Population Parameter

Population parameters, also termed population characteristics, are numerical expressions summarizing various aspects of the entire population. One common example is the population mean,

where F; is some characteristic of interest observed from the element i in the population of size N. Means, medians, proportions, and totals may be classified as descriptive parameters, while there are parameters measuring relationships, such as differences in descriptive parameters, correlation, and regression coefficients.

Although population parameters are sometimes considered unobservable, they are taken to be fixed and potentially measurable quantities using survey statistics. This is because sampling statistics are developed for well-specified finite populations that social science studies attempt to examine and that the population parameters depend on all elements in the population. Before any sort of data collection, population parameters actually are not known. When a census is conducted, all members of the population are observed (in theory), and the “exact value” of the population parameters becomes obtainable. And, by default, the measures taken by a census come to define what is the population “parameter,” even if the census is not likely to be exactly accurate. In reality, however, the census is a special case and is not a feasible option for measuring most population parameters.

Instead, social science studies use samples drawn from the population of interest. The population parameters are estimated using estimators. One example is the mean of the sample elements,

where yj is the same characteristics described previously but measured on the element j in the sample of size n. The sample mean, , is used as an estimator of the population parameter, , and a sample mean calculated from a particular sample is an estimate of the population parameters. The key feature of the sample statistics is their representativeness (or unbiasedness) of the population parameters, which is generated mathematically via a probability sample design. Because the sample elements are selected under a random mechanism in probability sampling, E() = is ensured, in theory.

It also should be noted that the sample statistics themselves are a random variable with a probability or sampling distribution and are dependent upon the sample design and the realized sample. Unlike population parameters that are constant, estimates from a particular sample may be different from those of another sample drawn from the same population, due to sampling variance and simply because a different set of sample units is selected. This is related to the fact that the unbiasedness of the sampling statistic (e.g. E =) is a property of the entire sampling distribution, not of a particular sample. Standard errors associated with the sample estimates measure this sampling variability.

A census provides parameter estimation without sampling errors, but it does not automatically imply that the parameters are measured without error, as the quantities calculated from census data are still subject to nonsampling errors, namely coverage, nonresponse, and/or measurement errors. For example, population values calculated from census data collected using inadequately trained interviewers and plagued by low response rates well may have larger errors than sample estimates from well-designed and administered survey data. In many cases, resources used for a census can be redistributed for a sample survey with better quality control—especially with respect to non-response and measurement errors. The sample estimates for population parameters are likely to be more accurate than the population values from a census. Apart from the cost issue, this is another reason why sample surveys are more widely used to study population parameters rather than a census.

...