• Characteristics of a well designed and well
• Populations, samples and random
• Sources of bias in sampling and surveys.
• Sampling methods, including simple
random sampling, stratified random
sampling and cluster sampling.
Populations, Samples, and Random Selection
The population in a statistical study is the entire group
of individuals, scores, measurements, etc. about which
we want information.
A sample is the part of the population from which we
actually collect information and is used to draw
conclusions about the whole.
Random Selection is a process of gathering a
representative sample for a particular study. Random
means the people are chosen by chance, each person
has the same probability of being chosen. When you
have a truly random sample, you reduce the chance that
the results are due to factors of the participants in the
Sources of Bias in Sampling and Surveys
Convenience Samples use a selection of individuals that are
easiest to reach, and Voluntary Response Samples where
respondents decide if they want to be included, are
common methods of data collection that will usually
produce biased results. These sampling methods will
usually favor one part of a population over another.
If the High School guidance office wanted to know if
students are interested in an AP Statistics elective, would
the district get accurate information if the counselors asked
the Calculus teachers to survey their students?
Sources of Bias in Sampling and Surveys (cont.)
Why would more accurate results be gathered in an
English or History class?
Would asking students to stop by the office at the end of
the day to fill out a questionnaire regarding testing
policies in the district yield valid results?
What could be changed to make this a more valid
Design Your Own Bad Sample
The school administration wants to gather
student opinion about parking on campus. It is
not practical to contact every student.
1.Give an example of a way to choose a sample
of students that is poor practice because it
depends on voluntary response.
2.Give an example of a way to choose a sample
of students that is poor practice that does not
depend on voluntary response.
A sample chosen by chance allows neither favoritism by the
sampler nor self-selection by respondents. All individuals have an
equal chance to be chosen.
A Simple Random Sample allows all members of a population an
equal chance of being selected, avoiding bias. Drawing names
from a hat works for small populations (students in a classroom)
but would not be practical when conducting a national survey.
Computer-generated Random Digits can be used when working
with large populations.
A Table of Random Digits is a long string of the digits 0, 1, 2, 3, 4,
5, 6, 7, 8, 9, where each entry in the table is equally likely to be any
of the 10 digits and the entries are independent of each other.
Systematic Sampling selects a starting point and then selects
every kth (such as 50th) element in the population.
Other sampling methods include Stratified Random Sampling,
and Cluster Sampling. Both involve the formation of subgroups
before collecting data.
Stratified Random Sampling subdivides the population into at
least two different subgroups (strata) so that subjects within the
same subgroup share the same characteristics (gender, age) then
draw a sample from each.
Ex. The Orange County DMV plans to test an on line registration
system by using a sample consisting of 20 randomly selected
men and 20 randomly selected women.
Cluster Sampling divides the population into sections (clusters),
randomly select some of those clusters, and then chooses all
members of the selected clusters.
Ex. Pre-election polls randomly select 30 precincts from a large
number of precincts, then survey all members from each of the
Identify which type of sampling is used: random, systematic,
convenience, stratified, or cluster.
1. A policy sobriety checkpoint stops and interviews every 5th driver.
2. An exit poll randomly selects specific polling stations and all voters
are surveyed as they leave the premises.
3. An engineering student measures the strength of fingers used to
push buttons by testing family members.
4. An IRS researcher investigates cheating on income taxes by
surveying all waiters and waitresses at 20 randomly selected
5. A marketing expert for MTV is planning a survey in which 500
people will be randomly selected from each age group of 10-19, 2029, …
6. A teacher surveyed all of his students to obtain a sample consisting
of the number of credit cards students possess.
7. A poll of 1550 adults, subjects were selected by using a computer
to randomly generate phone numbers that were called.