Point Estimate

Most statistical analysis is done with the desire to reach a conclusion or decision about one or more parameters associated with a population of interest (σtatistical inference). Two types of estimators are used to assist in reaching a conclusion: point estimators and interval estimators. The goal of estimation is to provide a ‘best guess’ at the true value of an unknown population parameter. To this end, a point estimator is a rule or function for computing a single quantity from a sample that will be used to approximate most closely a population parameter. Statistically, the point estimate is the value itself that is obtained when the rule is applied to sample data. Often the term point estimate is used to refer to any value computed from the data that is used to estimate a population parameter, even if it is not the ‘best’ estimator.

The point estimate is the most common way that an estimate is expressed. Table 1 contains a list of the names or symbols for commonly used estimators along with the population parameters they estimate. Note that often point estimators are descriptive statistics.

Point estimates are quick and easy to calculate. They allow for a first look at the population based on sample data. Researchers hope that the single value obtained for a point estimator will be close to the parameter it is estimating. Since a point estimate is a random variable, it is in some way distributed about the true value of the population parameter. However, since the point estimate consists of a single number or a single point on the real number scale, there is room for questions. For example, a point estimate does not tell us how large the sample was on which it is based. Nor does it tell anything about the possible size of the error.

Since a researcher will infer that the population parameter is equal to the value of the point estimator, a little more knowledge of statistical inference is necessary. Statistical inference differs from ordinary inference in that not only is an inference made, but typically a measure is provided of how good the inference is. The error of estimation for a particular point estimate is defined to be the absolute value of the difference between the point estimate and the true population value. For example, the error of estimation for the mean is |Xi − µ|. However, the magnitude of the error of estimation is unknown since the true population parameter value is unknown. If a probability sample was taken, then statistical reliability may be calculated for the estimate by either using a confidence interval or by using the bound on the error of estimation.

Sometimes a point estimate is referred to as the ‘realized value’ since it is the actual numerical value of a random variable. Also, the phrase ‘point estimate’ is sometimes used as an infinitive verb, as in the following: To point estimate is to compute a value from a sample and accept that value as an estimate of the unknown parameter.

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