Statistical Methods for Equilibrium Moisture Correlations

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Abstract
In the first paper of this series § there was presented a method for the treatment of equilibrium moisture data for textile fibers. Results of extensive statistical calculations were reported and analyzed. This paper presents the details of the methods which were used in arriving at those correlations. Of major interest is a means of calculating the best point of intersection of a series of lines and of evaluating the probability of the existence of such a common point on all lines. When it is suspected that the lines are parallel, the test of probability must be adapted to this eventuality. In general, the probabilities are estimated by analysis of variance. In this calculation, the individual lines are fitted to the experimental points by the method of least squares. They are then again fitted to the points with the additional condition of intersection or parallelism, which ever is thought to be more likely. The additional variance imposed by the added condition is then compared to that of the deviations from the simple individual least-squares lines and evaluated for probability by Snedecor ratios. Illustrative graphical material based on the Wiegerink data for degummed silk in positive sorption from dry condition to equilibrium state is presented to show the various procedures.

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