Wednesday, September 14, 2011

Measurement efficiency

While I was helping one of the undergraduates in our group yesterday I started thinking about the efficiency of measurements and how we can avoid wasting time in the laboratory with poorly planned experiments.

By an efficient measurement I mean an experimental procedure that extracts the most information possible from the collected data with the least effort. The second part of my definition, expending the least effort, is usually common sense. After all, I require nothing more than a ruler to measure the length of something that is nearly the size of the ruler. Pulsed radar or laser interferometry are obviously too complicated for this task.

However, it is usually common sense because people erroneously think that more data is always better. If a certain phenomenon is known to be a linear function of some variable, for example, then I only need to take enough data points to assign statistically meaningful values to the best-fit line's slope and intercept. I've frequently seen my colleagues painstakingly collect so many data points as to make their plot appear continuous when in fact the curve describing the data was unimodal or uniformly increasing or decreasing. Much less effort could have been expended by reducing the number of measurements performed in these cases [1].

These examples also help illustrate the first part of my definition of an efficient measurement—extracting the most information possible. In the example about the data modeled by a line, there are only two pieces of relevant information: the slope and intercept. In fact, if it weren't for noise and measurement uncertainty, only two data points would be needed to maximize the amount of information gained. More complicated situations would likely involve performing measurements to increase my belief in a certain conclusion but may not outright prove that conclusion true. In these cases, an efficient measurement would optimize my belief based on the data it provides.

There is one subtle point to an information theoretic viewpoint of measurements that I've failed to discuss so far. The information that is extracted depends entirely upon the hypotheses being tested. That is, information is not physical. Measurements of voltage across a piece of material are only relevant if I want to know the material's electrical properties. So identifying exactly what I want to know about my system before I measure something about it is crucial in optimizing my measurement's efficiency.

In summary, an efficient measurement simplifies the means of data collection while maximizing the amount of information provided by the data. The information that a measurement provides is determined by the questions asked of the experimentalist; therefore, measurement efficiency is judged against these questions.

[1] Automated data acquisition has to a large extent made the number of data points collected irrelevant, but perhaps it has also caused many of us to neglect the question of efficiency in the first place.