Statistic

A statistic is simply a numerical summary of the sample data. For example, data analysts often use familiar sample statistics such as sample means, sample variances and standard deviation, sample percentiles and medians, and so on to summarize the samples of quantitative data. For samples of categorical data, sample proportions, percentages, and ratios are typical sample statistics that can be utilized to summarize the data. In short, a statistic is simply a summary quantity that is calculated from a sample of data.

The counterpart of a statistic for the entire population is called a parameter. A statistic differs from a parameter in at least two aspects. First, a statistic describes or summarizes a characteristic of the sample, but a parameter refers to a numerical summary of the population from which that sample was drawn. Note that values of sample statistics depend on the sample selected. Because their values vary from sample to sample, sample statistics are sometimes called random variables to reflect that their values vary according to the sample selected.

Second, the value of a parameter is usually unknown or not feasible to obtain, but the quantity of a statistic can be directly computed from the sample data. The primary focus of most social research is the parameter of the population, not the sample statistic calculated from selected observations. Thus, if the population of one's research interest is small and data exist for an entire population, then one would normally explore the population parameter rather than the sample statistic. However, in most social studies, researchers still use sample statistics to make inferences on the values of population parameters because (a) populations for social research are usually very large, so it is impractical to collect data for the entire population; and (b) one can still have good precision in making inferences about (or guessing) the true values of population parameters if appropriate sampling techniques and statistical methods are utilized. For example, samples taken by professional polling and research institutions, such as the Gallup, the General Social Survey, and the National Election Study, typically contain about 1,000 to 2,000 subjects.

One important issue for using a sample statistic to predict or infer a parameter value is how accurate the prediction is. In other words, it is useful for data analysts to know the likely accuracy for predicting the value of a parameter by using a sample statistic. A conventional way to account for the uncertainty of predictions is to report the confidence intervals of point estimates of parameters. We usually use analogous sample statistics as the point estimates [Page 1074](e.g., sample mean and population mean, sample variance and population variance). In addition, researchers may also set a “desired precision” of prediction before data collection. This desired precision (also defined as error bounds) in turn can help researchers decide the required sample size for obtaining reliable sample statistics. More information on confidence intervals of sample statistics and the relationship between sample size and accuracy of estimation using sample statistics may be found in William L. Hays (1994), Alan Agresti and Barbara Finlay (1997), and Richard A. Johnson and Gouri K. Bhattacharyya (2001).

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