| There were two widely divergent
influences on the early development of statistical methods. Statistics had a
mother who was dedicated to keeping orderly records of governmental units (state
and statistics come from the same Latin root, status) and a gentlemanly gambling
father who relied on mathematics to increase his skill at playing the odds in
games of chance. The influence of the mother on the offspring, statistics, is
represented by counting, measuring, describing, tabulating, ordering, and the
taking of censuses—all of which led to modern descriptive statistics. The
influence of the father came modern inferential statistics, which is based
squarely on theories of probability. Descriptive statistics involves tabulating, depicting, and describing collections of data. These data may be either quantitative, such as measures of height, intelligence, or grade level—variables that are characterized by an underlying continuum—or the data may represent qualitative variables, such as sex, college major, or personality type. Large masses of data must generally undergo a process of summarization or reduction before they are comprehensible. Descriptive statistics is a tool for describing or summarizing or reducing to comprehensible form the properties of an otherwise unwieldy mass of data. Inferential statistics is a formalized body of methods for solving another class of problems that present great difficulties for the unaided human mind. This general class of problems characteristically involves attempts to make predictions using a sample of observations. For example, a school superintendent wishes to determine the proportion of children in a large school system who come to school without breakfast, have been vaccinated against flu, or whatever. Having a little knowledge of statistics, the superintendent would know that it is unnecessary and inefficient to question each child; the proportion for the entire district could be estimated fairly accurately from a sample of as few as 100 children. Thus, the purpose of inferential statistics is to predict or estimate characteristics of a population from a knowledge of the characteristics of only a sample of the population. |