A week or so back I walked into the lecture room to give a lecture on electromagnetic waves, and was promptly asked: "Marcus, how much statistics do you use in your research?" My initial reaction was to think "what has this got to do with electromagnetic waves?" and then, realizing that clearly it had nothing to do with EM waves, "what’s the ulterior motive to this question?", but kindly another student spelled it out more transparently. "Why do we have to do the statistics paper next year?".
We require our fourth year engineering students to do a paper on statistics in their fourth year. Obviously some students don’t relish this prospect.
The truth is that I don’t use much statistics at all in my work, beyond mean, standard deviation, and occasional use of a normal distribution. Once I think I got as far as a t-test. But that’s the nature of the work I do; it’s not statistically taxing. But what is necessary is a fundamental understanding that statistics does matter.
Most physics students have some idea of this, but it’s often full of misconceptions. A common one is that the ‘error’ in a measurement equals the ( ‘student-measured value’ minus the ‘real answer looked up in a databook’) divided by the ‘real answer’ times 100%. That’s not an ‘error'; that’s the percentage difference between your measurement and a text-book value. So, when I talk about uncertainly with my experimental physics class, I get them to think about what they would do if they didn’t have a textbook to look up the ‘right’ answer with – i.e. they were the very first people ever to do this experiment. That, of course, is the case for research. No ‘right’ answer to compare with.
I’ve found a task that’s worked well is to give them a fictional set of data for the acceleration due to gravity on ‘Planet Waikato’. I make it fictional so they have to lose the notion that acceleration due to gravity equals 9.81 m s-2, as the textbooks say it does for earth. They only have the data-set I give them to work on. Then I tell them they are building a rocket to leave Planet Waikato, and they need to know the acceleration due to gravity to within 1% uncertainty so they can select the right amount of fuel. Does the data given them allow them to know the acceleration due to gravity to within this uncertainty or not? That tends to get them thinking about how we can analyze results of experiments, and what we can say with confidence (and how much confidence) and what we can’t say with confidence. That’s basically what statistics is about.
Just how to do a t-test, ANOVA, chi-squared test, etc, and under what circumstances, I leave out completely. It’s something you can look-up, or consult a statistician for when you need to. The key thing is knowing that you need to.
The question is then, do we need an entire paper in year 4 for our engineers (but not our physicists) to instruct them in the way of statistics? Probably the best people to ask are our graduates, several years after graduation.