aay Approved For Release 2003/04/18 : CIA-RDP96-00787R000200150009-7 Four-State Electronic Random Number Generator This study provided an opportunity to determine whether the re- mote sensing capability could be extended to the perception of the internal state of a piece of electronic equipment. For this purpose, an automated experiment designed around a four-state electronic random number generator was initiated. The solid-state nachine has no moving parts and provides no sensory cue to the user as to its target genera~ - tion. In order to determine unambiguously whether a result was meaning- ful, the following strategy was used. First, the randomness of the machine was verified by over 10,000 pre-experiment trials (details given below). second, the subjects interacted with the machine to generate the datas. Third, for any subject whose score was gignificant, the statistics of the machine during the successful experiment were tabulated to insure that the machine had not departed from randomness in the period in which a significant result was obtained. Fourth, a ‘subject generating a good score was asked to repeat the entire experi- ment after a one-month lag period. Finally, the entire data analysis as carried out by an independent statistics group at SRI. CO. Riabard deaglelon), The machine configuration provides as a target one of four art slides chosen randomly ( = 1/4) by an electronic random generator. The generator does not indicate its choice until the subject indicates his choice to the machine by pressing a button (see Figure 11). (The Approved For Release 2003/04/18 : CIA-RDP96-00787R000200150009-7
Approved For Release 2003/04/18 : CIA- RDF 96- 00787R000200150009-7 machine has four stable internal states. .O-MHz square-wave oscillator sends pulses to an electronic "scale-of-four' counter which passes through each of its four states 250,000 tiines per second. The state of the counter ig determined by the length of time the oscillator has run, that is, the time between subject choices.) As soon as the subject indicates his choice, the target slide is illuminated to provide visual and auditory (bell if correct) feedback as to the correctness ’ or incorrectness of his choice. Until that time, both subject and experimenter remain ignorant of the machine's choice, so the experiment is of the double-blind type. Five legends at the top of the machine face are illuminated one at a time with increasing correct choices (6, 8, 10, .-.) to provide additional reinforcement. The machine choice, subject choice, cumulative trial number, and cumulative hit nunber are recorded automatically on a printer. Following trial number 25, the machine must be reset manually by depressing a RESET button. 'A methodological feature of the machine is that the choice of a . target is not forced. That is, a subject may press a PASS button when he wishes not to guess, in which case the machine indicates what its choice was. The machine thus scores neither a hit nor a trial and then ' goes on to make its next selection. Thus, the subject does not have to guess at targets when he does not feel that he has an idea as to which to choose. Approved For Release 2003/04/18 : CIA-RDP96-00787R000200150009-7
be Approved For Release 2003/04/18 : CIA-RDP96-00787R000200150009-7 Under the null hypothesis of random binomial choices with probability 1/4 and no learning, the probability of observing >k successes in n trials is approximated by the probability of a normal distribution value, n 1\ / > {k - — - —|//3n/16 4 2 ; ‘The design objective was to build a four-state machine, with each state equally likely to occur on each trial, independent of the past sequence of states. If the machine meets this objective, it should not be possible to devise a rule for future play that significantly differs “trom chance. A simple example of such a rule would be to select the machine state observed in the preceding trial; if this strategy were to produce scores significantly above chance (25 percent hits), we would reject the hypothesis of randomness of the machine under test. Before experimentation machines purchased from Aquarius Electronics, Albion, California, were extensively tested for randomness. Data were analyzed on a CDC-6400 computer, and the machine finally selected for use met established criteria for randomness. In developing randomness tests, we are guided in part by a knowledge of the machine logic. When one of the four choice keys or the pass key “is depressed, the current machine state is displayed; then a brief time after release of the key, a new machine state is established (but not shown to the subject) by sampling the instantaneous state of a high- Approved For Release 2003/04/18 : CIA-RDP96-00787R000200150009-7
Bes Approved For Release 2003/04/18 : CIA-RDP96-00787R000200150009-7 speed four-state electronic counter. For the machine to be randon, the times of dwell of the counter in. each of the four states must be ‘precisely equal; otherwise, the distribution of outcomes will be biased. The first randomness test is thus based on tallying the number of occurrences of each of the four states, This test should detect a stable bias, yet may miss a drifting bias. To test for this second possibility we also tally the distribution of outcomes in each group of 100 trials, then compute a likelihood ratio test statistic: (see below) for each group. Under the null hypothesis of equal likelihood ef the four states, these statistic values are distributed approxi- mately as chi-square with three degrees of freedom and their sum for m groups distributed approximately as chi-square with three m degrees of freedom, This test may also detect stable bias, but is not as powerful for this purpose as the first test. Variable bias of still a shorter period, if substantial, can be tested for by tallying the frequency with which the previous machine state is repeated; an overall repeat ratio ("all") significantly above 0.25 is indicative of such bias, If for any reason the machine were to fail to sample the counter to establish a new state, the previous machine state would be repeated. To test for this possibility, we tally the number of repeats following the depression of each key. A repeat ratio significantly greater than 0.25 should be considered a danger signal. Approved For Release 2003/04/18 : CIA-RDP96-00787R000200150009-7
