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Chapter 2

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Chapter 13 Notes
Chapter 12
Part I Answers
Chapter 12
Part II Answers
Chapter 13
Experimental
Design
Definitions:
1) Observational study - observe
outcomes without imposing any
treatment
2) Prospective study – Identifying
subjects in advance and collecting
data as events unfold
CORRECTION: #40 of unit questions change word
“allowed” to “followed”
Definitions:
3) Retrospective study – Identifying
subjects and use data from events
that have already occurred
4) Experiment - actively impose some
treatment in order to observe the
response
I’ve developed a new rabbit food, Hippity
Hop.
Rabbit Food
Helps rabbits develop
a shiny coat & gives
them more energy as
they grow.
100% of daily
vitamins &
essential oils!
Can I just make this claim?
NO
What must I do to make this claim?
Do an experiment
Who (what) should I test this on?
Rabbits
What do I test?
The type of food
5)Experimental unit – the single
individual (person, animal, plant,
etc.) to which the different
treatments are assigned
6) Factor – is the explanatory
variable
7) Level – a specific value for the
factor
8) Treatment – a specific
experimental condition applied to the
experimental units.
• Each factor/level combination
is a treatment
9) Response variable – what you
measure after the treatment is
applied.
• What is affected by the factor
I plan to test my new rabbit food.
What are my experimental units?
Rabbits
What is my factor?
Type of food
What is the response variable?
How well they grow
I’ll use my pet
rabbit, Lucky!
Hippity Hop
Not good
enough.
This might
have happened
any way.
Since Lucky’s coat is shinier &
he has more energy, then
Hippity Hop is a better rabbit
food!
10) Control group – a group that is
used to compare the factor against;
can be a placebo or the “old” or
current item
11) Placebo – a “dummy” treatment
that can have no physical effect
Not good enough. Lucky may have grown bigger
with the old food.
Old Food
Hippity Hop
Now I’ll use Lucky & my
friend’s rabbit, Flash.
Lucky gets Hippity Hop
food & Flash gets the
old rabbit food.
WOW! Lucky is bigger &
shinier so Hippity Hop is
better!
Not good enough. The rabbits must be randomly
assigned.
Old Food
Hippity Hop
The first five rabbits
that I catch will get
Hippity Hop food and
the remaining five will
get the old food.
The Hippity Hop rabbits have
scored higher so it’s the better
food!
Much better if the one evaluating doesn’t know
which food was given.
Old Food
5
73
98
Hippity Hop
Number
from
– 10.
Placethe
therabbits
numbers
in a1hat.
The
first
five numbers
The
remaining
rabbitspulled
get
from the
be the
the hat
old will
food.
rabbits that get Hippity Hop
food.
6
2
4the rabbits & found
I evaluated
5
9
10
that
Hop
1 the 3rabbits eating 7Hippity
8
are better than
the old food!
12) blinding - method used so that
experimental units do not know
which treatment they are getting
13) double blind - neither the
experimental units nor the evaluator
know which treatment was received
14.
Principles of Experimental Design
• Control of effects of extraneous
variables on the response – by
comparing treatment groups to a
control group (placebo or “old”)
• Replication of the experiment on
many subjects to quantify the
natural variation in the experiment
• Randomization – the use of chance
to assign subjects to treatments
The ONLY way to show cause &
effect is with a well-designed,
well-controlled experiment!
The ONLY way to show cause &
effect is with a well-designed,
well-controlled experiment!!
15. The ONLY way to show
cause & effect is with a welldesigned, well-controlled
experiment!!!
Example 1: A farm-product manufacturer wants
to determine if the yield of a crop is different
when the soil is treated with three different
types of fertilizers. Fifteen similar plots of land
are planted with the same type of seed but are
fertilized differently. At the end of the growing
season, the mean yield from the sample plots is
compared.
Experimental units? Plots of land
Factors? Type of fertilizer
Levels? Fertilizer types A, B, & C
Response variable? Yield of crop
How many treatments? 3
Example 2: A consumer group wants to
test cake pans to see which works the
best (bakes evenly). It will test aluminum,
glass, and plastic pans in both gas and
electric ovens.
Experiment units?Cake
Factors?
Levels?
batter
Two factors - type of pan & type of oven
Type of pan has 3 levels (aluminum, glass, & plastic
& type of oven has 2 levels (electric & gas)
Response variable? How
evenly the cake bakes
Number of treatments?
6
Example 3: A farm-product manufacturer wants
to determine if the yield of a crop is different
when the soil is treated with three different
types of fertilizers. Fifteen similar plots of land
are planted with the same type of seed but are
fertilized differently. At the end of the growing
season, the mean yield from the sample plots is
compared.
Why is the same type of seed used on all 15
plots? It is part of the controls in the experiment.
What are other potential extraneous variables?
Type of soil, amount of water, etc.
