Cr ec marenn antiemetic eg, aap EE ET Approved For Release 2003/04/18 : aa tia ele ala TABLE OF CONTENTS Overview I. . Statistical Analysis of the Machine Experimental Data. ..,.... Forward-Bakcward State Transition Analysis ... . see we wee Experimental Data Randomness Analysis... . , a cee eee Best Strategy. . 2... 0, ee ee ee ee nr II. Analysis of S2 Data Responses... eo. ee ee ee ee, Strategy of $2 a | Total Color Choices»... le State Transition Color Choice... ee ee ee, Hit Analysis we ee eee, Learning from Trial to Triad ee eee Learning Withina Trial 2... III. Miscellaneous... ... arn ee ee ee General Trial Information... . 2... eee eee, ‘Machine States ......,0~2.,., ee eee eee, Plots of Passes .....,, a (eee eee Subject.- Future Machine State Transition . . te ee Distribution of Machine State Colors for Machine 2 ....,..., = Approved For Release 2003/04/18 : CIA-RDP96-00787R000200150011-4
€ J a er Approved For Release 2003/04/18 : CIA-RDP96-00787R000200150011-4 Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure e . * * eel ed ed wW WD be MN Nm Nh Po rh oo | Dy. - Ww ine] WS WW WwW rn om FF WwW Pf Bo o1 — es @ 8 aon Distribution of Machine Yellows Over Trials Distribution of Machine Greens Over Trials Distribution of Blues Over Trials Distribution of Machine Reds Over Trials Distribution of Machine Colors When Samples are Taken Five at a Time Distribution of Machine Colors When Samples are Taken 100 at a Time Distribution of Machine Reds When the Samples are Taken 100 at a Time Machine Color Distribution for Machine 1 and Machine 2 on a Trial to Trial Basis $2 Color Choices Plot of Number of Hits/Trial Frequence Plot of Number of Hits ieedyone Success Ratio of Subject (both machines used Accumulative Probability of Succsss on Machine 1 Accumulative Probability of Success on Machine 2. Hits vs Trial Number for Machine 2 Total Number of Hits Within a Trial Selected Parameter Totals Listed by Trial Number Color States of Machine 1 During the Experiment _ Color States of Machine 2 During the Experiment Total Number of Passes of a Trial Total Number of Passes Summed of Sample Number Plot of Number of Hits per Trial and Number of Passes per Trial Approved For Release 2003/04/18 : CIA-RDP96-00787R000200150011-4 Page ‘(9 COnI NH 10 i 12 14 17 22 22 23 24 25 27 _ a9 32 34 35 36 37 39
Approved For Release 2003/04/18 : CIA-RDP96-00787R00020015001 1-4 Page Figure 3.7 State Transitions From Subject Choice to Future Machine State ce 40 Figure 3.8 Distribution of Yellows for Machine 2 - 42 Figure 3.9 Distribution. of Greens for Machine 2 7 42 Figure 4.0 Distribution of Blues for Machine 2 7 - 43 Figure 4.1 Distribution of Reds for Machine 2 ; 43 Approved For Release 2003/04/18 : CIA-RDP96-00787R000200150011-4
Approved For Release 2003/04/18 : CIA-RDP96-00787R00020015001 1-4 Overview An apparent phenomenon which defies the theory of probability occurs when Subject 2 plays this experimental game. He Significantly exceeds his probability of success, .25, by scoring over .29. The question that this report addresses is: Is there a statistical or logical reason why he did so well? The methodology used to attack this problem and the resulting conclusions are summarized below. This summary can also serve as an outline to this detailed report. I. Il. Statistical Analysis of the Machine Experimental Data Pre-experiment data analysis discovered a non-random characteristic through the examination of forward-backward state transitions (j.e., Red-Blue, Blue-Red). However, the coefficient of correlation between the forward and backward States of .538 for the experimental data, .49 for Machine 1 data and .48 for Machine 2 data were considered low enough that this approach was dropped. Pre-experiment state transitions had a coefficient of correlation of .93. The experimental data randomness analysis consisted of axamining the distribution of color totals and the distribution of each color taken over various combinations and permutations of the data. No evidence of non-randomness was discovered. Analysis of the Subjects' Data Responses The subject's responses were analyzed with the emphasis on the discovery of his strategy or the unveiling of a trend which would give * him a statistical advantage. The possibilities investigated produces no solid reason how he was able to be so successful. However, in one > case there is a strong indication why he was able to succeed. It appears that. he was learning the states of Machine 2. The details of this are in Approved For Release 2003/04/18 : CIA-RDP96-00787R000200150011-4
Approved For Release 2003/04/18 : CIA-RDP96-00787R00020015001 1-4 . the remainder of the report. ed Miscellaneous | The report contains a section entitled "Miscellaneous" for the purpose of displaying detailed data which wasn't directly required by the above more general analysis. Details such as how many successful choices in the color red during the 50th trial were there, or what was the relationship of the number of passes to the number of successes. - The terminology used is as follows: the term "trial" refers to the string of machine states and corresponding choices from the time the subject begins until. he makes 25.non-passing choices. A sample is a “machine state and/or subject choice (including passes). There are (25 + # passes/trial) samples in each trial. Approved For Release 2003/04/18 : CIA-RDP96-00787R000200150011-4