This post was triggered by reading Michael McCarthy’s blog post on “Statistical Inference in Ecology”. In it he asks about writing a chapter on statistical inference for an ecology textbook and is trying to tackle that perennial problem: how much maths can you include and still make it readable and understandable?
In section 2 of the chapter “A short overview of some probability and sampling theory” I thought the issue boiled down to the question:
First there is the argument that equations put biologists off because of maths anxiety. There may be some truth in that but I think there is another argument. A sizeable proportion of biologists in the UK have never studied calculus so have no idea what an integral sign means. In the UK I’d estimate this proportion to be about two-thirds based on the maths qualifications bioscience students start their degree with and the mathematical content of a bioscience degree (ref). Obviously this varies widely so these figures are estimates but nevertheless a good starting point.
If a biologist hasn’t studied calculus then including an equation such as this is the equivalent of putting a quote in another language. Just the other day I was reading a novel which had lots of quotes of poems in French. I stopped reading because I wasn’t able to translate the French and the author didn’t translate it into English. And it’s a horrible feeling, leaving me pretty fed up and the book in the recycling bin. It didn’t motivate me to go and learn French I’m afraid!
How would you translate this equation? A graph and narrative explanation is a possibility. You could include the equation but provide a visual and narrative explanation alongside it so that the reader gets the message that the integral sign just means getting the area and the x and x+dx at the bottom and top of the integral sign just show you the two boundary points.
In my experience using multiple modes, for example narrative and visual, works best – does anyone have other ideas?