+
Chapter 4: Designing Studies
Section 4.1
Samples and Surveys
The Practice of Statistics, 4th edition – For AP*
STARNES, YATES, MOORE
+
2
Chapter 4
Designing Studies
 4.1
Samples and Surveys
 4.2
Experiments
 4.3
Using Studies Wisely
+ Section 4.1
3
Samples and Surveys
Learning Objectives
After this section, you should be able to…

IDENTIFY the population and sample in a sample survey

IDENTIFY voluntary response samples and convenience samples

DESCRIBE how to use a table of random digits to select a simple
random sample (SRS)

DESCRIBE simple random samples, stratified random samples, and
cluster samples

EXPLAIN how undercoverage, nonresponse, and question wording
can lead to bias in a sample survey
+
Activity:
Hiring
Discrimination
Directions:
- Without looking, remove beads one at a time until 8
beads have been chosen.
- Count the number of female pilots selected. Record this
value in the table in your notes.
Simulation
+
5
Activity: The Federalist Papers

The Federalist Papers are a series of 85 essays supporting the
ratification of the U.S. Constitution. At the time they were
published, the identity of the authors was a secret known to
just a few people. Over time, however, the authors were
identified as Alexander Hamilton, James Madison, and John
Jay.

The authorship of 73 of the essays is fairly certain, leaving 12
in dispute. However, thanks in some part to statistical analysis,
most scholars now believe that the 12 disputed essays were
written by Madison alone or in collaboration with Hamilton.

There are several ways to use statistics to help determine the
authorship of a disputed text. One example is to estimate the
average word length in a disputed text and compare it to the
average word lengths of works where the authorship is not in
dispute.
6
and Sample
+
 Population
Definition:
The population in a statistical study is the entire group of individuals
about which we want information.
A sample is the part of the population from which we actually collect
information. We use information from a sample to draw conclusions
about the entire population.
Population
Sampling and Surveys
The distinction between population and sample is basic to
statistics. To make sense of any sample result, you must know
what population the sample represents
Collect data from a
representative Sample...
Sample
Make an Inference about the
Population.
+
7
Populations and Samples
The student government at a high school surveys
100 of the students at the school to get their
opinions about a change to the bell schedule
Population
All students at the school
Sample
100 students surveyed
+
8
Populations and Samples
The quality control manager at a bottling company
selects a sample of 10 cans from the production
line every hour to see whether the volume of the
soda is within acceptable limits
Population
All cans produced that hour
Sample
10 cans inspected
+
9
Populations and Samples
Think of your own example!
Be ready to share with the class in 2
minutes!
10
to Sample Badly
Definition: Convenience Sample
Choosing individuals who are easiest to reach results
in a convenience sample.
Convenience samples often produce unrepresentative
data…why?
Definition: Bias
The design of a statistical study shows bias if it
systematically favors certain outcomes.
Sampling and Surveys
How can we choose a sample that we can trust to
represent the population? There are a number of
different methods to select samples.
+
 How
+ AP EXAM TIP ALERT
When you describe bias, you will be expected
to describe the DIRECTION of the bias.
Example: Explain how using a convenience sample of
students in your statistics class to estimate the
percentage of all high school students who have a
graphing calculator could result in bias.
Answer: This sample would probably include a much
higher percentage of students with a graphing
calculator than in the population of the entire high
school because a graphing calculator is required for
the statistics class. This method would
overestimate the percentage of students with a
graphing calculator.
11
12
to Sample Badly
samples are almost guaranteed to
show bias. So are voluntary response samples, in
which people decide whether to join the sample in
response to an open invitation.
Definition:
A voluntary response sample consists of people who
choose themselves by responding to a general appeal.
Voluntary response
show
bias that
because
Voluntarysamples
responses
means
people
people with strong
opinions
(often
in once!
the same
can respond
more
than
Think
direction) are
most
likely to Idol
respond.
about
American
or Dancing with the
Stars – you can vote multiple times per
phone number or email address!
Sampling and Surveys
 Convenience
+
 How
+
13
Check your understanding: Pg 211

A farmer brings
a juice company
several
crates
of
Answer:
Convenience
sampling.
This
could
oranges
week.
A company
inspector
at
lead
him each
to think
that
the oranges
are looks
of better
10 oranges from the top of each crate before
quality
than they actually are. He might
deciding whether to buy all the oranges.
overestimate the amount of high quality
Answer:
oranges inVoluntary
the bin! response sampling. Only those
who feel particularly strongly about the issue are
 The ABC program Nightline once asked whether the
likely
to respond. In this case, people who are
United Nations should continue to have its
happy
with the
what
theywere
want and
headquarters
in location
the Unitedhave
States.
Viewers
are
lesstolikely
to respond.
This method
might
invited
call one
telephone number
to respond
“Yes” and anotherthe
for percentage
“No.” There was
a chargewho
for are
underestimate
of people
callingand
either
number. More than
168,000 callers
happy
overestimate
the percentage
of people
responded,
and 67% said “No.”
who
are unhappy.
14
to Sample Well: Random Sampling
The statistician’s remedy is to allow impersonal chance to
choose the sample. A sample chosen by chance rules out both
favoritism by the sampler and self-selection by respondents.

