Point Estimate

Point estimates are single numeric quantities (i.e. “points”) that are computed from sample data for the purpose of providing some statistical approximation to population parameters of interest. For example, suppose surveys were being designed to estimate the following population quantities: (a) the proportion of teenagers within a school district who consumed at least one alcoholic beverage last year, (b) the mean number of candy bars consumed last week by county hospital nurses within a state, (c) the total number of text messages sent by cell phone customers of a particular cell phone provider within the last month, (d) the correlation between education and annual expenditures on magazine subscriptions within the past year for U.S. citizens. In every case, a single numeric quantity, or statistic, can be computed from collected sample data to estimate the population parameters of interest. In contrast to point estimates, interval estimates are computed using point estimates to provide an estimated range of values for the parameter.

Point estimates generally have a form that is consistent with the population parameter they are intending to estimate; for example, a sample mean is used to estimate a population mean; a sample proportion is used to estimate a population proportion; a sample correlation coefficient is used to estimate the population correlation coefficient. Within the context of survey research, point estimates can also be computed with or without survey weights. Moreover, point estimates are subject to sampling variability in that the values of the point estimates for a given parameter may vary from different samples of the same size selected from the same population.

For example, consider a sample of 10 students selected from a school district using a multi-stage probability sampling design to estimate the mean number of days absent from school during the most recent semester. These data are provided in Table 1.

One unweighted point estimate for the population parameter is given simply by the sample mean computed by dividing the sum of all 10 data points by 10. From the table, the sum of all the data points (sum of second column) is 47, so the unweighted point estimate given by the sample mean is 4.7 days absent for the semester. Because of the survey design, a weighted point estimate could also be computed using the Horvitz-Thompson estimator, which divides the weighted sum of all 10 data points by the sum of [Page 586]the weights. From the table, the numerator of the weighted point estimate is 1,032 (column 4 sum) and the denominator is 240 (column 3 sum), so the weighted point estimate is given by 1032/240 − 4.3 days absent for the semester.