2 - The Origins of Probability and Statistics

Summary

Which was which he could never make out

Despite his best endeavor.

Of that there is no manner of doubt—

No possible, probable shadow of doubt—

No possible doubt whatever.

(William S. Gilbert, “The Gondoliers”)

Unlike many discoveries in public health and medicine, the concept of the risk factor had its origins in two disciplines unrelated to the study of health and disease: probability and statistics. The two disciplines were combined when probability theory was applied to the analysis of the population and mortality data being gathered by statisticians. The new quantitative statistical methods were soon recognized by some as useful for resolving medical controversies, but others considered them worthless or contrary to the goals of scientific medicine.

Probability

A probability, as applied to human behavior, is a ratio in which the numerator is the number of persons who experience events of interest and the denominator is the total number of persons who are able to experience those events. For example, the probability that a person in a certain age and sex group will die is calculated by dividing the number of persons in the group who die by the total number of persons in the group. Probabilities are characteristics of groups rather than individuals. They also require at least two possible outcomes (in this case death and non-death). If only one outcome can occur, the situation is deterministic, not probabilistic. Probability theory was conceived by continental European mathematicians and scientists in the 1650s and 1660s. By 1700 they agreed on terminology and devised some fundamental mathematical techniques.

Probability mathematicians from the seventeenth to the mid-eighteenth centuries were restricted to certain kinds of data for their calculations. Games of chance were particularly convenient because the numerical values of both the numerator and the denominator can be calculated by assuming symmetry. For example, a die has six sides and it can be assumed from symmetry that each side has an equal probability of coming up. Probabilities are much more difficult to obtain for events that require actual enumerations. The probability that a resident of a city will die during a specified time period requires counting both the number of deaths in the city during the period and the number of residents in the city who were alive at the beginning of the period.