Does this experiment have a placebo? Explain
NO – a placebo is not needed in this experiment
Experiment Designs
16.
• Completely randomized – all
experimental units are
allocated at random among all
treatments
Treatment group 1
response
Treatment group 2
variable
Treatment group 3
Treatment A
Treatment B
Treatment C
Treatment D
Randomly assign
experimental units to
treatments
Completely randomized design
17.
Group 2
Treatment 1
Treatment 2
Treatment 3
Random
Assignment
Group 1
Random
Assignment
• Randomized block – units are
blocked into groups and then
randomly assigned to treatments
Treatment 1
Treatment 2
Treatment 3
response
varaible
Treatment A
Treatment B
Treatment A
Treatment B
Put
into homogeneous
Randomly
assign
groups
experimental
units to
treatments
Randomized block design
18.
•Matched pairs –
a special type of block design
– match up experimental units
according to similar characteristics &
randomly assign one to one treatment
& the other automatically gets the
2nd treatment
Treatment A
Treatment B
experimental
Next,Pair
randomly
assign
units
according
to
one unit
from
a pair to
specific
Treatment
A. The
characteristics.
other
unit gets
Treatment B.
This is one way to do a matched
pairs design – another way is to have
the individual unit do both
treatments (as in a taste test).
19) Confounding – When the levels of
one factor are associated with the
levels of another factor so their
effects cannot be separated, we say
that these two factors are confounded
Confounding can arise from a badly
designed multifactor experiment.
A credit card bank wanted to test the
sensitivity of the market to two factors:
the annual fee charged for a card and
the annual percentage rate charged.
The bank sent out 50,000 offers with a
low rate and no fee, and 50,000 offers
with a higher rate and a $50 fee.
Guess what happened?
Confounding can arise from a badly designed multifactor
experiment.
A credit card bank wanted to test the sensitivity of the
market to two factors: the annual fee charged for a card
and the annual percentage rate charged.
The bank sent out 50,000 offers with a low rate and no
fee, and 50,000 offers with a higher rate and a $50 fee.
People preferred the low-rate, no-fee
card. But the bank couldn’t answer their
original question.
What should they have done?
Confounding can arise from a badly designed multifactor
experiment.
A credit card bank wanted to test the sensitivity of the
market to two factors: the annual fee charged for a card
and the annual percentage rate charged.
The bank sent out 50,000 offers with a low rate and no
fee, and 50,000 offers with a higher rate and a $50 fee.
People preferred the low-rate, no-fee card. But the bank
couldn’t answer their original question. What should they
have done?
They needed four treatments:
- Low rate & no fee
Does the bank
- High rate & no fee
want to use all 4
possible
- Low rate & $50 fee
treatments?
- High rate & $50 fee
Example 4: An article from USA
Today reports the number of victims
of violent crimes per 1000 people. 51
victims have never been married, 42
are divorced or separated, 13 are
married, and 8 are widowed.
Is this an experiment? Why or why
not? No, no treatment was imposed on people.
What is a potential confounding
Age – younger people are more at risk
variable? to be victims of violent crimes
Example 5: Four new word-processing
programs are to be compared by measuring
the speed with which standard tasks can
be completed. One hundred volunteers are
randomly assigned to one of the four
programs and their speeds are measured.
Is this an experiment? Why or why not?
Yes, a treatment is imposed.
What type of design is this?
Completely randomized
Factors? Levels?
one factor: word-processing program with 4 levels
Response variable?
speed
Example 5: Four new word-processing
programs are to be compared by
measuring the speed with which standard
tasks can be completed. One hundred
volunteers are randomly designed to one
of the four programs and their speeds are
measured.
Can this design be improved?
Yes, you could a design where each person uses
each program in a random order.
This is considered a type of matched pair design.
Example 6: Suppose that the manufacturer wants
to test a new fertilizer against the current one on
the market. Ten 2-acre plots of land scattered
throughout the county are used. Each plot is
subdivided into two subplots, one of which is
treated with the current fertilizer, and the other
with the new fertilizer. Wheat is planted and the
crop yields are measured.
What type of design is this?
Why use this method?
Matched - pairs design
Each 2-acre plot probably gets
equal rainfall. Probably has
same soil too.
When does randomization occur?
Randomly assigned treatment to
first acre of each two-acre plot
20.
Randomization reduces bias by spreading
any uncontrolled variables evenly
throughout the treatment groups.
21.
Blocking also helps reduce variability.
20.
Randomization reduces bias by spreading
any uncontrolled variables evenly
throughout the treatment groups.
21.
Blocking also helps reduce variability.
