Statistic

Statistic, a singular noun, has three meanings: (1) an observed number or event, (2) a mathematical operation (and the resulting number) performed on sample data, and (3) an operation (and the resulting number) obtained from a sampling distribution. The plural form for each of these three cases is statistics. A fourth meaning of the word statistics is a branch of mathematics devoted to the analysis, interpretation, and presentation of empirical data. Statistics, as a branch of mathematics, is a singular noun. In most contexts statistic (with an s) refers to this branch of mathematics, which scientists and others use to analyze data from empirical studies.

In conversational use, statistic means a single number or a single event. The 84 in 84 people attended the reunion is a statistic. Statistic sometimes conveys a sense of the impersonal. His death was just a statistic uses statistic in the same way as Josef Stalin's famous quote to Winston Churchill, “A single death is a tragedy; a million deaths is a statistic.”

In the discipline of statistics, a descriptive statistic is a mathematical operation that captures some characteristic of a sample of observations. Each operation has a formula and, of course, each formula has a name. For a sample, the mean (ΣX/N) is a descriptive statistic, as is the median, standard deviation, and the 95th percentile, each of which has its own formula. Not only is the formula itself called a statistic, but the resulting numerical value can be referred to as a statistic. Thus, the expressions, M = 98.2°F, standard deviation (SD) = 12 points, z = −1.50, and 95% confidence interval (CI) = 0.50, −2.25 each qualify as a statistic and are often referred to as sample statistics. The corresponding population characteristics are called parameters. Although almost all research reports focus on statistics calculated from samples, the purpose of research is to discover relationships among populations. Thus, the most satisfactory statistics are those that provide mathematically unbiased estimates of parameters. The sample mean qualifies; the sample mode does not.

A statistic is also a value from a sampling distribution. A sampling distribution is a collection of sample statistics derived from a mathematical formula rather than empirical observations. Both the graphical form of the collection and the mathematical formula that produces the collection are called sampling distributions. Sampling distributions that researchers commonly use include inferential statistics such as the t distribution, chi-square distribution, and the F distribution. Thus, t, χ2, and F values calculated from data are inferential statistics. In the same way that an expression such as M = 98.2°F or SD = 12 points is called a statistic, t = 2.03, χ2 = 3.84, and F = 1.84 are each called inferential statistics. The relationship of inferential statistics to research design is an intimate one. “An adequate experimental design involves not only a satisfactory plan for conducting the trial, but also an appropriate statistical method for evaluating the results. The two can ill be divorced” (Snedecor, 1946, pp. xv—xvi).

In general discourse, the word statistic is not a neutral word, and the connotation that accompanies it can be negative or positive, sometimes strongly so. Context and past usage determine the connotation. The phrase, just a statistic, conveys a negative tone of dismissal. The common expression, you can prove anything with statistics, is similarly dismissive. The phrase lies, damned lies, and statistics, attributed to Disraeli but found first in the writings of Mark Twain, even equates statistics with falsehood.

...