I spent a couple of years working on the University of Guelph animal care committee as the “non-user representative”. The committee has a composition mandated by law, including a member of the community from outside the university and several other roles. I was a faculty member from a department that did not use animals at all. The committee is supposed to review proposals involving animals to make sure the animals are needed, that the number of animals used is as small as possible, consistent with getting accurate results, and we are supposed to make sure the arrangements for the care of the animals are adequate.
Working on this committee taught me that squid, octopus, and cuttlefish are the only invertebrates that you are required by law to give an interesting habitat too, e.g. there must be toys. It also taught me that most people designing animal experiments don’t know enough about designing experiments.
I was a bit of a trouble maker on the committee and the guy that followed me, a statistician, made a lot of trouble. This post will, perhaps, explain why. Look at the design below. It has a number of interesting properties. It has six line segments and one circle. If we suspend disbelief and call these seven objects lines then this thing obeys some familiar rules.
- Two points define one, and only one, line.
- Any two lines intersect in a unique point.
- Every line is made of three points.
- Every point is on three lines.
This object is the Fano Plane. The Fano plane is the smallest example of a nontrivial finite geometry. It turns out it can be used in animal care.
Suppose we are testing seven drugs lettered A, B, C, D , E, F, and G to figure out if two drugs cross-react badly. Then there are 21 pairs of drugs to test: AB, AC, AD, AE, AF, AG, BC, BD, BE, BF, BG, CD, CE, CF, CG, DE, DF, DG, EF, EG, and GH. If our first step is to inject mice with all possible pairs of drugs, then we need 21 mice. Suppose, instead, we use the Fano plane. Use seven mice, each associated with one of the lines, and inject three drugs, corresponding to the points on the lines, into each mouse. Every pair of drugs is tested, once each, and we save fourteen mice. This can be good because we like small furry animals or even because it saves money.
For this to be a good scientific technique, drug cross reaction, or suppression of the cross-reaction by a third drug, must be very rare – which they are, especially if you use what you know about the mechanism of action of the drugs to design the experiment. So what’s the issue here?
Sir Ronald A Fisher is a remarkable man. One of his many accomplishments was the creation of the discipline of Design of Experiments within statistics. The mice-saving application of the Fano plane is an example of an experimental design. In general, experimental designs ensure that experiments can answer the questions that they set out to ask, and do so relatively efficiently. Here is a question: was design of experiments even mentioned in your statistics class? This, of course, presumes you’ve had one.
One of the most common complaints that I hear from my colleagues in statistics is that other scientists and academics consult them only after having done their experiments.
Statisticians can vet your experiment ahead of time. They may be able to save money or mice or they may be able to make your experiment more powerful. There is a whole branch of statistics concerned with designing effective questionnaires and surveys. Have you ever felt that a survey you were taking was missing the point?
Badly designed experiments, in a biology lab or surveying organization, waste time and money and may manage not to answer the question at all. One of the big plenary talks at CIBCB this year (I’m just back from that conference as I write this ) was about the methods used to evaluate if young athletes are at risk for sudden death from heart attack. It turns out that the current questionnaire-based method does not gather much of the information needed to tell if a young athlete is at risk for sudden death from heart attack. The speaker had performed an information-content analysis and proposed a more effective evaluation method. The problems were things like assuming that an athlete knows the cardiac health history of his family or, and this is big, that he will tell the truth about it if it could keep him off the team. I was convinced, but I’m not a member of the testing authority.
Occupy Math feels that the education of everyone else about what statistics can do is deeply neglected. It is all very well to take classes that teach you about means and medians, t-tests and Z-tests, but there is also a need to learn about all the cool things you can get a statistician to help you with. This is another place where fear of math costs us resources and even lives. Ever had a bad experience with statistics? Tell us about it by commenting or tweeting.
I hope to see you here again,
Department of Mathematics and Statistics
University of Guelph, Ontario, Canada