Statistical Significance of Results

The reliability of results may be judged by statistical as well as economic criteria. In general, the figures used are not exact. They are often derived from samples, or otherwise more or less inadequate for the problem under consideration. In addition, a number of minor explanatory causes are omitted; this seems to be the chief reason why observed and calculated values of x1 in general do not coincide, and this lack of coincidence is responsible for a certain ambiguity in the results obtained. The question arises whether limits may be indicated for this uncertainty. As nothing is known about the factors omitted, it can be answered only if certain additional hypotheses are made.

Various methods of statistical testing have been worked out, using different hypotheses and leading, therefore, to different results. Some account of these methods will now be given. The non-mathematical reader should be warned that their comprehension will make somewhat greater demands on his attention than has the foregoing exposition of the method of multiple correlation analysis itself; and he may perhaps prefer to take the remainder of this chapter, together with Appendix A, on trust.

The classical method goes back to Laplace and Gauss. It will be considered here in the final form that has been given to it by Professor R. A. Fisher.