Approved For Release 2003/04/18 : CIA-RDP96-00787R00020015001 1-4 I. . Statistical Analysis of the Machine Experimental Data Forward-backward State Transition Analysis SG1l In a previous memorandum (Memo ORD 2240-75, 12 dune 1975 tof the question of randomness with the emphasis on state transitions as an indication of non-randomness was addressed. The data used in the investigation consisted of pre-experiment trials. The purpose of this section is to do a similar investigation using the actual data which occurred during S2's experiment. Table 1 presents all possible transition frequencies. All transitions ‘should have equal probability. YELLOW » GREEN BLUE RED YELLOW 204 199 99 216 GREEN oe 192 218 222 207 BLUE 211 206 228 222 RED | 209 206 223 221 Restructuring into a two-by-six table as in Ref | produces : Y/G—Y/B Y/R G/B G/R B/R FORWARD 199 199 216 222 _ 207 222 BACKWARD 192, 211s 209. 206 206. 223 The conclusion based on pre-experimental data was that these state-pairs show a very strong relationship between forward and backward transition frequencies (coefficient of correlation =,93). However, computing the coefficient of correlation, Poo actual data = .58, it becomes apparent that the degree of dependence is slightly reduced. Therefore the dependence of forward to backward states can no longer be considered as a strong indicator of non-randomness. - Approved For Release 2003/04/18 : CIA-RDP96-00787R000200150011-4
fee ae NT nae a RRNA ethan OO Approved For Release 2003/04/18 : CIA-RDP96-00787R00020015001 1-4 The data used in the above discussion consisted of trials from both machine: 1 and machine 2. Since non-randomness, made apparent by the state transitions, clearly existed for pre-exper imental data, the investigation of the experimental data continued to include a search for this trend in the individual machines. The transitions (including identity) are as follows: Machine 1 YELLOW GREEN BLUE RED. YELLOW 9 79 88 92 GREEN - 8 = 87 | 86 88 BLUE 85 a 82 90 87 RED 91 91 83 92 Machine 2 | . YELLOW GREEN BLUE RED YELLOW 108 120 | 1 124 GREEN. 107. 131 136 19 BLUE. 1260 124 138 135 RED 118 | 115 140 129 Computing the two coefficients of correlation, = ,4934 P machine 7] s2 data and P machine 2 ~ 4838 s2 data it is obvious that the forward and backward transitions are even less dependent than in the combined case. Thus ended the search for non-randomness througn state transition. Approved For Release 2003/04/18 : CIA-RDP96-00787R000200150011-4 9
’ Approved For Release 2003/04/18 : CIA-RDP96-00787R000200150011-4 As a by-product the following table is produced for general information. BOTH MACHINES MACHINE 1 MACHINE 2 . “MEAN . =!) MEAN SD MEAN SD FORWARD 210.8 10.7 86.6 4.27 124 9.74 BACKWARD | 207.8 — 9.00 86.2 3.92 | 121 11.25 TOTAL DATA POINTS 3483 | 1446 2037 COEFF OF COV 9843 4934 -- 4838 Approved For Release 2003/04/18 : CIA-RDP96-00787R000200150011-4
472% Experimental Data Randomness Analysis | gas? - Approved For Release 2003/04/18 : CIA-RDP96-00787R00020015001 1-4 The machine data used during the S2 experiment has been combined, summarized and/or permuted in an attempt to establish evidence or randomness or non- randomness. If an obvious indication of non-randomness would have evolved | this task would be simplified because it would have become a closed form problem (i.e., the solution would be - the data has non-randoni characteristics). However, what has resulted_is that various forms_of the data have been examined with all indicating that the data is random. | : oe Tables, plots and commentary are presented in this section to demonstrate randomness and in some cases just. to provide general information concerning the machines data. The distribution of the colors collectively and for each machine is as follows: | Yellow Green Blue | Red Total Mean Machine 1 * 365 353 356 372 | 1446 361.5 Machine 2 475 : 505 538 519 2037 509.25 TOTAL 840 858 89) 89] 3483 870.75 Machine 1. was not used in as many trials as machine 2 (44 trials to 56 for machine 2), thus the difference in totals. The standard deviation of binomial distribution with n=3483 and p=1/4 is 25.56 which would imply that each separate number is reasonably close to. the mean. . Accepting the distribution of the totals consider the distribution of the colors throughout the experiment. The popluations used for this investigation consisted of the first 25 samples of each trial (100 trials total). This . population is acceptable since the distribution of its totals was reasonable and since the performance of S2 was approximately the same (success-29.61%) for this subset. Approved For Release 2003/04/18 : CIA-RDP96-00787R000200150011-4 4
Approved For Release 2003/04/18 : CIA-RDP96-00787R000200150011-4 _ The. following three approaches comprise the strategy used to attack the question of color distribution. | 1. Each trial (abbreviated to 25 samples) as analyzed separate interval. 2. The data (2500 samples) is divided into intervals of five samples sae each. This will indicate unusual repetitions either within the interval or interval-by-interval. 3. . The data is reformatted into 25 intervals of 100 samples, where the _nth interval consists of the nth sample in each trial. The results of approach 1 is shown in Figures 1.1.a, 1.1.b, 1.1.c, and T.1.d. The binomial distribution for this strategy (n=25 p=1/4) is mean 6.25 | ~ and the variance 4.69. The plots indicate randomness throughout the 100 trials. | | The results of approach 2 are similar to approach 1 and are shown in the four tables in Figure 1.2. The plots indicated randomness but are not shown because of monotomy.. The binomial distribution mean is 1.25 and the “variance 940. | é The binomial distribution mean and variance for approach 3 is 25 and 18.75 respectively (Figure 1.3). A plot of the data (Figure 1.4) for the "RED" case because of the concern for the higher variance and ranges. The 13th sample seems to have an unusually high frequency of "RED" (44%). However in general this investigation has not produced a significant non-random characteristic. Approved For Release 2003/04/18 : CIA-RDP96-00787R000200150011-4 5 ;