Background

    The concept of randomness is historically a recent development (in the 1700's). Even more recently in the 20th century, randomness and probability (involving subatomic particles) have been embraced by quantum physics.

	Einstein: "God does NOT play dice with the Universe!"
	Some people reject the notion of randomness on religious or philosophical grounds. They do not accept the idea that events in our world can occur randomly. Whether or not you share this belief, you can still have fun trying to act randomly in this exercise.

You might want to consider this controversial idea: If you believe in the notion of "free will," then you must believe that human behavior is ultimately random! If you could know ahead of time what course of action a person would choose, then his/her choice is not completely "free." If the choice is determined by past history, personality, or current forces, then how could the choice result from "free will?" Freedom implies some capriciousness or haphazardness. Because the behavioral psychologist B.F. Skinner believed that our behavior was totally determinedby our past history, genetic endowments, and current forces, he denied the possibility of free will, or even freedom.

What exactly does the word "random" mean?

• Dictionary definitions emphasize the notion of "apparent absence of cause, planning, or design," "lack of method or system," or "accidental, haphazard." Statistical definitions, which we will use in this exercise, involve the inability to predict outcomes or to find any pattern in a series of outcomes. To level 2 and level 3 for more on definition problems
•  
• Some people use the word to mean that something can't be explained with current theory (In which case this is just admitting ignorance or that the theories are lousy.). Or they might mean that the causes can never be fully specified. The implication here is that all events are deterministically caused, but our knowledge of the causes will always be incomplete, making them act as if they were randomly determined. The distinction is between an event being indeterminate (truly caused by chance) versus being indeterminable (governed by variables we cannot measure).

  Why you should care about randomness--even if you don't gamble

  1. You are curious about what causes things to happen. The only way scientists can prove causation is to rule out the possibility that a potential cause and an effect are associated by chance or randomness. Before we accept the claim that drug X cures disease Z, we have to determine that the improvement is better than what we would expect by chance alone.
  2. Every-day transactions use random numbers. When you use an automatic teller machine, your requests and account information are encrypted with a "key" which is usually randomly generated. If this process is flawed and the criminals know how it is flawed, they can clear out your account!

     Many important systems (including the military's security of nuclear weapons) depend on randomness or encryption which supposedly cannot be broken by hackers. Recently, the media reported that the most commonly used "64-bit DES" encryption algorithm was broken by scientists who used only $250,000 worth of computers running for only 57 hours. Before we can feel safe from criminals or terrorists, we'll need to develop a more elaborate system of encryption!!

  3. Notions of fairness or lack of bias require that decisions be made without preference. One way to demonstrate this is to submit the decisions to statistical analyses and show that the decisions fit a random pattern. An example of randomization failure: the 1969 draft lottery.

  
  

  Instructions for generating an imaginary series of coin flips:
  

  1. Click on the "your imaginary sequence" in the text box below,
  2. locate the 'H' and the 'T' keys which will represent the outcomes of Heads or Tails of your imaginary coin flips.
  3. Clear your mind and try to act randomly, typing H's or Ts; the computer will stop you after you have typed 100 outcomes (usually by beeping on most platforms).

  Type in your imaginary sequence below:

  ---

  Skip the following button and link if this is your first sequence. Otherwise click on analyze and then on the goto link to see how you did go to summary table of results

   Now for some ways to test for randomness:

