Section 1.4 Other Effective Sampling Methods
¶Definition 1.4.1. stratified sampling.
a simple random sample is drawn from each non-overlapping subgroup (or stratum) into which the population has been separated.Works best when individuals in each stratum are similar in some way and we want to make sure each stratum type is represented. The size of each simple random sample is proportional to the number of individuals in the stratum from which it is selected. (e.g. separating individuals into age groups)
Definition 1.4.2. systematic sampling.
a starting point, \(p\text{,}\) is randomly selected and then every \(k\)th subject is included in the sample, where
The brackets, \(\lfloor x \rfloor\text{,}\) mean round \(x\) down to the nearest integer, or take the floor of \(x\text{.}\) Subjects in the sample are numbered:
Works best when individuals are arranged sequentially but you’re not sure how many total individuals there are because you don’t have a frame of the population (e.g. files in a drawer, people coming out of a building exit polling, etc.).
Definition 1.4.3. cluster sampling.
the population is divided into sections or clusters; all individuals from randomly selected clusters are included in the sample.
Works best when individuals are grouped geographically so it makes logistical sense to sample this way, but location does not affect your variable of interest; clusters are heterogeneous like the population.
Definition 1.4.4. convenience sampling.
sampling subjects who are easy to get (bad sampling method).
Works best when: NEVER!! (not random)
Definition 1.4.5. self-selected sampling.
a convenience sample where individuals are self-selected (another bad sampling method).
Works best when: NEVER!! (not random, favors those with stronger opinions)
Definition 1.4.6. multi-stage sampling.
a sample that is selected in multiple stages, each of which might use a different method of sampling.
Works best when: The population is organized hierarchically but no list exists.
Reading Questions Identify the Sampling Method Part I
1.
The fifth person exiting the student center and every 12th person afterward is interviewed. Answer2.
Two out of the six parking lots on campus are randomly selected and every driver in the two lots receives a questionnaire. Answer3.
Each registered student is assigned a number, 20 numbers are randomly generated and the corresponding students are interviewed. Answer4.
Six buildings on campus are randomly selected and every 4th person who exits each building is included in the sample. Answer5.
Randomly select 10 males and 10 females in the activity center to be interviewed. Answer6.
Every person in my class that sits next to me in Math 1040 is interviewed. Answer7.
A pile of questionnaires is left on a table in the library with a sign that says, “Please complete.” AnswerReading Questions Identify the Sampling Method Part II
For each scenario determine which type of sampling is used.
1.
To estimate the percentage of defects in a recent manufacturing batch, a quality control manager selects every 8th chip that comes of the assembly line starting with the 3rd until she obtains 140 chips. Answer2.
To determine customer opinion of its boarding policy, Southwest Airlines randomly selects 60 flights during a certain week and surveys all passengers on the flights. Answer3.
A member of Congress wishes to determine her constituency’s opinions regarding estate taxes. She first divides her constituency into three income classes: low-income households, middle-income households, and upper-income households. She then takes a simple random sample of households from each income class. Answer4.
In an effort to identify whether an advertising campaign has been effective, a marketing firm conducts a nation wide poll by randomly selecting individuals from a list of known users of the product. Answer5.
A radio station asks its listeners to call in their opinion regarding the use of U.S. forces in peace keeping missions. Answer6.
A college official divides the student population into five classes: freshman, sophomore, junior, senior and graduate student. The official takes a simple random sample from each class and asks the members’ opinions regarding student services. AnswerReading Questions Systematic Sampling Example
The human resources department at a company wants to conduct a survey regarding employee morale. The department has a list of all 400 employees at the company and wants to do a systematic sample of size 20. To do this they randomly select the 8th employee and then select every 20th person. Which workers will be surveyed?