These are Glossary entries F-J. For Additional Notes, click on the bar within or at the end of the entry.
F G H I J
Factorial x. Written conventionally as x! The factorial of x is the product of all integers from x down to and including 1, thus 3! = (3)(2)(1) = 6. Factorials arise naturally in Binomial and Combinatorial situations. We here use a further refinement of notation for partial factorials.
Feller Principle. The principle that you cannot tell, from an average rate, anything about the distribution of the data that led to that rate. The principle was articulated by ourselves in contemplation of some bonehead errors made in the application of the Poisson Distribution; see Lesson 16 and especially the answer to Problem 8a.
Frequency Profile. This is our term for a list or diagram of the possible outcomes of an experiment or series of observations, together with their probabilities. Thus, the outcome possibilities for tossing one unbiased coin twice are HH, HT, TH, and TT, each with probability p = 0.250. The conventional term, which we find misleading, is Sample Space.
Function of x. Written conventionally as f(x). If y = f(x), then for every value of x we can calculate (by the formula which defines the function) a corresponding value of y. This general notation is convenient when we do not know, or don't care to write, the formula linking x and y. One example of writing out the function is f(x) = 3x, whence the equation y = 3x.
f(x) = Function of x.
G Factor. Short for Gnedenko Factor.
Gnedenko Factor. The presence of higher motivation in human beings, offered as a specific refutation of the supposed implications of the Prisoner's Dilemma problem. Named for Boris Vladimirovich Gnedenko.
Greek Letters. For a refresher, see our separate page. We follow convention in preferring to use Greek letters for features of a population, and the corresponding Latin letters for features of a sample from that population. Thus the sample mean is here written as m, and the population mean as m (mu; Greek "m"). Some peculiarities of Greek orthography prevent this convention being carried out more systematically: for instance, lower case Greek nu or N (n) effectively coincides with lower case English v.
Hawthorne Effect. Improvement in performance resulting not from the specific changes made, but from an increase in morale due to the mere fact that changes are being made. Named for the General Electric plant at Hawthorne, Michigan, where the effect was first noticed. The possibility of a Hawthorne Effect complicates experiment design. Compare Placebo Effect.
i = r( -1), the square root of minus 1. With e and p, this somewhat counterintuitive quantity is one of the irrational trinity of numbers which govern equations of growth. See the Note to e.
Interval Data. Data points whose labels tell us, not only the relative sequence of the respective items, but also how far it is between one item and another. Thus, if we replace our ordinal-data list of sack race finishers (One, Two, Three, Four, Five) with their race times in seconds (58, 63, 79, 80, 98), we have converted from ordinal to interval data, and know much more about the pattern of success in the race. We can now analyze the associated heights to see not only whether height confers an advantage in sack racing, but, if so, how much. Interval or exact-number data is home territory for Parametric statistics, though most situations can also be handled by Nonparametric analysis as well. Compare Nominal
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