Preamble
This article describes experimental procedures for determining whether a coin is fair or not fair. There are many statistical methods for analyzing such an experimental procedure. This article illustrates two of them.
Both methods prescribe an experiment (or trial) in which the coin is tossed many times and the result of each toss is recorded. The results can then be analysed statistically to decide whether the coin is "fair" or "probably not fair". It is assumed that the number of tosses is fixed and cannot be decided by the experimenter.
- Posterior probability density function, or PDF (Bayesian approach). The true probability of obtaining a particular side when a fair coin is tossed is unknown, but the uncertainty is initially represented by the "prior distribution". The theory of Bayesian inference is used to derive the posterior distribution by combining the prior distribution and the likelihood function which represents the information obtained from the experiment. The probability that this particular coin is a "fair coin" can then be obtained by integrating the PDF of the posterior distribution over the relevant interval that represents all the probabilities that can be counted as "fair" in a practical sense.
- Estimator of true probability (Frequentist approach). This method assumes that the experimenter can decide to toss the coin any number of times. He first decides on the level of confidence required and the tolerable margin of error. These parameters determine the minimum number of tosses that must be performed to complete the experiment.
An important difference between these two approaches is that the first approach gives some weight to one's prior experience of tossing coins, while the second does not. The question of how much weight to give to prior experience, depending on the quality (credibility) of that experience, is discussed under credibility theory.
Read more about this topic: Checking Whether A Coin Is Fair
Famous quotes containing the word preamble:
“Virginity is now a mere preamble or waiting room to be got out of as soon as possible; it is without significance. Old age is similarly a waiting room, where you go after life’s over and wait for cancer or a stroke. The years before and after the menstrual years are vestigial: the only meaningful condition left to women is that of fruitfulness.”
—Ursula K. Le Guin (b. 1929)