Chapter 5 Sampling: good and bad methods AP Standards Producing Data: IIB4

Sampling Methods BAD Voluntary response Convenience samples GOOD Simple random samples (SRS) stratified sampling cluster sampling systematic sampling multi-stage sampling

Voluntary response A voluntary response sample consists of people who choose themselves by responding to a general appeal. Voluntary response samples are biased because people with strong opinions, especially negative opinions, are most likely to respond. Example of voluntary response sample is Call- in opinion polls. See Example 5.3

Convenience samples Convenience sampling is choosing individuals who are easiest to reach. Example of convenience samples is interviewing at the mall. See Example 5.4

Bias A sampling method is biased if it systematically favors certain outcomes A statistic is said to be unbiased if the mean of its sampling distribution equals the mean of the population

Simple random sample (SRS) A Simple random sample (SRS) of size n consists of n individuals from the population chosen in such a way that every set of n individuals has an equal chance to be sample actually selected. Simple random sample (SRS) attacks bias by giving all individuals an equal chance to be in the sample Example of Simple random sample (SRS) is pulling name out of a hat. See pp

Probability Sample- sample chosen by chance Stratified sampling To select a stratified random sample, first divide the population into groups of individuals, call strata, that are similar in some way that is important to the response. Then choose separate SRS in each stratum and combine these SRSs to form the full sample. In stratified sampling we study a random sample of individuals in every stratum. Example of stratified sampling is you might divide a population of high schools into public schools, catholic schools, and other private schools. See example 5.6 Cluster sampling Cluster sampling divides the population into groups, or cluster. Some of these clusters are randomly selected. Then all individuals in the chosen clusters are selected to be in the sample. In cluster sampling we study all the individuals in the chosen cluster, and none of the individuals in the other cluster. Example, if one wanted to do a study involving the patients in the hospitals in NYC, it would be costly and time-consuming to obtain a random sample of patients since they spread over a large area. Instead select a few hospital randomly and interview the patients in cluster. See example 5.7

Systematic sampling Researchers obtain systematic samples by numbering each subject of the population and then selecting every k th subject. When using systematic sampling, you must be careful about how the subjects in the population are numbered. For example, suppose there were 2000 subjects in the population and a sample of 50 subjects were needed. Since 2000 ÷ 50 = 40, then k = 40, and every 40 th subject would be selected; however, the first subject (numbered between 1 and 40) would be selected at random. Suppose subject 12 were the first subject selected; then the sample would consist of the subjects whose numbers were 12, 52, 92, etc., until 50 subjects were obtained. See example 5.5

Multi-stage sampling A multistage random sample is constructed by taking a series of simple random samples in stages. This type of sampling is often more practical than simple random sampling for studies requiring "on location" analysis, such as door-to-door surveys. For example, in a multistage random sample, a large area, such as a country, is first divided into smaller regions (such as states), and a random sample of these regions is collected. In the second stage, a random sample of smaller areas (such as counties) is taken from within each of the regions chosen in the first stage. Then, in the third stage, a random sample of even smaller areas (such as neighborhoods) is taken from within each of the areas chosen in the second stage. If these areas are sufficiently small for the purposes of the study, then the researcher might stop at the third stage. If not, he or she may continue to sample from the areas chosen in the third stage, etc., until appropriately small areas have been chosen.

Assignment TPS 5.2, 5.6, 5.7, 5.9, 5.11, 5.24, 5.26, 5.32