Sampling

POPULATION refers to the entire group of people or objects about which information is desired.  A study that examines data on the entire population is called a CENSUS.  However, conducting a census is rarely feasible. A SAMPLE is a typically small part of the population.  If the sample is selected carefully, so that it is representative of the entire population, useful information can be gained.  The number of observational units in a sample is called the sample size. 

The essential idea of sampling is to learn about the whole by studying a part.

It is important to test the sample selected for BIAS.  A sampling procedure is said to be biased if it tends systematically to over-represent certain segments of the population and systematically to under-represent others. Bias can occur in "convenience samples" or voluntary response samples where members of the population decide for themselves whether or not to participate.  When lists of subjects are selected from a sampling frame such as telephone books, vehicle registration records, etc, it may not be representative of the population desired.

Inn order to avoid biased samples, it is reasonable to give every member of the population the same chance of being selected.  The selection method should ensure that every possible sample has an equal chance of being the sample ultimately selected.  This is called SIMPLE RANDOM SAMPLING (SRS).  A completely random sample can employ the use of a random number generator on a calculator or computer. 

Important NOTE:  a PARAMETER is a numerical characteristic of the POPULATION, while a STATISTIC  is a numerical characteristic of a SAMPLE...hint parameter and population both begin with "p".  A statistic is an unbiased estimate of a parameter  if the values of the statistic from different samples are centered at that parameter value.

Sampling Senators (Senate99.ftm)  page 265

Getting the same sample proportion and same sample mean from all samples would be desirable.  However, more likely is the possibility of sampling variability.  The value of sample quantities varies from sample to sample.

The PRECISION of a sample statistic refers to its variability from sample to sample. Precision is related to sample size.  sample means and proportions from larger samples are more precise/closer together than those of smaller samples.  Statistics from larger samples provide a more accurate estimate of the corresponding population parameter.

As long as the population is large relative to the sample size (at least 10 times as large), the precision of a sample statistic depends on the sample size but not on t he population size.  so, a sample of size 1000 creates an equally precise estimate whether the population size is 100,000 or 250,000,000.

Summary:  A poor method of collecting data can lead to misleading or meaningless conclusions.  Simple random sampling is a means of selecting a sample that will most likely be representative of the population.