Other Sampling Methods

The basic idea of sampling is straightforward: take an SRS from the population and use your sample results to gain information about the population. Sometimes there are statistical advantages to using more complex sampling methods. One common alternative to an SRS involves sampling important groups (called strata) within the population separately. These “sub-samples” are combined to form one stratified random sample. Definition: To select a stratified random sample, first classify the population into groups of similar individuals, called strata. Then choose a separate SRS in each stratum and combine these SRSs to form the full sample.

Stratified Disadvantages Advantages More precise unbiased estimator than SRS Less variability Cost reduced if strata already exists Disadvantages Difficult to do if you must divide stratum Formulas for SD & confidence intervals are more complicated

Activity: Sampling Sunflowers Use Table D or technology to take an SRS of 10 grid squares using the rows as strata. Then, repeat using the columns as strata.

Discussion An administrator wants to estimate the average amount of time students spend traveling to school. The plan is to stratify the students according to grade level and then take a simple random sample from each grade. What is potentially good and potentially bad about this plan? (Might try to stratify according to distance from school. That variable probably has the biggest effect on time.) Your assignment is to estimate the mean number of hours spent studying by students at MHS. Discuss how you would set up a stratified random sampling plan to accomplish this task. (Ideally, we would want all of the students who study a lot in one stratum and those who do not study much in another. This would be impossible to arrange, but what can we do?)

Other Sampling Methods Although a stratified random sample can sometimes give more precise information about a population than an SRS, both sampling methods are hard to use when populations are large and spread out over a wide area. In that situation, we’d prefer a method that selects groups of individuals that are “near” one another. Definition: To take a cluster sample, first divide the population into smaller groups. Ideally, these clusters should mirror the characteristics of the population. Then choose an SRS of the clusters. All individuals in the chosen clusters are included in the sample.

Cluster Samples Advantages Disadvantages Clusters may not be representative of population Formulas are complicated Advantages Unbiased Cost is reduced Sampling frame may not be available (not needed)

Cluster Example At Kansas State University, a professor wanting to find out about student attitudes randomly selects a certain number of classes to survey and he includes all the students in those classes. Note: The ideal situation occurs when it is reasonable to assume that each cluster reflects the generally population. If that is not the case or when clusters are small, a large number of clusters must be selected to get a sample that reflects the population.

Systematic Sampling Systematic sampling is a procedure that can be employed when it is possible to view the population of interest as consisting of a list or some other sequential arrangement. A value k is specified (a number such as 25, 100, 2500…). Then one of the first k individuals is selected at random, and then every kth individual in the sequence is selected to be included in the sample. Example: In a large university, a professor wanting to select a sample of students to determine the student’s age, might take the student directory (an alphabetical list) and randomly choose one of the first 100 students) and then take every 100th student from that point on.

Systematic Random Sample Advantages Unbiased Ensure that the sample is distributed across population More efficient, cheaper, etc. Disadvantages Large variance Can be confounded by trend or cycle Formulas are complicated

(a) Simple Random Sample (b) Stratified Random Sample Example: Sampling at a School Assembly Describe how you would use the following sampling methods to select 80 students to complete a survey. (a) Simple Random Sample (b) Stratified Random Sample (c) Cluster Sample