INTERVAL ESTIMATION

in statistics, evaluation of a parameter (mean, standard deviation, proportion) of a population by computing an interval, or range of values, within which the parameter is most likely to be. The likelihood is specified by a probability, commonly chosen as 95 or 99 percent. The interval containing a population parameterfor example, the mean, symbolized by the Greek letter mu, mis established by calculating that statistic from values measured on a random sample taken from the population and by applying the knowledge (derived from the mathematical theory of probability) of the fidelity with which the properties of a sample represent those of the entire population. The probability tells what percentage of the time the assignment of the interval will be correct, but not what the chances are that it is true for any given sample. Of the intervals computed from many samples, a certain percentage will contain the true value of the parameter being sought. Intervals can be established only when the distribution of large samples tends to normal and the distribution of small samples tends to Student's t-distribution or the chi-square distribution (see Student's t-test). The intervals are called confidence intervals; the end points of an interval are called upper and lower confidence limits. The probability is called the confidence coefficient.