  1. One definition of randomness implies that the number of heads equals the number of tails. With an unbiased coin, there should, on average, be 50 heads in 100 flips. According to statistical theory, the number of heads will equal the number of tails only in an infinite series of flips. Since 100 outcomes is far less than infinite, the number of heads will not equal exactly 50 and will vary around that value with a normal distribution (level 2 + 3 stats digression). About two-thirds of the time, random processes will yield between 45-55 heads. Rarely (less than 5% of the time), will the number of heads fall outside the 41-59 range.
  2. The concept of runs: number and length. A run is a repeated outcome. A run is defined as a sequence of repeating heads or tails. A new run occurs when a new symbol appears. For example, if 3 flips of a coin produce "HTT," there are two runs: one of length 1--the first H, and one of length 2 --the second and third "T." Many people mistakenly think that a random coin toss would produce alternating sequences of HTHTHTHT... Although a randomly flipped coin might produce this once in a while, it is highly unlikely. Failures in randomness could produce too many runs (more than 60) or too few (less than 40) in a given sequence, and their length could be either too short (less than 4) or too long (more than 10).level 2+3 stats digression.
  3. Serial dependencies or autocorrelations: One randomness requirement is that there are few patterns and they don't repeat very often. Thus, the fact that an H has occurred on a flip should not influence whether an H happens on the next flip. The alternating heads/tails pattern above violates this requirement because every time an H occurs, it is followed by a T, creating a pattern. This can only occur if the coin could "remember" what had happened on the previous flip.

     In random sequences, the probability of an H happening on the next flip should be unchanged by what happened in the previous flip, two flips before, etc. If the probability of a head following a head is different from the probability of a head following a tail by more than .20, then there is a serial dependency problem which suggests a lack of randomness. level 2 + 3 elaboration

  Now that you know the types of tests which will be done on your sequence, test your understanding

  If you are now ready to see how random your sequence was, click the "analyze" button.

    YOUR RESULTS:

  number of heads:    numer of runs:   longest run:

  For level 3-- conditional probabilities:

  What does it all mean?

  How does your random sequence stack up to the one theoretically predicted to be random? If you can't remember what the values of the 4 statistical tests should be, click here to go to a summary table of results where the expected values are displayed along with the results for your sequence.

  Most people generate a sequences which have too many runs, runs which are too short, and too many/few heads. By the way, please wait until later on in this exercise to try entering another imaginary coin flip series.

  Why might someone have too many/few heads?

  1. People won't bother to keep track of the number of heads as they respond. But this begs the question, why would they prefer one response ( H) over another (T)?
  2. People may be superstitious, associating heads or tails with good things.
  3. People may unconsciously prefer one letter over the other and type it more often. People named "Tom" may type "T" more often than people named "Harry."
  4. The way the keyboard is set up, most people will type "H" with their right-hand finger and "T" with their left-hand finger. Maybe left-handed people will type "T" more often and right-handed people "H" because it is a more dominant response.

  If you were like most people, your random sequence wasn't so random, especially in terms of the number of runs and their length. There are a number of reasons why.

  The gambler's fallacy occurs because people assume that chance or randomness is self-correcting. So, if "red" has won 5 times in a row at the roulette wheel, people think that "black" is due. Assuming the roulette wheel is fair, the probability of black is unchanged. This fallacy may be due to people's misunderstandings of conditional probabilities. digression: a probability teaser (levels 1-3).

  A related fallacy is the hot hand fallacy. People think that repeating outcomes are caused by (unseen) forces and don't recognize them as being the result of chance. For example Gilovich, Vallone, and Tversky (1985) have shown that basketball players may think they are in a shooting streak even though their pattern of hits and misses doesn't deviate from what you would expect to happen by chance. Gilovich finds that people see streaks when the events do not deviate from a random process. People think that events repeat less often than they actually do. This causes them to view random events as being significant or meaningful when they really aren't.

  These two fallacies will lead you to make up coin flip sequences which have runs which are too short and with too many runs to be truly random. Applying the fallacies (level 2 and 3 digressions).

  What does a "random" sequence look like?

  
  

  THE COIN FLIP:

  Some processes, like coin flipping, are not truly random and are called "pseudo-random." If you knew which side of the coin was facing up and exactly how much force was applied to the flip, you would know how the flip would turn out. Diaconis, a magician/mathematician, has taught himself how to apply the right amount of force so he can flip silver dollars in any pattern he wishes. He uses this ability in his "psychic" demonstrations! (He can't consistently flip a coin with less mass than a silver dollar).

  Take out a coin and flip it 100 times, recording the outcomes in the text box below. If you want the computer to use a random number generator to produce the sequence of t's and h's, click on the "have computer generate" button.

