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CHAPTER FIVE
Sampling and Probability
NOTE TO INSTRUCTORS
In this chapter, students learn a number of
fundamental concepts including probability and
inference testing. Many students find inference
testing confusing. Because students will need to
use inference testing in future chapters, you
should plan to spend extra class time on this
concept. Make sure that students understand the
differences between Type I and Type II errors by
using everyday examples in your explanations, many
of which can be found in the textbook. For
example, consider using the jury decision example
or the pregnancy test example described, as well
as the classroom activity entitled “Application
Through
Study
Design”
and
its
corresponding
handout (Handout 5-2), to help students apply
their knowledge of Type I and Type II errors.
OUTLINE OF RESOURCES
I.
Samples and Their Populations
 Discussion Question 5-1 (p. 42)
 Classroom Activity 5-1 : What’s Your Sample? (p.
42)
 Discussion Question 5-2 (p. 43)
 Classroom Activity 5-2: Sampling Scavenger Hunt
(p. 43)
II.
Probability
 Discussion Question 5-3 (p. 44)
 Discussion Question 5-4 (p. 44)
III. Inferential Statistics
 Discussion Question 5-5 (p. 45)
IV.
Type I and Type II Errors
 Discussion Question 5-6 (p. 45)
 Classroom Activity 5-3: Application Through Study
Design (p. 45)


V.
Errors
VI.
Online Resources (p. 45)
Additional Readings (p. 46)
Next Steps: The Shocking Prevalence of Type I
Handouts
 Handout 5-1: Sampling Scavenger Hunt (p. 47)
 Handout 5-2: Application Through Study Design (p.
48)
CHAPTER GUIDE
I.
Samples and Their Populations
1. Samples can exist in two forms: random samples
and convenience samples. A random sample is one
in which every member of the population has an
equal chance of being selected in our study. A
convenience
sample
is
one
that
uses
participants
who
are
readily
available.
Although random sampling is ideal, it is
usually not done because it is expensive, timeconsuming, and often impossible.
2. Generalizability or external validity refers
to the researchers’ ability to apply the
findings from one sample or in one context to
other samples or contexts.
3. Replication reduces the risks and increases
the
rewards
of
sampling
because
we
are
attempting to duplicate our scientific results,
ideally in a different context or with a sample
that has different characteristics.
4. Although convenience sampling is more often
used, it limits our external validity because
we can never be certain that our findings will
apply to the population as a whole. One way to
deal with this limitation is to replicate our
study. If we find the same results, we can be
more confident in our findings.
> Discussion Question 5-1
Why is a random sample typically not collected? Develop a
research question, and determine how we would need to
organize the study to use random sampling.
Your students’ answers should include:
 Random sampling is expensive and is not easy to
achieve without bias.

An example of a good research question would be:
For the elderly living in the Boston area, does
the context in which they recover affect the time
it takes them to recover?
Classroom Activity 5-1
What’s Your Sample?
This activity would make an excellent homework
assignment, or it can be used as an in-class
activity if you have access to electronic journals
in your class.
 Have your students retrieve a primary-source
psychology research article in an area of
interest. Ask them to report to the class what
sample was used in the study.
 How many articles used true random sampling
versus convenience sampling? Include in the
discussion the issues of generalizability. Have
the students discuss the different types of
convenience sampling represented in the articles.
5. You should be especially critical of volunteer
or self-selected samples. These are convenience
samples in which participants actively choose to
participate.
> Discussion Question 5-2
What is a volunteer sample? What is a real-life example of
when you would use this?
Your students’ answers should include:
 Volunteer sampling is a selection method in which
participants actively choose to participate in a
study. A volunteer sample is a kind of
convenience sample that is suspicious in nature
because volunteers are likely to be very
different from a randomly selected sample and may
have many characteristics in common, such as
income, education, geography, personality, and
needs.
Real-life example of when to use the method would
be:
 Volunteer sampling is very often used because it
is the most convenient method of all. If we want
to just obtain a quick 100 participants, this is
usually the best way to proceed. So, if we want
to get a quick sense of what productivity is like
in our corporations, we would ask for volunteers
to participate in our study. However, we’d need
to wonder whether there is something special
about those workers who decide to participate in
our study as opposed to those who decide not to
participate.
Classroom Activity 5-2
Sampling Scavenger Hunt
In this activity:
 Students will search the psychology literature or
newspapers for examples of convenience sampling
and answer questions about the sampling methods.
See Handout 5-1, found at the end of this
chapter, for suggested questions to ask.
 Alternatively, as the instructor, you could
provide the students with examples and use the
questions from the handout in your discussion.
II.
Probability
1. Confirmation bias is our usually unintentional
tendency to pay attention to evidence that
confirms what we already believe and to ignore
the evidence that would disconfirm our beliefs.
2. An illusory correlation is the phenomenon of
believing one sees an association between
variables when no such correlation exists.
3. One
type
of
probability
is
personal
probability, which refers to an individual’s
opinion or judgment about the likelihood that
an event will occur. Although this sense of
probability is often used in everyday language,
when
mathematicians
or
statisticians
use
probability, they’re referring to something
more precise.
4. Probability is the likelihood that a certain
outcome
will
occur
out
of
all
possible
outcomes.
5. Statisticians use the term expected relativefrequency probability for the expected outcome
if an experiment is repeated many, many times.
> Discussion Question 5-3
How does subjective (or personal) probability differ from
expected relative-frequency probability? Why do
mathematicians or statisticians prefer to use expected
relative-frequency probability rather than subjective
probability?
Your students’ answers should include:
Subjective probability is our best guess, or a
personal estimate, that an event will occur
whereas expected relative-frequency probability
is the expected outcome if an experiment were
repeated many, many times.
 Expected relative-frequency probability is more
objective and, in the long run, quite
predictable. Subjective probability is not
scientific, and results from one guess to the
next are unpredictable.

