10.1 Statistics - General Description

It is often said that statistics can be used to ``prove'' anything. Properly used and interpreted, this simply is not true. Rather, statistics uses mathematical analysis for two related purposes: analysis of error and estimation of the quality of predicted values. Analyzed correctly and objectively, statistics cannot ``prove'' erroneous theories, at least with the quality of the data. Errors in ``proof'' arise from errors in the data, but careful researchers do not extrapolate conclusions beyond those supported by data.

Let's take a shooting example to show how ridiculous the ``prove anything'' idea of statistics really is. Suppose you shot a ten round group at 100 yards; you shot well with a good load and printed a 1/2 inch group. Using this shot group data, you make a prediction that you have a 90% chance of the next shot hitting twelve feet behind you. Clearly a mistake in the analysis has been made. This shows how blindly following a number, simply because it appears on a calculator display or computer print-out, can lead to erroneous conclusions.

The key to properly using a statistical analysis of measured data is to:

1. Understand the particular measurement being made (analysis of errors)
2. Interpret the measurements for a particular set of data

Oversimplification of either of these steps is what leads to false conclusions. This is done all the time with popular political polling and advertising, where purposeful misrepresentation of the data may have a political or financial motivation. Further, one cannot 'throw out' measured data simply to improve the statistical result. Oversimplification and omitting data are two of the tricks used when statistics is wrongfully used to ``prove'' a point. Manipulators get away with these tricks because of the mathematical nature of statistics and the seeming complexity of the field.