated by adding up the data values and dividing by the number of data values you have.

“Significant” is a more slippery customer because the statistical meaning is very specific, or at least it should be. In general English significant means important, or large, or noteworthy. But in statistical English it has a very specific definition, related to testing hypotheses. The outcome of a hypothesis test is significant if the outcome is unlikely to have occurred by chance. How unlikely is unlikely? The bar is usually set at 5 percent, so that if an outcome has a less than 5 percent probability of occurring purely by chance, then the outcome is deemed to be statistically significant.

So statistical English can start to sound rather repetitive because of the specific meanings attached to various words. This is to be expected, indeed it’s quite normal (in the general English sense of the word!) and so there’s no need to go hunting around for alternatives to “significant” if that’s how the test turned out. Some researchers take care to separate out the concepts of statistical significance and practical significance. Just because the difference between two groups turns out to be statistically significant, doesn’t mean that there’s any practical significance in the difference. This is particularly important to remember in the context of trials of new health treatments. There may be a significant difference between the new drug and the old one in statistical terms, but in practical terms the effect of the drugs is identical. The new drug is unlikely to be approved on the basis of a statistical significance alone.

Now you know about lexical ambiguity, what to do about it? Lists of lexically ambiguous words are available in the statistics education literature. You could figure out how they relate to terms in a language familiar to you if that language is something other than English.

You could familiarise yourself with appropriate usage of these words by listening to experts in statistical analysis speak about their work, and reading their results.

Finally, you can write and speak them yourself so that you feel confident when you’re using an appropriate turn of phrase, even if it sounds a little awkward at first.

If you follow these suggestions then like Humpty Dumpty, you too can be master of all these lexically ambiguous terms!

Associate Professor Alice Richardson is Director of the Statistical Consulting Unit (SCU) at the Australian National University. Her research interests are in linear models and robust statistics; statistical properties of data mining methods; and innovation in statistics education. In her role at the SCU she applies statistical methods to large and small data sets, especially for research questions in population health and the biomedical sciences.