Cognitive Practical Report

Cognitive Practical Report

Introduction
The study of random sequence generation raises some interesting theoretical issues in human memory, cognition, and behaviour. Randomness is a subjective concept used throughout multiple areas of psychological and mathematical research to explain the manners in which humans participate in experiments by generating random responses (Wagenaar p 65 1972). The problem with studying prior research on the ability of humans to generate random numerical sequences is that investigators employ such a variety of experimental conditions and definitions of mathematical randomness (Wagenaar p 65 1972). Budescu (p 25-39 1987) suggested that only theories which are based on the notion of a “subjective concept of randomness” are consistent with the results of these experiments because of the multiple ideas humans have regarding randomness. Therefore, it is important to examine previous research and theoretical contentions when developing and distributing random number generation experiments.

Theoretical Background
In traditional human random sequencing theory, the contention has been long established that humans may simply be incapable of comprehending randomness because the short term memory presents prearranged sequences, making it reasonable for the participant to anticipate sequential patterns because they expect sequential patterns (Peterson and Ulehla p 1-4 1965). Human subjects have difficulty in generating sequences that satisfy accepted requirements for randomness, which has been attributed to faulty cognitive operations or concepts of randomness (Treisman and Faulkner p 337 1987). Falk and Konold (p 301 1997)  explained that the general approach of the mathematical theory of complexity, which identifies the length of the shortest program for reproducing a sequence with its degree of randomness based on the attempt of a human to mentally encode the numerical sequence. The question of the ability of human participants to behave randomly is one of cognition, where it is assumed that a human participant is unable to be random because of inherent memory, but other studies have shown participants who learned to generate sequences that were indistinguishable from computer-generated random numbers (Neuringer p 74 1986).

Yet other researchers like Reed and Johnson (p 593 1994) found that changes in sequencing of random numbers exist because learning and memory is an implicit human characteristic that cannot be separated by simple instruction. Bird and Heyes (p 262 2005) compared the ability of participants to perform random sequences, finding that observational learning was indicated when the introduction of a new sequence was associated with more reaction time elevation in observers than in controls. Yaakov (1992) examined that a human is incapable of simulating a random generator fail in the rate of each event, because there is over-alternation between events that stems from attempts to produce within short-term memory limitations a typical sequence in the standard task, but that the higher altercations were due to proportion of events (numerical sequencing) than the actual ability to generate a random numerical sequence.

Prior Experiments
Bakan’s (p 127-1311960) early experiment involved requiring human participants to fabricate the actions of random coin flips. Each participant was to create a sequence of heads and tails responses that was entirely random. The focus of this experiment was that the participant was not supposed to create a cognitive pattern. Bakan (p 127-1311960) found that even though the participants were asked to create random number generation, the responses were not random. The heads and tails respondents created patterns, regardless of their instructions. Bakan (p 127-1311960) also found that the participants produced massive sequences of heads and tails, but created only small runs of heads or tails, which differs greatly from a true random response because there is a discernable pattern that can be shown by a mathematical formula.

Rapoport and Budescu (p 352-363 1993) further examined the ability of humans to generate random numerical sequences. They studied random number generation of humans within three conditions: 1) Face to face repetitive zero-sum game; 2) Face to face non-repetitive zero-sum game; and 3) Individually generated random binary responses. While this was a largely complicated experiment, the base theory was to act as the anti-hypothesis of previous research. According to Rapoport and Budescu (p 352-363 1993), a majority of prior research had logical and methodological difficulties.

Rapoport and Budescu (p 352-363 1993) sought to eliminate some of the behavioural altercations that may have been involved in previous research. Their results showed that participants were able to generate binary sequences that satisfy standard tests of randomness more successfully when they participate in 2-person strictly competitive games inducing them to conceal their choices and protect themselves from their own frailty to maximize gain Rapoport and Budescu (p 352-363 1993).

Aims and Design
The aim of the experiment explained further in the methodology section was to use similar but different strategies for showing human behaviours in random number generation as those utilized by Rapoport and Budescu (1993). The aim of the experiment is to compare human responses to specific game conditions. This is similar to Rapoport and Budescu (1993) in that the game conditions were set as a zero-sum two-player game.

The independent variables selected in this experiment are Tasktype; Told; and History. Tasktype refers to the conditions placed on the participants in the experiment as Game, Sequence, or Random. Game condition is similar to Rapoport and Budescu (1993) first condition of face to face zero-sum play, where the participants were competitive with one another. The Sequence condition is similar to the Game condition except that participants must first develop a sequence of numerical selections and then proceed to face to face zero-sum competition. The final Tasktype independent variable is Random, where the condition was established as being similar to Rapoport and Budescu (1993) individual condition, where the participants were asked to generate individual sequences of the numbers 1, 2, and 3 without knowledge of the other two game conditions, thus creating an independent variable that can be utilized as a type of benchmark against the previous conditions. The independent variable Told refers to informing the participant if they were playing the game against a computer or another human at random assignation. History acted as an independent variable where the participants could either view or were not able to view the previous choices in number generation, however when playing under the Game condition both opponents (human and human or human and computer) were shown while in the Sequence and Random conditions only the participant’s choices were shown.

Hypothesis Statement
The aims and designs allow for three hypotheses to be formed. The primary hypothesis is that “deviation of the actual proportions of runs from expected should be less in the Game condition than the Sequence condition, which in turn should be less than the Random condition.” This hypothesis was developed to consider that Random refers to less researcher and competition interaction with the participants, thus allowing for less random number generation, relying on previous research of Bakan (1960) where participants simply listed random number sequences, thus creating more deviation of runs because of the previous established principles that humans do not randomly generate numerical sequences because of cognitive behaviour.