  Now type your actual coin flips below:

  ANALYSIS OF COMPUTER OR COIN SEQUENCE RESULTS:

  number of heads:    number of runs:   longest run:

  For level 3-- conditional probabilities:

  go to summary table of results

  How well did the pseudo-random or coinflip data fit a random pattern?

  You shouldn't be too surprised if your coinflip/computer data pattern falls short of these tests randomness. That's why they are called "pseudo-random" generators!

  The actual coin flip sequence should be pretty close to the random pattern (assuming you can flip a coin pretty well), but the JAVASCRIPT generator used in this exercise is not very good. It will probably fail one of the randomness tests. Level 3: Link to a real (radioactive decay) random number generator (which unfortunately outputs only hexadecimal numbers)

  Can people behave randomly?

  Research has shown that humans are not capable of responding randomly when told to do so. However, Heuringer (1986) has shown that people can be trained to respond randomly-- if they are given trial by trial feedback (about whether their response is random) much like what this exercise does. But it took 30 -40 repetitions of this exercise to "condition" them to respond with random patterns [and you thought flipping a coin 100 times was boring]!

  Why do you suppose it is so hard for us to respond randomly?

  (type your answer in the box)
  

  O.K., why?

  Why do you think people have such a hard time even understanding and recognizing randomness, let alone behaving randomly?

  
  

  O.K., why?

  Assessing what you have learned from all this

  One measure of insight would be to redo your imaginary series and see if you get closer to randomness. Your first set of results have already been included in the table below (along with the statistical norms, color coded).

  Now all you have to do is:

  1. click on the "go to the imaginary input box" below
  2. delete the contents (the old sequence) by double clicking in the box and then hitting the delete key
  3. type in a new sequence
  4. click on the "I'm done" (which will check for illegal characters),
  5. then click on the "analyze" button. Don't forget to do this!
  6. The computer will write the results into the table, so click on the "go to summary results" or use your browser's "back" button to return to the table.
  7. If you want to make more than 3 attempts, the computer will overwrite the "third attempt" row with the additional trials.

  go to the imaginary input box

  	N of Heads	N of Runs	Longest Run	prob (H given H)	prob (H given T)	Prob diff.
  Usual	45 - 55	46 - 56	6 - 8	43 - 57	43 - 57	-.10 to +.10
  Unusual	40 - 44 or 56 - 60	41 - 45 or 57 - 61	4, 5 or 9, 10	36 - 42 or 58 - 64	36 - 42 or 58- 64	-.20 to -.11 or +.11 to +.20
  Statistically Significant	<40 or > 60	<41 or > 61	1,2,3 or > 10	<36 or > 64	<36 or > 64	<-.20 or > +.20
  Your 1st attempt
  Your 2nd attempt
  Your 3rd attempt
  Coin 1st attempt
  Coin 2nd attempt
  Coin 3rd attempt

  If you want to play around with the JAVASCRIPT random number generator or try flipping a coin again, just click on this text go to coin flip input.  As with the imaginary sequences, the results will be written into the table above.

  Because insight doesn't always produce changes in behavior, a more common way to assess your understanding is to take a quiz

  References

  Fiske, S. T. & Taylor, S. E.(1991). Social Cognition, Chapter 9, New York: McGraw-Hill.

  Gilovich, T. (1991) How We Know What Isn't So, Chapter 2, New York: Free Press.

  Gould, S. J. (1988, August 18). Streak of Streaks. New York Review, 8 -10.

  Lopes, L. L. (1982). Doing the Impossible: A note on induction and the experience of randomness. Journal of Experimental Psychology: Learning, Memory and Cognition, 8, 626-636.

  Neuringer, A. (1986). Can people behave randomly?: The role of feedback. Journal of Experimental Psychology: General, 115, 62 -75.

  Plous, S. (1993). The Psychology of Judgment and Decision Making, Chapter 14, New York: McGraw-Hill.

  Skinner, B.F. (1971). Beyond Freedom & Dignity. New York: Bantam.

  The END