APPENDIX 153 



and we conclude that we are dealing with real cycle phenomena and a reliable 

 method of analysis. 



PROBABILITY TESTS 



We now take up such matters as the tendency of an observer to favor 

 certain cycle lengths (resulting in spurious emphasis on special values in the 

 periodogram) and the recognition of real and unreal cycles. To investigate 

 such problems by means of probability curves is illuminating. 



A general method, used in the Tree-Ring Laboratory, for obtaining a 

 lot-drawn or random curve is the following. Each year represented in a 

 sequence of measurements of ring widths of a specimen or group to be used is 

 marked on a slip of paper. All slips are then thoroughly mixed in a container, 

 and drawn out at random without replacements. The values corresponding 

 to the years drawn are put down in the order of drawing, and a curve is made 

 from the series. This represents a quite accidental or probability arrange- 

 ment, whose frequency distribution, however, is of course identical with that 

 of the original curve. Each curve is then put into the cycleplot form. 



Recognition Tests — A test was made with four 500-year lot-drawn curves, 

 to which were added two 500-year real curves of northern Arizona tree-growth, 

 and the analysis carried through by the rack method of simultaneous or con- 

 current analysis, every curve appearing for a moment in front of the cyclo- 

 graph window and then giving place to its neighbor. Both real curves were 

 recognized at once, by their evident similarity in the cyclograms. 



A second and more extensive recognition test was made with a group 

 comprising 27 lot drawings and 6 genuine curves. They received simultane- 

 ous analysis, five and six at a time, with two real curves for comparison; one 

 was put in rack at the top, the other at the bottom, and the unknowns in 

 between. The analysis was made in six sets. It is to be noted that the real 

 curves among the unknowns were from the same geographic area (and hence 

 contained approximately the same cycles) as the two comparison curves. 

 Nevertheless, the results were quite gratifying: 

 Of 6 called genuine, 5 were genuine. 

 Of 2 called possibly genuine, 1 was genuine. 

 Of 25 called false, 25 were false. 



We may conclude from this that when the curves are subjected to simul- 

 taneous analysis as above, the probability of picking out the real from the 

 false is quite high. 



Cycle Preference Tests — To test whether there was any preference in the 

 matter of assigning particular cycle lengths and to test for characteristics of 

 cycles in random sequences, a group was made up with considerable care 

 consisting of 37 cycleplots of which 6 were genuine. All were individually 

 analyzed without knowledge as to which were genuine and thus all received 

 treatment as if they were real. 



The periodogram values of the first 15 of the lot-drawn curves were 

 compared with the values for the remaining 16. A correlation coefficient 

 of 0.016 ± 0.117 was found, indicating completely random distribution of 