6. In probability, we use the term trial to refer
to each occasion that a procedure is carried
out. Our result of the trial is known as the
outcome, and success refers to an occurence of
the outcome for which we’re trying to determine
the probability.
> Discussion Question 5-4
Imagine that you flip a coin 50 times. How would you use
the terms trial, outcome, and success to describe this
task?
Your students’ answers should include:
 Trial would refer to the number of times you
flipped the coin.
 Outcome would refer to the number of heads and
tails when tallied.
 Success would depend on what is being tested: If
you are testing for the probability of heads,
then success is heads.
7. Probability refers to the proportion that we
expect to see in the long run. The proportion
is the number of successes divided by the
number of trials. In contrast, the percentage
is
just
the
probability
or
proportion
multiplied by 100.
8. The term independence in probability refers to
when the outcome of each trial does not depend
in any way on the outcome of previous trials.
III. Inferential Statistics
1. A control group is a level of the independent
variable that does not receive the treatment of
interest in a study. It’s designed to match the
experimental group (the group receiving the
treatment or intervention of interest) in all
ways but the experimental manipulation. In
other words, the experimental group receives
the
experimental
manipulation
whereas
the
control does not.
2. The null hypothesis is a statement about
populations that most often postulates that
there is no difference between populations or
that the difference is in a direction opposite
from that desired by the researcher.
3. In contrast, the research hypothesis, or
alternative hypothesis, postulates that there
is a difference between populations or that
there is a difference in a certain direction.
4. When we perform an experiment and obtain
results that we analyze, we can either reject
the null hypothesis or fail to reject the null
hypothesis. We do not use the word accept
during formal hypothesis testing.
> Discussion Question 5-5
What is the difference between the null hypothesis and the
research, or alternative, hypothesis? Why do we never
accept the null hypothesis or the research hypothesis?
Your students’ answers should include:
 The null hypothesis and the research, or
alternative, hypothesis are opposites: The null
hypothesis postulates that there is not a
difference between populations or that the
difference is in a direction opposite from that
desired by the researcher; whereas the research
hypothesis postulates that there is a difference
between populations or, sometimes, that there is
a difference in a certain direction, positive or
negative.
 We never accept either hypothesis because there
are too many ways in which a real difference in
the population might not get picked up by a
sample.
IV.
Type I and Type II Errors
1. A Type I error occurs when we reject the null
hypothesis but the null hypothesis was correct.
Type I errors are considered to be extremely
detrimental to research because people might
take
action
(e.g.,
perform
additional
experiments) based on a mistaken finding.
2. A Type II error occurs when we fail to reject
the null hypothesis, but the null hypothesis
was false.
> Discussion Question 5-6
Why are Type I errors considered to be particularly
detrimental to research?
Your students’ answers should include:
 A Type I error is like a false-positive in a
medical test. Researchers consider the
consequences of a Type I error to be particularly
detrimental, possibly even harmful, because
people often take action based on a mistaken
finding.
Classroom Activity 5-3
Applications Through Study Design
In groups or as a discussion with the entire
class, develop a research question and design a
study. Use Handout 5-2, found at the end of this
chapter, to apply concepts from the chapter to
your study design.
V.
Errors
Next Steps: The Shocking Prevalence of Type I
1. Because of the flaws inherent in research,
numerous null hypotheses are rejected falsely,
resulting in Type I errors.
Some researchers
have suggested that nearly half of published
medical findings are Type I errors!
2. It is important to be aware of our own
confirmatory biases that might affect our
tendency to believe research findings without
appropriate questioning.
Online Resources
This interactive Web site covers the basic logic
of probability; use it in class as a demonstration
or have students work on it on their own:
http://www.mathgoodies.com/lessons/vol6/intro_prob
ability.html
This interactive probability Web site includes a
number
of
different
problems
and
their
interpretations:
http://www.cut-the-knot.org/probability.shtml
Use this resource to help teach probability:
http://www-stat.stanford.edu/~susan/surprise/
Additional Readings
Nickerson, R. S. (2004). Cognition and Chance: The
Psychology of Probabilistic Reasoning. Mahwah, NJ:
Lawrence Erlbaum Associate Publishers.
One of the problems in teaching statistics to
many of our psychology students can be traced to a
more general problem in human cognition. This book
focuses on cognition, raising issues related to
our
understanding
(or
lack
thereof)
of
probabilistic reasoning.
Packel, E. W. (2006). The Mathematics of Games and
Gambling, 2nd ed. The Mathematical Association of
America.
This book discusses games of chance (e.g.,
roulette, craps, blackjack), social games (e.g.,
backgammon), and other gambling activities (e.g.,
lotteries),
bringing
out
their
mathematical
aspects. It also includes information on game
theory and game-related exercises.
PLEASE NOTE: Due to formatting, the Handouts are only available in Adobe
PDF®.