1 - Decision

Summary

If your experiment needs statistics, you ought to have done a better experiment.

(Ernest Rutherford)

Science is about decision. Building instruments, collecting data, reducing data, compiling catalogues, classifying, doing theory – all of these are tools, techniques or aspects which are necessary. But we are not doing science unless we are deciding something; only decision counts. Is this hypothesis or theory correct? If not, why not? Are these data self-consistent or consistent with other data? Adequate to answer the question posed? What further experiments do they suggest?

We decide by comparing. We compare by describing properties of an object or sample, because lists of numbers or images do not present us with immediate results enabling us to decide anything. Is the faint smudge on an image a star or a galaxy? We characterize its shape, crudely perhaps, by a property, say the full-width half-maximum, the FWHM, which we compare with the FWHM of the point-spread function. We have represented a dataset, the image of the object, by a statistic, and in so doing we reach a decision.

Statistics are there for decision and because we know a background against which to take a decision. To this end, every measurement we make, and every parameter or value we derive, requires an error estimate, a measure of range (expressed in terms of probability) that encompasses our belief of the true value of the parameter. We are taught this by our masters in the course of interminable undergrad lab experiments.