So for all the budding mathematicians out there I want to share with you more details of which statistical tools I use day-to-day.
So the first thing to say is that, long gone is the pen and squared paper. Here showing your working involves creating a document with a series of the commands or functions you have run in your statistical computer package of choice. Generally I am interested in seeing if there is a relationship between two measures. I would say that the most common methodology I use is regression, perhaps more familiar to you as fitting a line to data. We routinely have to deal with a range of confounders (that is additional factors such as gender or age that may induce an association between the two variables of interest) and linear models have the flexibility for this.
There is often an expectation that as we deal with complex data, we must use super complicated mathematical formula to cope. This isn’t always necessary (at least not initially), so why make it harder than it needs to be? Keeping the analysis simple, helps makes the interpretation easier. Implementing a more advanced test (likely accompanied by an impressive name such as ‘dynamic time warping’) may give you a great sense of achievement. But this is often short-lived, lasting until someone asks, “So what does this mean?” and you try to translate the underlying hypothesis into a biological concept.
The most important factor, is to keep in mind what scenarios the statistical test is designed for and understanding or recognising its limitations. Unfortunately, there are many biological measures (genetics being a particularly good example of this) that flaunt common statistical assumptions. This can be the biggest challenge as often an appropriate test does not exist, so you have to get creative to see how far you can stretch the one you are using. However I think this is whether statisticians need to think a little bit more like other scientists, who routinely accept that no approach is perfect and every experiment has limitations, the key is to acknowledge them.