Applications of the theory of error to the interpretation of trends. (Q1439895)

From the text: The three main objects of the present paper may be summarized briefly as follows: 1. To show that a consideration of the probable error of a trend is always appropriate, and furthermore, that it is frequently necessary if sound conclusions are to be formed. 2. To point out the chief problems encountered in correctly estimating and interpreting probable errors of linear trends and to indicate methods of surmounting these difficulties. 3. To present a method for giving a comprehensive graphic representation of the range of error of a trend. At certain points we must be content to let our statements stand with little proof. To include complete mathematical demonstration would involve transgressing the proprieties of round table discussion, even though the requisite time were available. We can only hope that to a group of statisticians such as this the truth of the more important of our assertions, at least, will be sufficiently apparent with but a general indication of their basis. See also JFM 55.0928.05.