Random sampling, the use of chance to select a sample, is
the central principle of statistical sampling.
Definition:
A simple random sample (SRS) of size n consists
of n individuals from the population chosen in such a
way that every set of n individuals has an equal
chance to be the sample actually selected.
In practice, people use random numbers generated by a
computer or calculator to choose samples. If you don’t have
technology handy, you can use a table of random digits.
Sampling and Surveys

+
 How
+
15
Choosing an SRS in our classroom
# 1 – I need an SRS of size 4. I will put
all of your names into a hat and pick out 4
names.
 Option
# 2 – To be equitable, I want a sample
with 2 girls and 2 boys. I need two hats now –
one with only girls’ names and the other with
only boys’ names. Is this still an SRS?
 Option
 Answer:
NO. A sample of 4 students that has for
example all boys, all girls, or some other mixture
other than 2 and 2 cannot be chosen. In an
SRS, every possible sample of size 4 needs
to have the same chance of being chosen.
16
to Choose an SRS with Table D
How to Choose an SRS Using Table D
Step 1: Label. Give each member of the population a
numerical label of the same length.
Step 2: Table. Read consecutive groups of digits of the
appropriate length from Table D.
Your sample contains the individuals whose labels you
find.
Sampling and Surveys
Definition:
A table of random digits is a long string of the digits 0, 1, 2, 3,
4, 5, 6, 7, 8, 9 with these properties:
• Each entry in the table is equally likely to be any of the 10
digits 0 - 9.
• The entries are independent of each other. That is,
knowledge of one part of the table gives no information about
any other part.
+
 How
17
Problem: Use Table D at line 130 to choose an SRS of 4 hotels.
01 Aloha Kai
02 Anchor Down
03 Banana Bay
04 Banyan Tree
05 Beach Castle
06 Best Western
07 Cabana
69051
08 Captiva
09 Casa del Mar
10 Coconuts
11 Diplomat
12 Holiday Inn
13 Lime Tree
14 Outrigger
15 Palm Tree
16 Radisson
17 Ramada
18 Sandpiper
19 Sea Castle
20 Sea Club
21 Sea Grape
22 Sea Shell
23 Silver Beach
24 Sunset Beach
25 Tradewinds
26 Tropical Breeze
27 Tropical Shores
28 Veranda
64817 87174 09517 84534 06489 87201 97245
Sampling and Surveys

How to Choose an SRS (Page 213)
+
 Example:
69 05 16 48 17 87 17 40 95 17 84 53 40 64 89 87 20
Our SRS of 4 hotels for the editors to contact is: 05 Beach Castle,
16 Radisson, 17 Ramada, and 20 Sea Club.
+
18
Another Example: Mall Hours
The management company of a local mall
plans to survey a random sample of 3 stores
to determine the hours they would like to
stay open during the holiday season. Use
Table D at line 101 to select an SRS of size 3
stores.
+
19
SRS or Not?
There are 1400 Students at Santa Paula
High School. You ask the 44 students
in your Statistics class to take a survey.
NO – Not every possible group of 44
students at SPHS has the same
chance of being chosen because most
of the students are not in Statistics.
This is a convenience sample.
+
20
SRS or Not?
There are 100 kids playing soccer in the
park. You ask the 10 kids in line at the
drinking fountain to answer a question.
NO – Not every possible group of 10
kids has the same chance of being
chosen. This is a convenience sample.
+
21
SRS or Not?
There are 100 kids playing soccer in the
park. You decide to ask 5 girls and 5
boys to answer a question.
NO – Not every possible group of 10
kids has the same chance of being
chosen. A group of 10 boys or a group
of 8 boys and 2 girls does not have the
same chance as the method you
decided to use.
+
22
SRS or Not?
There are 100 kids playing soccer in the
park. You use team rosters to randomly
select 10 kids to survey.
YES –every possible group of 10 kids
has the same chance of being chosen.
This is a Simple Random Sample
(SRS).
+
23
Replacement: with or without?
Sampling with replacement allows individuals to be
selected more than once. Their names go back
into the hat after each selection.
Sampling without replacement does not allow
individuals to be selected more than once. Once
they are chosen, their name does not go back into
the hat.
If you are using table D to select a SRS, you simply
indicate that you are “skipping” repeats.
If you are using a calculator to select a SRS,
generate extra numbers because the calculator
samples with replacement.
+
24
Sampling Methods: The River
 Suppose
we wanted to estimate the yield of
our corn field. The field is square and divided
into 16 equally sized plots
(4 rows x 4 columns). A river runs along the
eastern edge of the field. We want to take a
sample of 4 plots.
 Using
a random number generator or table
D, pick a simple random sample (SRS) of 4
plots
25
Sampling Methods
The basic idea of sampling is straightforward: take an SRS
from the population and use your sample results to gain
information about the population. Sometimes there are
statistical advantages to using more complex sampling
methods.

