Transcript Chapter 5 - WordPress.com

Conducting A Study
• Designing Sample
• Designing Experiments
• Simulating Experiments
Introduction
 Observational study: observes and measure
variables regarding individuals; no
influence.
 Experimental: imposes some treatment on
individuals to observe their responses.
Introduction
 Population: The collection of people,
animals, or things to study
 Sample: A subset of the population
 Parameters: Calculations on the entire
population
 Statistics: Calculations on sample data set
Introduction
 Bias: If the sample is not representative of
the population, but differs substantially in
the characteristic of interest, we say that the
sample is biased.
 Census: attempts to contact every individual
in the entire population.
Designing Samples:
Suppose we want to gather information about a
group of people.
 If the group is small (for example, all students in this
class) we can study each group member directly.
 If, however, the group is very large (for example, all
students in the school), studying each member of the
group may not be feasible.
 The method we use to select the sample is called the
sample design. The design of the sample is very
important. If the design is poor, the sample will not
accurately represent the population.
Designing Samples:
 Here’s the most important overarching
concept regarding obtaining samples:
 Probability Sample: “a sample chosen by
chance. We must know what samples are
possible and what chance, or probability,
each possible sample has.”
Types of Sample Designs:
 Voluntary Response Sample
 People choose themselves to be in the sample
by responding to a general appeal
 Example: We post an advertisement in Bay
Eagle asking ESHS students to respond
 Problem: People with strong opinions (often
strong negative opinions) tend to reply, so they
are overrepresented
Types of Sample Designs:
 Convenience Sample
 Individuals who are easiest to reach are chosen
for the sample
 Example: We use students in this class as our
sample
 Problem: This group may not be diverse
enough to accurately represent all students at
ESHS
Types of Sample Designs:
 Both Voluntary Response Samples and
Convenience Samples result in a sample that
is not representative of the population. These
are biased samples because they favor
certain outcomes.
 Random selection eliminates bias from
sample choice.
Types of Sample Designs:
 Simple Random Sample (SRS)
 Individuals are selected so that all possible
combinations of individuals are equally likely to
be in the sample
 Example: Generate a list of student ID numbers
for all students at ESHS; then randomly select
student ID numbers and choose those students
for the sample
How to Select a SRS
 We will actually do this in class together.
Other Types of Sample Designs:
 Systematic Random Sample
 The first individual is chosen at random; then a
system or rule is used to choose all other
individuals
 Example: Obtain an alphabetized list of all
students at ESHS. Choose every 5th person on
the list.
Other Types of Sample Designs:
 Stratified Random Sample
 Divide the population into groups of similar
individuals; choose a SRS in each group to
form the full sample
 Example: Divide all of the students at ESHS
into four groups: freshmen, sophomores,
juniors, and seniors; the choose a SRS from
each grade level
Other Types of Sample Designs:
 Multistage Sample
 Select several groups; within each group,
select a subgroup; within each subgroup select
individuals for the sample.
 Example: Select several departments within the
school (Math, English, Art). Within each of
those departments, select several teachers.
Choose several students within each class.
Other Types of Sample Designs:
 Cluster Sample
 Select several groups; within each group,
select several subgroups; within each subgroup
select ALL individuals for the sample.
 Example: Select several departments within the
school (Math, English, Art). Within each of
those departments, select several teachers.
Choose ALL students in each class.
 Although random selection eliminates
bias from our choice of sample, it does
not guarantee that our sample is
representative of the population.
 Potential problems include:
Potential problems include:
 Undercoverage:
 Some groups are left out of the process of
choosing the sample
 Example: Students in SCROC, early release,
on suspension, or absent may be left out of the
sample
Potential problems include:
 Nonresponse:
 An individual chosen for the sample cannot be
contacted or refuses to cooperate
 Example: A student chosen for the sample may
refuse to divulge information or may be absent
Potential problems include:
 Response Bias
 The behavior of the individual or interviewer
may influence the accuracy of the response
 Example: Students may lie about drug or
alcohol use
Potential problems include:
 Wording of Questions
 Confusing or leading questions influence
responses; poorly worded questions will not yield
accurate responses.
 Example 1: “In a recent study, students in an
Algebra I course were given a 25 question basic
skills test. On average, students used a
graphing calculator to answer 21 out of 25
