Random sampling methods

Gathering information about an entire population often costs too much or is virtually impossible. Instead, we use a sample of the population. A sample should have the same characteristics as the population it is representing. Most statisticians use various methods of random sampling in an attempt to achieve this goal. In each form of random sampling, each member of a population initially has an equal chance of being selected for the sample. Each method has pros and cons.

Besides simple random sampling, there are other forms of sampling that involve a chance process for getting the sample. Other well-known random sampling methods are the stratified sample, the cluster sample, and the systematic sample.

To choose a stratified sample, divide the population into groups called strata and then take a proportionate number from each stratum. For example, you could stratify your college population by department and then choose a proportionate simple random sample from each department. To choose a cluster sample, divide the population into clusters and then randomly select some of the clusters; all members from these clusters are in the cluster sample. For example, if you randomly sample four departments from your college population, the four departments make up the cluster sample. To choose a systematic sample, randomly select a starting point and take every nth piece of data from a listing of the population. For example, suppose you have to do a phone survey. Your phone book contains 20,000 residence listings. You must choose 400 names for the sample.

Which sampling method is being used in each scenario?

The quiz-score table below shows six sets of quiz scores (each quiz counts 10 points) for an elementary statistics class. Each column is a set of 10 scores. The table is used in the following exercises to practice each sampling method.

The instructions for the quiz-score table show how to create each type of sample using a random number generator. For a stratified sample by column, number each row 1–10, then use randInt(1,10) to pick three rows from each column, recording the scores in those rows. For a cluster sample, use randInt(1,6) to pick two column numbers; all 20 scores in those two columns form the cluster sample. For a simple random sample of 15 scores, number all 60 scores 1–60 and use randInt(1,60) fifteen times. For a systematic sample of 12 scores, pick a random starting score, then count every tenth score (wrapping around if needed) until you have 12.

How many quiz scores are in a cluster sample that picks two columns?

The following examples ask you to identify the type of sampling used in each scenario. The options are simple random, stratified, systematic, cluster, or convenience.

1. A soccer coach selects six players from a group of boys aged eight to ten, seven players from a group of boys aged 11 to 12, and three players from a group of boys aged 13 to 14 to form a recreational soccer team. This is stratified because the coach takes a proportionate number from each age group.
2. A pollster interviews all human resource personnel in five different high tech companies. This is cluster because the companies are clusters and all members of the selected companies are interviewed.
3. A high school educational researcher interviews 50 public high school teachers and 50 private high school teachers. This is stratified because the researcher takes a proportionate number from each type of school.
4. A medical researcher interviews every third cancer patient from a list of cancer patients at a local hospital. This is systematic because the researcher takes every third patient.
5. A high school counselor uses a computer to generate 50 random numbers and then picks students whose names correspond to the numbers. This is simple random because each student has an equal chance.
6. A student interviews classmates in their algebra class to determine how many pairs of jeans a student owns, on the average. This is convenience because the student interviews whoever is easily available.

Which sampling method is used when a principal polls 50 first-years, 50 sophomores, 50 juniors, and 50 seniors?