Approved For Release 2003/04/18 : CIA-RDP96-00787R000200150009-7 We also tally the initial machine states following reset and the transitions between states. In each case, the number of occurrences of each of the four possible outcomes should be approximately equal. When repeats are deleted from the sequence of trials ("nondiagonal transi- tions"), the four states should also be approximately equal in frequency. In testing the null hypothesis of four equally likely outcomes of a trial, a likelihood ratio test is used. The statistic i i=1 under the null hypothesis is distributed approximately as chi-square with three degrees of freedom, with rejection for large values of this statistic.* The computer program used in testing randomness includes a subroutine for computing the probability of a chi-square value as large or larger than that observed. In testing the null hypothesis that the probability of a.repeat is 0.25, the binomial probability of obtaining the observed number K or more repeats in N trials is computed. For K greater than 1000, a normal distribution approximation is computed, assuming the statistic K - 1/2 fx ( N : 0.28) 3/16 to be approximately normal with mean zero and standard deviation one. » ee en er ee re ae RY *Alexander Mood, Introduction to the Theory of Statistics (McGraw Hill, New York, 1950). Approved For Release 2003/04/18 : CIA-RDP96-00787R000200150009-7
be Approved For Release 2003/04/18 : CIA-RDP96-00787R000200150009-7 The typical test pattern used was six passes followed by 25 choices of one color, repeating this for each of the four colors. In this way each of the five keys other than resetwere given approximately equal use. Typically, 2000 to 6000 trials were made in each sitting. In the absence of any unusual results in the randomness tests, a minimum of 10,000 trials were made pefore using a machine with experimental subjects. With 10,000 trials, the expected fraction of repeats is 0.25 with a standard deviation of 3/200 = 0.00866. A computer listing of the results of randomness tests is included in Table l. No significant departures from randomness were observed. Subject Data Data was collected from subjects Sl through 56. Each subject was asked to complete 100 25-trial runs (i.e., a total of 2500 trials each). The results are tabulated in Table 2. (One subject, S3, declined to complete the 2500-trial run, indicating a lack of rapport with the machine and, hence, a lack of motivation for the task.) For the six subjects, only one ($2) scored significantly above chance. For the 2500 trials that subject averaged 29.36 hits/100 trials rather than the expected 25/100, a result whose a priori probability under the null hypothesis is p = 3x10, His scores are plotted in Figure 12. The statistics of the machine during the successful run of subject $2 were tabulated for the entire 3488 machine transitions (2500 choices, Approved For Release 2003/04/18 : CIA-RDP96-00787R000200150009-7
oe Approved For Release 2003/04/18 : CIA-RDP96-00787R000200150009-7 Table 1 PRE-EXPERIMENT RANDOMNESS TESTS * pec ne eA ER tT A RAL A LOE SL COR LS GTS ES rn en ee a a A IE I Buttons ; Number ne £ Chi-Sq. Yellow | Green | Blue ° 4 emenense mee fan mee ree mney free net oe ———— ee rs er eer mr Initial states 107 116 113 464 1.986 0.57 Transitions Y 728 764° 765 3047 2.573 0.46 To G 777 784 773 3197 6.745 0.08 Feo B 776 796 810 3155 1.158'| 0.76 R 187 852 803 3247 2.877 0.41 All states 3175 | 3312 | 3264 13110 5.667 | 0.18 Nondiagonal transitions 2340 2412 2341 9519 2.630 0.45 Diagonal ; transitions 728 784 810 805 3127 5.414 |° 0.15 as | |... Bionomial Key N-Trials Repeats Ratio 1 __. _ Prob. Diagonal Yellow | . 2774 705 0.2541 0.313 transitions ; as a function Green _ 2755 674 0.2446 0.748 of key press Blue 2761 706 0.2557 0,250 Red 2742 667 0.2433 0.793 Pass 1614 375 0.2323 0,953 All 12646 3127 0.2473 0.763 ee ee EE I AG ST ee a em erence eee Randomness in groups of 100 trials: Chi-sq. = 299.6141 . D.F. = 345 Prob. = 0.9628 ce ee a ee a A SL Approved For Release 2003/04/1 8: CIA-RDP96-00787R000200150009-7
To iol et: topo, e «pleas Approved For Release 2003/04/18 : CIA-RDP96-00787R000200150009-7 TABLE 2 FOUR-STATE ELECTRONIC RANDOM NUMBER GENERATOR MEAN SCORE/100 TRIALS BINOMIAL SUBJECT OVER 2500 TRIALS PROBABILITY Sl 25.76 0.22 7 82 29.36 3 x 10 S3 : 24.67 (750 trials) 0.60 84 25.76 0.22 $5 "25.20 - 0.42 S6 25.40 0.33 -4 S7 27.88 4.8 x 10 (replication) . - 5 All trials 26.47 1.1 x 10 (15750 trials) fat tate Approved For Release 2003/04/18 : CIA-RDP96-00787R000200150009-7 f
- Tees a Approved For Release 2003/04/18 : CIA-RDP96-00787R000200150009-7 TABLE 3 - MID-EXPERIMENT RANDOMNESS TESTS . BUTTONS ; Number of Binon. | ve1row lercon| piwe | Red| Trials Chi~Sq. Prob. Initial States 0.80 Transitions “0.80 To 70.30 1 -0.70 >0.80 ‘JA11 States 0.50 Nondiagonal . Transitions 70.50 Diagonal Transitions >0.70 Approved For Release 2003/04/18 :' CIA-RDP96-00787R000200150009-7
mere be: Approved For Release 2003/04/18 : CIA-RDP96-00787R000200150009-7 te Bow 4 . 4 30 Out of 100 trials/run. 20 HITS/RUN 10 ) 10 20 © 30 RUN NUMBER - 100 Trials/fRun p= } per trial FIGURE 12 DATA SUMMARY FOR SUBJECT 2 Approved For Release 2003/04/18 : CIA-RDP96-00787R000200150009-7