questions. Do you think graphing calculators are
overused?”
Potential problems include:
 Wording of Questions
 Example 2: “By using a graphing calculator,
students in an Algebra I course are able to
make visual connection between equations and
their graphs, reinforcing difficult concepts. Do
you think graphing calculators are overused?”
 Example 3: “Do you like English or Math?”
 Example 4: “Do you like school?”
Designing Experiments:
 If we want to observe individuals and record
data without intervention, we conduct an
observational study.
 If we want to examine a cause and effect
relationship, we impose a treatment and
conduct an experiment.
 If we want to compare the effects of different
treatments, one of which is no treatment
(control group), we conduct a comparative
experiment
Designing Experiments:
 The individuals on which the experiment is done are
called experimental units.
 If the units are people, they are called subjects.
 The experimental condition we apply to the units is
called the treatment.
 The explanatory variables (causing a change in the
other variables) are called factors.
Designing Experiments:
 The factors may be applied in different levels.
 When designing an experiment we want to minimize
the effect of lurking variables so that our results are
not biased.
 Because we may not be able to identify and eliminate
all lurking variables, it is essential that we use a
control group.
Designing Experiments:
 The control group gets a fake treatment
(placebo) to counter the placebo effect
and/or any other lurking variables present.
 Having a control group allows us to compare
the results of the treatments.
Experimental Design
 Step 1: Choose treatments
 Identify factors and levels
 Control group
 Step 2: Assign the experimental units to the
treatments
 Matching (place similar units in each treatment group)
 Randomization (randomly assign units to each treatment
group)
Principles of Experimental Design:
1.Control the effects of lurking
variables by comparing several
treatments (include a control group if
possible).
2.Use randomization to assign
subjects/units to treatments.
3.Replicate the experiment on many
subjects/units to reduce chance
variation in the results.
Principles of Experimental Design:
 Note: An effect is called statistically
significant if it is too great to be caused
simply by chance.
 The concept of “statistical significance”
is covered second semester.
Principles of Experimental Design:
 Even a well-designed experiment can
contain hidden bias, so it is extremely
important to handle the subjects/units in
exactly the same way.
 One way to avoid hidden bias is to
conduct a double-blind experiment.
 In a double-blind experiment, neither the
subjects nor the people who have contact
with them know which treatment a subject
has received.
Types of Experimental Design:
 In a matched pairs design, there are
only two treatments. In each block,
there is either:
 a single subject receiving both treatments, or
 a pair of subjects, each receiving a different
treatment
Types of Experimental Design:
 In a completely randomized design, all
subjects are randomly assigned to treatment
groups.
 In a block design, subjects are first split into
groups called blocks. Subjects within each
block have some common characteristic (for
example: gender, age, education, ethnicity,
etc.) Then, within each block, subjects are
randomly assigned to treatment groups.
Simulating Experiments:
 Question: In a class of 23 unrelated
students (no twins!), what is the chance
that at least two students have the
same birthday? In a room of 41
people? In a room of 50 people?
Simulating Experiments:
 To determine the chance of this event,
we can:
1.Conduct an experiment and measure the
outcomes (Problem: we have to find many
classes of the correct size, time, effort)
2.Calculate the theoretical probability using the
mathematical laws of probability (Problem: the
formulas can be complicated or involve higher
mathematics)
3.Simulate an experiment using a model that is
similar to this real life event
Simulating Experiments:
 Using a model to imitate a real life event
is called simulation. A well-designed
model will yield accurate results for a
large number of trials.
Simulating Experiments:
Steps Involved in Simulation
1.State the problem or describe the
experiment
2.State the assumptions
3.Assign a digit to each outcome
4.Simulate many repetitions
5.State your conclusions
Example:
1. In a class of 23 unrelated students, what is the
chance that at least two students have the same
birthday?
2. We assume all possible birthdays are equally likely,
and that one student’s birthday is independent of
the other students’ birthdays.
3. Assign numbers 1-365 to each day of the year.
4. Randomly choose 23 numbers and look to see if
any are duplicated. Record the results in a table.

randInt (1, 365, 23)  L1

Repeat until you have completed many trials.
Example:
Number of students
with the same
birthday
None
At least 2
Total # of Trials
Tally
Relative
Frequency
5.In a class of 23 unrelated students, the
chance that at least two students have the
same birthday is approximately _______.