‘Approved For Release 2000/08/10 : CIA-RDP96-00787R000200010007-4 5. Basic Research Summary The basic research program to date has been spread over a number of subjects and over number of activities, generating a considerable amount of data. It was deemed desirable in the first half of the research program ‘to cover ag much material as possible in a horizontal development in order to de te mine the best subjects and the fruitful directions for concentrated effort in the second half of the program. We intend to concentrate on analysis of the large amounts of data . already obtained while subjects are involved in extramural medical and psy- chological testing. Based on the findings, a few carefully-chosen items will be culled for final specific testing following discussion with client representatives. Approved For Release 2000/08/10 : CIA-RDP96-00787R000200010007-4
ee Approved For Release 2000/08/10 : CIA-RDP96-00787R000200010007-4 APPENDIX 1 Randomness Tests of Four-State Electronic Random Stimulus Generator 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 from 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 re ject the hypothesis of randomness of the machine under test. Before experimentation, four machines, purchased from Aquarius Electronics, Albion, California, were extensively tested for randomness. Data were analyzed on a CDC-6400 computer, and three machines finally selected for use in screening met established criteria for randomness. In developing randomness tests, wer-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-speed four-state elec- tronic counter. For the machine to be random, 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 randomess test is thus based on tallying the number of occurrences of each of the four states. This Approved For Release 2000/08/10 : CIA-RDP96-00787R000200010007-4
cAPRKQVER Fiat Release,2000/08/10.: GLA-RPP96-00787R090200040007;4... 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 of the four states, these statistic values are distributed approximately as chi-square with three degrees of freedom and their sum for m groups distributed approxi- mately 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 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 con- sidered a danger signal. We also tally the initial machine states following reset and the tran- sitions 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 transitions"), 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 + Alexander Mood, Introduction to the Theory of Statistics (McGraw Hill, New York, 1950). Approved For Release 2000/08/10 : CIA-RDP96-00787R000200010007-4
Approved For Release 2000/08/10 : CIA-RDP96-00787R000200010007-4 4 . n/a “2D n, Zn (4 /: ) i=1 Ry under the null hypothesis is distributed approximately as chi~square with three degrees of freedom, with rejection for large values of this Statis- tic. 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. on 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 N wa oe 25 —_— ( N 3/16 . to be approximately normal with mean zero and standard deviation one, The typical test pattern used was six passes followed by twenty-five choices of one color, repeating this for each of the four colors. In this way each of the five keys other than rest were given approximately equal use. Typically, 2,000 to 6,000 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 before using a machine with experimental Subjects. With 10,000 trials, the expected fraction of re- peats is 0.25 with a standard deviation of 3/200 = 0, 00866. A sample computer listing of the results of randomness tests on Machine 4 is included in Table 1. Of the four machines tested, three were found suitable for use in screening activity. The fourth machine was returned to the manufacturer for adjustment. e Approved For Release 2000/08/10 : CIA-RDP96-00787R000200010007-4
_ Approved For Release 2000/08/10 : CIA-RDP96-00787R000200010007-4 Table 1 RANDOMNESS TESTS~-MACHINE 4 of Y G B Initial states Transitions All states Nondiagonal transitions | N-Trials Repeats | Ratio Binomial | Diagonal P Prob. transitions Yellow 0.2541 Green A. 0.2446 Blue ; | 0.2557 Red "0.2433 Pass 0.2323 All 0.2473 Randomness in groups of 100 trials: Chi~sq. = 299.6141 D.F. = 345 Prob. Approved For Release 2000/08/10 : CIA-RDP96-00787R000200010007-4