Individuals are selected so that all individuals are equally likely to be selected Example: 1. Generate a list of student ID numbers for all students at WA 2. Randomly select student ID numbers 3. Choose those students for the sample

The first individual is chosen at random Then a system (or rule) is used to choose all other individuals Ex: Obtain an alphabetized list of all students at WA. We want to select a sample of 100 students to be in our sample. 1600/100 = 16 Pick a random digit 1-16 (using random number chart or calculator) and then every 16 th student from there.

1. Divide the sampling frame into groups where each group has a similar characteristic (homogeneous). These groups are called strata (plural stratum) 2. Choose the strata because you have a special interest in the opinions of these groups within the population or because the individuals in each stratum resemble each other. Example - Race, gender, age, income, etc Take a separate SRS in each group and combine these to make up our complete sample.

Example: You are interested in getting opinions about the spirit assembly. You suspect that students in each grade might have different opinions so you want to make sure that each grade (9 th, 10 th, 11 th, and 12 th ) is represented. Get a list of all Freshmen, Sophomores, Juniors and Seniors(these are your strata). Choose an SRS within each grade level and combine these to make up the entire sample. Strata – The distinct groups we create from the population/sample

~ Reduces bias in our survey (groups are not underrepresented) ~Reduces variability from sample to sample (individuals in each stratum (plural for strata) are more similar than the population as a whole) However, this method can violate one of the most appealing properties of SRS: Stratifying samples need not give all individuals in the population the same chance to be chosen.

~A sampling method where the sampling frame (the list from which the sample is selected from) is divided into mixed groups that are representative of the population (heterogeneous). ~An SRS is taken from each group (or you can take an entire group) ~Choose an SRS within each group (sometimes these are already formed for you) to form the full sample or randomly select an entire group to be your sample.

Ex: You want to know information from the seniors about the parking at WA. Divide all of the seniors at WA into homerooms (these are your mixed groups). Choose 1 student from each homeroom using an SRS, or else randomly choose an entire homeroom. Cluster sampling is usually selected as a matter of convenience, practicality, or cost.

1. Administrators at a private boarding/day school want to investigate the attitudes of students at their school about the faculty’s commitment to teaching. About 65% of the school’s 1000 students are boarding students (live on campus). The remaining 35% are day students (commuters). The student government will pay the costs of contacting about 100 students. You suspect that boarding students and commuters might respond differently.

2. You would like to select a sample of individuals that are going to “The Nutcracker” December 20, There are 400 seats in a select theater and tickets are sold out. You want to survey 50 people. 3. Suppose you wanted to assess the reading level of a textbook based on a random sample of the words used. The book has 1000 pages. You can assume all pages of the book are pretty similar in terms of reading level.

 All sampling must include randomization.  The key for those that are not Simple Random Samples is HOW the groups are chosen.  Stratified RS: groups will be homogeneous  Cluster RS: groups will be heterogeneous  Systematic RS: groups are chosen numerically  In many real world applications a Multi-stage Sampling design is used (2 or more of the above designs are used consecutively).