This document discusses different sampling methods for collecting data from a population. A census collects data from the entire population but can be inaccurate, expensive, or impossible for large populations. Common sampling methods include simple random sampling, cluster sampling, stratified sampling, systematic sampling, and multi-stage sampling. Each method has advantages and disadvantages related to representation, equal chance of selection, and practicality. Potential sources of bias include undercoverage, nonresponse, and response biases that can occur depending on the sampling design and data collection process.

3. Census
A sample that consists
of the entire population

4. Why would we not do a
census?
1) Not accurate for a large population
2) Very expensive
3) Perhaps impossible
4) If using destructive sampling, you
would destroy population
• Breaking strength of soda bottles
• Lifetime of flashlight batteries

5. Simple Random Sample
1. number the population
2. use a method to randomly select the desired
sample size from entire population
Advantages: every member of population always
has equal chance of being selected
Disadvantages: sample may not be
representative of population; difficult with
large populations

6. Cluster Random Sample
1. divide population into clusters
2. use a method to randomly select one or more
clusters
3. Perform a census within each of the clusters
Advantages: can work well if population is easy
to divide or there are established clusters
Disadvantages: not everyone has equal chance of
being chosen; selected clusters may not be
representative of population

7. Stratified Random Sample
1. divide population into strata
2. use a method to randomly select a sample
from each strata
Advantages: guarantees representation from
each strata
Disadvantages: not everyone has equal chance
of being chosen; strata (of interest) may be
difficult to determine; population may be
difficult/laborious to sort

8. Systematic Random Sample
1. use sample size and population size to
determine (estimate) “magic number”
2. use a method to randomly select number using
“magic number” as range; add to determine
corresponding selections
Advantages: allows rapid method to select from
large population; helps provide representation
throughout population
Disadvantages: not everyone has equal chance of
being chosen; sample may not be representative

9. Multi-Stage Random Sample
1. use a method (SRS, cluster, stratified)
to randomly select (large) groups
2. use a method (SRS, cluster, stratified to
randomly select (smaller) groups
3. repeat until participants are chosen

10. Role of Sampling Design
Statistical inference provides ways to answer
specific questions from data with some
guarantee that the answers are good ones.
Statistical inference will not be accurate if the
method of collecting data is flawed.

11. Other Sampling Designs
Suppose the principal is interested in finding
out if MacArthur students think more trees
should be planted. She makes an
announcement and instructs students to
come by her office to let her know if tree
planting is an issue they support. Will this
sample of students give her an accurate
picture of all students’ feelings at
MacArthur?

12. Voluntary Response
A voluntary response sample consists of
people who choose themselves by
responding to a general appeal.
Voluntary response samples over represent
people with strong opinions.

13. Other Sampling Designs
The principal is surprised to find most of the
students coming in her office are in favor of
the tree planting. Feeling that maybe her
design may not have worked, she ventures
into the hallways and starts asking students.
Will this sample of students give her an
accurate picture of all students feelings at
MacArthur?

14. Convenience Sample
In a convenience sample the interviewer
makes the choice. It is a self selected
sample
Convenience samples produce bias results and
show favoritism

15. What type of sampling method is
appropriate for the given situations?
1) Before implementing a plan designed to
reduce flight time, and hence conserve fuel
and energy, the US Air Force needs an
estimate of the total number of miles flown by
a particular type of aircraft during a given
month. Air Force records show that there are
1500 aircraft of this type at 96 different
airfields around the country.

16. 2) Time Magazine wishes to know
whether its readership is satisfied with the
current format used for printing the
magazine.
3) As part of an appraisal of the retail
value of homes in Dallas a sample of
homes will be taken to find the average
value of a house.

17. Random-random sample practice
1. simple random
sample
2. convenience sample
3. cluster sample
4. voluntary response
5. systematic sample
6. stratefied sample
1. MacArthur seniors
2. UT graduates
3. Blender magazine
subscribers
4. Texans
5. national pet stores
6. Travis middle school

18. Cautions about sample surveys
Suppose we use a random sample in a survey, what
could confound our results?
Bias is any systematic failure of a sampling method
to represent its population
undercoverage
 the issue occurs when a sampling design misses a part of
the population
nonresponse bias
 the issue occurs when a significant part of the population
refuses to participate in the survey or cannot be contacted
• voluntary response bias – individual chooses whether to
participate in a sample

20. response bias
 the issue occurs when the person asking the question
makes the respondent uncomfortable and possibly
influence their answer
• wording of question occurs when a question is leading and
attempts to persuade a respondent toward a particular answer
Remember: sample results sometimes simply
do not necessarily match the population.

23. Identify potential problems
To obtain a sample of households, a television
rating service dials numbers taken at random from
telephone-directories.
Teen magazine sent a mail-in questionnaire to 500
randomly selected subscribers. One of the
questions was the following: “Knowing that the
cover price would likely increase, would you
prefer the number of advertisements in the
magazine to be limited.?”

24. Identify potential problems
To evaluate the reliability of cars owned by
its subscribers, Consumer Reports magazine
publishes a yearly list of automobiles and
their frequency-of-repair records. The
magazine collects the information by
mailing a questionnaire to subscribers and
tabulating the results from those who return
it.

25. Identify potential problems
For a survey of student opinions about high
school athletic programs, a member of the
school board obtains a random sample of
students by listing all high school students
and using a random number table to select
30 of them. After making phone calls last
weekend, she notes six of the students said
that they didn’t have time to participate in
the survey.

26. Defining Important Terms
population: the entire group of interest
sample: the selected group that information was
collected from
sample variability: sample to sample difference
sample design: refers to the method used to choose the
the sample from the population
good: simple random sample, cluster, stratified,
systematic
 poor: voluntary response, convenience sampling
randomization: random selection in which each individual is
given a fair, random chance of selection; the use of chance or
probability during the selection process

27. Remember!
Bias is introduced by the way a sample is selected or how
the data is collected from the sample.
Increasing sample size does not reduce bias; but the
degree of accuracy can be improved
Bad sample designs yield worthless data.
Sample results are only estimates of the population.
A poor design systematically favors certain outcomes or
results.
Since we deliberately use chance, the results obey the
laws of probability allowing fairly consistent results
(within a margin of error).