One common alternative to an SRS involves sampling
important groups (called strata) within the population
separately. These “sub-samples” are combined to form one
stratified random sample.
Definition:
To select a stratified random sample, first classify the
population into groups of similar individuals, called
strata. Then choose a separate SRS in each stratum
and combine these SRSs to form the full sample.
Sampling and Surveys

+
 Other
26
Sampling Methods
a stratified random sample can sometimes
give more precise information about a population
than an SRS, both sampling methods are hard to
use when populations are large and spread out over
a wide area.
 In
that situation, we’d prefer a method that selects
groups of individuals that are “near” one another.
Definition:
To take a cluster sample, first divide the population
into smaller groups. Ideally, these clusters should
mirror the characteristics of the population. Then
choose an SRS of the clusters. All individuals in the
chosen clusters are included in the sample.
Sampling and Surveys
 Although
+
 Other
27
Sampling at a School Assembly (218)
Describe how you would use the following sampling methods
to select 80 students to complete a survey.

(a) Simple Random Sample

(b) Stratified Random Sample

(c) Cluster Sample
Sampling and Surveys

+
 Example:
+
28
Example: Hotel on the Beach
29
for Sampling
The purpose of a sample is to give us information about a
larger population.

The process of drawing conclusions about a population on the
basis of sample data is called inference.
Why should we rely on random sampling?
1)To eliminate bias in selecting samples from the list of
available individuals.
2)The laws of probability allow trustworthy inference about the
population
• Results from random samples come with a margin of
error that sets bounds on the size of the likely error.
• Larger random samples give better information about the
population than smaller samples.
Sampling and Surveys

+
 Inference
30
Surveys: What Can Go Wrong?
Most sample surveys are affected by errors in addition to
sampling variability.

Good sampling technique includes the art of reducing all
sources of error.
Definition
Undercoverage occurs when some groups in the population
are left out of the process of choosing the sample.
Nonresponse occurs when an individual chosen for the sample
can’t be contacted or refuses to participate.
A systematic pattern of incorrect responses in a sample survey
leads to response bias.
The wording of questions is the most important influence on
the answers given to a sample survey.
Sampling and Surveys

+
 Sample
+
31
Sampling Errors & Nonsampling Errors
A sampling error has to do with choosing the
sample.
-
Voluntary response
- Undercoverage
A nonsampling error happens after the sample
has been chosen.
Nonresponse
- Response bias
Wording of questions
-
-
+
32
Check your understanding (p224)
#1a – sampling error
#1b – nonsampling error
#1c – Sampling error
#2 – By making it sound like disposable diapers are
not a problem in the landfill, this question will result
in fewer people suggesting that we should ban them.
The author of the question highlights several other
items that take up more space in the landfill, which
makes it look like disposable diapers are really not a
problem.
33
Activity: See no evil, hear no evil?
Follow the directions on Page 206

Turn in your results to your teacher.

Teacher: Right-click (control-click) on the graphs to edit the counts.
Sampling and Surveys

+
34
Section 4.1
Samples and Surveys
Summary
In this section, we learned that…

A sample survey selects a sample from the population of all
individuals about which we desire information.

Random sampling uses chance to select a sample.

The basic random sampling method is a simple random sample
(SRS).

To choose a stratified random sample, divide the population into
strata, then choose a separate SRS from each stratum.

To choose a cluster sample, divide the population into groups, or
clusters. Randomly select some of the clusters for your sample.
+
35
Section 4.1
Samples and Surveys
Summary, con’t
In this section, we learned that…

Failure to use random sampling often results in bias, or systematic
errors in the way the sample represents the population.

Voluntary response samples and convenience samples are
particularly prone to large bias.

Sampling errors come from the act of choosing a sample. Random
sampling error and undercoverage are common types of error.

The most serious errors are nonsampling errors. Common types of
sampling error include nonresponse, response bias, and wording
of questions.
+
36
Looking Ahead…
In the next Section…
We’ll learn how to produce data by designing
experiments.
We’ll learn about
 Observational Studies vs. Experiments
 The Language of Experiments
 Randomized Comparative Experiments
 Principles of Experimental Design
 Inference for Experiments
 Blocking
 Matched Pairs Design