Approved For Release 2000/08/15 : CIA-RDP96-00792R000500350002-3 UNCLASSIFIED III METHOD OF APPROACH (U) A. (U) Continuum Search-—-Statistical Approach (U) The first~order requirement in carrying out a continuum-search effort is to determine an appropriate method of evaluation. The approach chosen here is a modification of a procedure developed by Dean Radin at Bell Laboratories for evaluating geometric—distance scores in a perceptual task.* In this approach, one begins by assuming that the target area of interest is in the form of a square (a useful, but not necessary, requirement). A grid system is then laid down over the square in the form of ann x n matrix (20 X 20, say), to yield n? separate grid elements (400 for a 20 x 20 grid, for example). Using this grid as an approximation to a continuum, one can then calculate exactly the a priori chance distribution that any given search response would lie at any given distance from a particular target location. From this, an evaluation can be made on the quality of response (see Figure 1). (U) In the 20 x 20 case, for a target square not on the edge, there is one chance in 400 of the searcher landing directly on the target square by chance, four chances in 400 of being one unit away (above, below, and to the sides), four chances of being V2 units away, and so forth. Counting out from any particular target square, the inhibition of responses beyond the boundary of the overall square (at certain distances in certain directions) is easily taken into account in the counting process. Thus, an exact calculation can be made on the basis of straightforward counting (taking into account edge effects) for the probabilities of all possible target/response pair distances. One result of these calculations for the 20 X 20 case (taken as standard) is Table 1, in which the mean distance from each given target square to all possible response squares in the grid is displayed. As a reference, the grand mean chance expectation (MCE) target response pair distance in the 20 x 20 grid is 10.41 units. *(U) Radin, D., “Evaluating Geometric Distance Scores in a Perceptual Task,” Research in Parapsychology 1981, pp. 163-164, Scarecrow Press, Inc., Metuchen, NJ (1982). -4- Approved For ReleasU PIW@A8 ASS $] F-HEID96 -00792R000500350002-3
Approved For Release /08/1 <1 4] 4 6-00792R000500350002-3 PP ONCLASSI Prob (d) UNCLASSIFIED FIGURE 1 (U) SEARCH MATRIX (U) Thus, if the search area of interest is 20 km x 20 km, the MCE distance for random attempts to locate a random target is 10.41 km. B. (U) Discrete Search—-Statistical Approach (U) Im the discrete search case (one choice from among K possibilities), the appropriate evaluation statistic is the cumulative binomial distribution. The parameters are as follows. (U) We define a trial as a single attempt to pinpoint a target as being at one of K possible target locations. Let p = 1/K be the probability of a chance hit in the location attempt in a single trial, and q = 1 ~ p be the probability of a chance failure in a single trial. Approved For ReleaswANGsdoAS SAK ed 96-00792R000500350002-3
. - -00792R000500350002-3 Approved For Release ICLA SsikieD 00 Table 1 (U) TABLE OF MEAN DISTANCES (Beginning Row 1, left to right, square (1,1), (1,2)..., through upper left—hand quadrant of 20 x 20 matrix) .O4415, - 48960, 1.91840, -69934, - 40802, -83167, -20110, - 97406, -83167, - 23547, . 54992, . 31541, . 31976, . 70606, - 97108, -72981, »87571, . 24699, .46895, 22171, -50216, -86094, .O4665, » 79433, . 20110, -04992, . 70647, - 45003, - 97406, . 31541, - 45003, .19049, -82211, 15851, .27849, -01685, . 74596, .07989, -19254, - 92986, 8. 9. 8. 9. 8. 9. 7. 9. 7. 8. 7. NO~DOWMOOMWO Grand Mean = 10.41513 UNCLASSIFIED (U) In a series of location attempts, the important statistic is the probability of obtaining at least R hits in N trials, by chance, because this distribution establishes the basis against which the efficiency of the search method must be compared. This statistic is given exactly by the cumulative binomial (Bernoulli) distribution. -6- Approved For Releadd IN4GbdNS SERIE D> 96-00792R000500350002-3
Approved For Release 2000/08/15 : CIA-RDP96-00792R000500350002-3 UNCLASSIFIED (U) Probability of at least _ N N! pighi - (1) R hits in N trials ~ il (NI 4 Although probabilities are listed for several representative values in published tables,* it is perhaps most convenient to calculate them directly with the aid of a standard programmable calculator. A program for the Hewlett-Packard HP 41-C series calculator is provided for convenience as Table 2, (U) To complete discussion of the binomial distribution, we note that the mean number of hits expected by chance in N trials is b= Np, while the standard deviation (measure of expected spread about the mean) is given by o = WNpq (U) Throughout the statistical evaluations, whether for continuum or discrete search, we shall adhere to the standard convention that a result obtained in testing can be interpreted as evidence for psychoenergetic access if the probability of that result occurring by chance is less than p = 0.05, “(U) Tables of Cumulative Binomial Probability Distribution, Harvard University Press, Cambridge, MA (1955). -_ 7 _ Approved For ReleasWAGdaAS SHR iD 96-00792R000500350002-3
Approved For Release CARPE LR SSPRIE BS 707 2 ROooso0ss0002-3 Table 2 (U) HP 41-C PROGRAM: CUMULATIVE BINOMIAL DISTRIBUTION BL4LEL "CUM EIN" 444LBL 15 H? 5f1 2 43 REN AS 8 46 ¥=8? 84 $70 a1 4? GTO 1? AS "G PRIQRT Pe 48 310 14 46 PROMPT 494LBL 16 a7 STO 82 5A RCL 12 8 LK oi REL i4 89 STG a2 je 18 RCL G2 S32 RCL ti tl CHS née if 1 ge 370 11 la + 56 | 14 STO a4 a? ST- {2 5 LH ne 1 16 STO a5 59 ST- i4 f “NR HITS?" 6a RCL id 18 PROMPT ei X=8? 19 570 Bé 62 GTO 1? 28 “NR TRIALS?" 62 GTO 16 21 PROMPT 64#LBL 17 22 STO a? 65 RCL 11 PI4LBL a8 646 LN 24 RCL WF? 67 ROL 18 23 RCL 6 G+ 26 - 69 Ete 2? 370 89 78 ST+ 81 28 REL @5 7L RCL 61 29 # 72 TOWE @ 38 RCL BE f3 PSE 31 RCL 86 ‘4 i 32 * 79 57+ #6 33 + 76 RCL a6 346570 18 fi | 35 78 - 36 $70 11 79 RO} 7 a? ROL BP BA NYE 39 «570 {2 Qi CTO 88 39 REL 86 82 RCL Ai 49 BCL &9 83 "PF, R OR MORE=" 41 s3Y¥? 84 ARCL X 4? G70 15 85 AYIE: 43 KOSY 86 BEEP 8? END UNCLASSIFIED -s- Approved For Releady SMG bAYS Sd LEB 96-00792R000500350002-3