The secondary hypothesis states that “in the Game condition the deviation of actual proportions of runs from expected should be less in the Told-person condition than in the Told-computer condition.” This hypothesis is not similar to previous research in that the majority of previous research did not utilize a computer to human condition, however, the hypothesis is founded on the theoretical perspective that strategy selection is based on competition, so it can be theorized based on Rapoport and Budescu (p 354 1993) where “theory predicts that the players will select strategies with the property that the resulting utility for Player 1 (Player 2) is the maximum entry in its column (row) and the minimum entry in its row (column).”

The third hypothesis is that “in the Game condition the deviation of actual proportions of runs from expected should be less in History-none than in History-given.” This hypothesis is founded on the contention of Rapoport and Budescu (1993) where participants requested to create random sequences are unable to do so, but participants creating random sequences in a competition form are able to do so by using the basis of random as a strategy, thus when a participant must compete based on memory, a strategy of randomness is formed utilizing History for competition purposes.

Discussion
The expectation in the primary hypothesis was that the Random condition should have the maximum deviation over Sequence and Game, however results showed that runs-deviation is minutely different between Random and Sequence, although Sequence is a lower deviation than Random. Game deviation is the lowest, as predicted by the hypothesis. Thus, the primary hypothesis is correct.

The secondary hypothesis states that “in the Game condition the deviation of actual proportions of runs from expected should be less in the Told-person condition than in the Told-computer condition.” This hypothesis is not similar to previous research in that the majority of previous research did not utilize a computer to human condition, however, the hypothesis is founded on the theoretical perspective that strategy selection is based on competition, so it can be theorized based on Rapoport and Budescu (p 354 1993) where “theory predicts that the players will select strategies with the property that the resulting utility for Player 1 (Player 2) is the maximum entry in its column (row) and the minimum entry in its row (column).”

The second and third hypotheses were combined into one table to show the deviation of Told-person and Told-computer within the Game condition only because of technical difficulties analyzing the results in the Sequence and Random conditions. The expectation for the secondary hypothesis was that the Told-person independent variable would be less than the Told-computer, and the History-none independent variable deviations would be less than in the History-told deviations. The chart below combines the results, where the cross sectional result of Told-person to History-none was expected to be less than the deviation of Told-computer to History-told. This hypothesis is supported by the results in the chart below, which shows that there is significant differentiation between Told-person and History-none is actually a much larger deviation from Told-computer to History-told, which is significant that a participant with no history will deviate from the sequential random number generation expectations than a participant competing against a computer with History-told.

In conclusion, the overall objective of showing that competition impacts random sequence generation in human competitive strategies is positively expressed, which supports Rapoport and Budescu (1993) theory regarding zero-sum game conditions, and also supports the previous literature that random sequence generation can be learned when perceived in the appropriate subjective cognitive arena, as examined earlier by Reed and Johnson (p 593 1994) and Bird and Heyes (p 262 2005) where participants were able to form a cognitive strategy of randomness when the experiment is framed appropriately without direct researcher intervention and instruction. Perhaps, then, the concern of the ability of humans to create random number sequences does not lie in the ability of a person to actually be random, but in the ability of a person to learn a strategy or to gain better results with less researcher instruction.

Further research should compare instructed participants to non-instructed participants. For example, it would be interesting to note if there is a difference between participants specifically ordered to create a random numerical sequence and persons simply told to record any numbers they wish. While this would obviously not be a true experiment without selected conditions and variables, the possibility is that participants are instigated by researcher intervention, and thus without random-specific instructions may or may not create random information.

References
Bakan, Paul (1960) Response-Tendencies in Attempts to Generate Random Binary Series The American Journal of Psychology, Vol. 73, No. 1 (Mar., 1960), pp. 127-131

Bird, Geoffrey; Heyes, Cecilia; (2005) Effector-Dependent Learning by Observation of a Finger Movement Sequence Journal of Experimental Psychology: Human Perception and Performance, Vol 31(2), Apr 2005. pp. 262-275.

Budescu, David V (1987) A Markov model for generation of random binary sequences.  Journal of Experimental Psychology: Human Perception and Performance, Vol 13(1), Feb 1987. pp. 25-39.

Falk, Ruma; Konold, Clifford (1997) Making sense of randomness: Implicit encoding as a basis for judgment. Psychological Review, Vol 104(2), Apr 1997. pp. 301-318.

Neuringer, Allen (1986) Can people behave ‘randomly?’: The role of feedback.  Journal of Experimental Psychology: General, Vol 115(1), Mar 1986. pp. 62-75.

Peterson, Cameron R.; Ulehla, Z. J. (1965) Sequential patterns and maximizing. Journal of Experimental Psychology, Vol 69(1), Jan 1965. pp. 1-4.

Rapoport, Amnon; Budescu, David V. (1992)  Generation of random series in two-person strictly competitive games. Journal of Experimental Psychology: General, Vol 121(3), Sep 1992. pp. 352-363.

Reed, Jonathan; Johnson, Peder (1994) Assessing implicit learning with indirect tests: Determining what is learned about sequence structure.  Journal of Experimental Psychology: Learning, Memory, and Cognition, Vol 20(3), May 1994. pp. 585-594.

Treisman, Michel; Faulkner, Andrew (1987) Generation of random sequences by human subjects: Cognitive operations or psychological process?  Journal of Experimental Psychology: General, Vol 116(4), Dec 1987. pp. 337-355.

Wagenaar, W. A. (1972) Generation of random sequences by human subjects: A critical survey of literature.  Psychological Bulletin, Vol 77(1), Jan 1972. pp. 65-72.

Yaakov Kareev(1992) Not that bad after all: Generation of random sequences. Journal of Experimental Psychology: Human Perception and Performance, Vol 18(4), Nov 1992. pp. 1189-1194.