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Chance

The word chance originated in the Latin word for “to fall.” Chance occurs the way things just happen to fall. Like a coin toss, chance events occur unpredictably, without any apparent or knowable causes, or by accident—the latter word deriving from the same Latin root. Although chance is a very useful word in everyday language, its status as a term in measurement and statistics is much more ambivalent. On the one hand, the word is almost never treated as a technical term. Thus, it is seldom given a precise definition, or even an intuitive one. Indeed, it is rare to see chance as an entry in an index to any book on measurement and statistics.

On the other hand, both the concept and the word permeate articles and books on these subjects. It is especially hard to imagine writing a statistics textbook without having recourse to the word on numerous occasions. Furthermore, the word chance is used in a wide variety of ways. In particular, we may distinguish chance as probability, as unknown determinants, as technique, and as artifact.

Chance as Probability

What is now called probability theory had its origins in a famous exchange of letters between the mathematicians Pierre de Fermat and Blaise Pascal concerning games of chance. As a consequence, early mathematical treatments would be identified as the “logic of chance” (John Venn) or the “doctrine of chance” (Abraham de Moivre). But by the time Pierre-Simon Laplace published his classic Analytical

Theory of Probabilities, the word chance had seemingly ceased to have scientific content, thereby returning to the status of a mundane word. It had been replaced by the word probability.

Despite this shift in significance, chance is still used to refer to the probability of an event or set of events—whether or not they concern outcomes in games of chance. When used in this manner, chance is often treated as something tantamount to a rough measure of how much we should anticipate an event's occurring. Some events may have a good chance of happening, others a very poor chance, yet others a middling chance. Two events can also be said to have an equal chance of happening (e.g., the balls in urn models all have an equal chance of being chosen). Here, chance functions as a generic term that encompasses more specialized and precise concepts, including an event's probability (the number of times an event happens divided by the total number of times it could have happened) and an event's odds (the probability of an event occurring divided by the probability of an event not occurring).

One could argue that it is no longer proper to use such a vague word when more-precise terms are readily available. Yet the very imprecision of chance can prove to be an asset in certain contexts. In particular, chance becomes serviceable when a more precise term is unnecessary to convey a statistical idea. For example, a simple random sample can be defined as a sample in which each case in the entire population has an equal chance of being selected for inclusion. Substituting “probability” for “chance” may not necessarily improve this definition, especially given that the actual probability may not be known or even calculable.

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