Sample Survey¶

Explain commonly used sampling methods.

Simple random sample¶

Every member and set of members has an equal chance of being included in the sample.
Technology, random number generators, or some other sort of chance process is needed to get a simple random sample.
Example: A teachers puts students’ names in a hat and chooses without looking to get a sample of students.
Pros: Random samples are usually fairly representative since they don’t favor certain members.
Cons: Some groups may have no members being selected.

The population is first split into groups. The overall sample consists of some members from every group. The members from each group are chosen randomly. That is, each group has at least one member being selected.
Example: A student council surveys 100 students. It is known that in the population the ratio of the freshmen, sophomores, juniors and seniors is 4:3:2:1. Then they can get random samples of 40 freshmen, 30 sophomores, 20 juniors, and 10 seniors.
Pros: A stratified sample guarantees that members from each group will be represented in the sample, so this sampling method is good when we want some members from every group.
Cons:
- Requires a stratification variable, which can be difficult.
- May also be expensive to implement since every group is visited.
- Requires small within-group difference and large across-group difference.

The population is first split into groups. The overall sample consists of every member from some of the groups. The groups are selected at random.
Example: An airline company wants to survey its customers one day, so they randomly select 5 flights that day and survey every passenger on those flights.
Pros: A cluster sample gets every member from some of the groups, so it’s good when each group reflects the population as a whole.
Cons: Larger error than simple random sampling since the selected members are clustered.

Members of the population are put in some order. A starting point is selected at random, and every \(k\)-th element from the population is selected, where \(k=\frac{\text{population size}}{\text{sample size}}\).
Example: A principal takes an alphabetized list of student names and picks a random starting point. Every \(20^{\text{th}}\), start superscript, start text, t, h, end text, end superscript student is selected to take a survey.
Pros: Easy to implement. Smaller error than simple random sampling since the members are more evenly distributed.
Cons: Require the order to be irrelevant to the experiment. If periodicity is present and the period is a multiple or factor of the interval used, the sample is especially likely to be unrepresentative of the overall population, making the scheme less accurate than simple random sampling. For instance, \(\circ \bullet \circ \circ \circ \bullet \circ \circ \circ \bullet \circ \circ\) and \(\circ \bullet \bullet \bullet \bullet \circ \circ \circ \circ \circ\).