Chapter 12 Part I Answers
4. (chapter 12) The Gallup Poll interviewed 1423 randomly selected
American citizens September 10-14, 1999, and reported that when
“asked which type of content bothers them most on TV, 44% of
Americans identify ‘violence,’ 23% choose ‘lewd and profane language,’
while 22% say ‘sexual situations.’”
a) Population: U.S. citizens
b) Parameter of interest:
Type of content that bothers most on TV
c) Sampling Frame: All U.S. adults
d) Sample: 1423 randomly selected U.S. citizens
e) Sampling Method: Unknown
f) Sources of Bias: None apparent
Chapter 12 Part I Answers
5. (chapter 12) Researchers waited outside a bar they had randomly
selected from a list of such establishments. They stopped every 10th
person who came out of the bar and asked whether he or she thought
drinking and driving was a serious problem.
a) Population: Adults of drinking age
b) Parameter of interest:
Proportion who think drinking & driving is a
serious problem
c) Sampling Frame: Adults at particular bar
d) Sample: every 10th person leaving the bar
e) Sampling Method: Systematic sampling
f) Sources of Bias: Only asking adults that have probably
been drinking --- Undercoverage
Chapter 12 Part II Answers
11. In a large city school system with 20 elementary schools, the
school board is considering the adoption of a new policy that would
require elementary students to pass a test in order to be promoted to
the next grade. The PTA wants to find out whether parents agree with
this plan. Listed below are some of the ideas proposed for gathering
data. For each, indicate what kind of sampling strategy is involved
and what (if any) biases might result.
a) Put a big ad in the newspaper asking people to log their opinions on
the PTA website.
This is a voluntary response sample. Only those who see
the ad, feel strongly about the issue, and have web access
will respond.
Chapter 12 Part II Answers
11. In a large city school system with 20 elementary schools, the school board is
considering
the adoption of a new policy that would require elementary students to pass a test in
order to be promoted to the next grade. The PTA wants to find out whether parents
agree with this plan. Listed below are some of the ideas proposed for gathering data.
For each, indicate what kind of sampling strategy is involved and what (if any)
biases might result.
b) Randomly select one of the elementary schools and contact every
parent by phone.
This is cluster sampling, but probably not a good idea. The
opinions of parents in one school may not be typical of
the opinions of all parents.
Chapter 12 Part II Answers
11. In a large city school system with 20 elementary schools, the
school board is considering
the adoption of a new policy that would require elementary students
to pass a test in order to be promoted to the next grade. The PTA
wants to find out whether parents agree with this plan. Listed below
are some of the ideas proposed for gathering data. For each, indicate
what kind of sampling strategy is involved and what (if any) biases
might result.
c) Send a survey home with every student, and ask parents to fill it out
and return it the next day.
This is an attempt at a census, and will probably suffer from
nonresponse bias.
Chapter 12 Part II Answers
11. In a large city school system with 20 elementary schools, the
school board is considering
the adoption of a new policy that would require elementary students
to pass a test in order to be promoted to the next grade. The PTA
wants to find out whether parents agree with this plan. Listed below
are some of the ideas proposed for gathering data. For each, indicate
what kind of sampling strategy is involved and what (if any) biases
might result.
d) Randomly select 20 parents from each elementary school. Send them
a survey, and follow up with a phone call if they do not return the survey
within a week.
This is stratified sampling. If the follow-up is carried out
carefully, the sample should be unbiased.
Chapter 12 Part II Answers
12. In a large city school system with 20 elementary schools, the school
board is considering
the adoption of a new policy that would require elementary students to
pass a test in order to be promoted to the next grade. The PTA wants to
find out whether parents agree with this plan. Listed below are some of
the ideas proposed for gathering data. For each, indicate what kind of
sampling strategy is involved and what (if any) biases might result.
a) Run a poll on the local TV news, asking people to dial one of two
phone numbers to indicate whether they favor or oppose the plan.
This sampling method suffers from voluntary response
bias. Only those who see the show and feel strongly will
call.
Chapter 12 Part II Answers
12. In a large city school system with 20 elementary schools, the school
board is considering
the adoption of a new policy that would require elementary students to
pass a test in order to be promoted to the next grade. The PTA wants to
find out whether parents agree with this plan. Listed below are some of
the ideas proposed for gathering data. For each, indicate what kind of
sampling strategy is involved and what (if any) biases might result.
b) Hold a PTA meeting at each of the 20 elementary schools and tally the
opinions expressed by those who attend the meetings.
Although this method may result in a more representative
sample than the method in part a), this is still a voluntary
response sample. Only strongly motivated parents attend
PTA meetings.
Chapter 12 Part II Answers
12. In a large city school system with 20 elementary schools, the school
board is considering
the adoption of a new policy that would require elementary students to
pass a test in order to be promoted to the next grade. The PTA wants to
find out whether parents agree with this plan. Listed below are some of
the ideas proposed for gathering data. For each, indicate what kind of
sampling strategy is involved and what (if any) biases might result.
c) Randomly select one class at each elementary school and contact each
of those parents.
This is multistage sampling, stratified by elementary
school and then clustered by grade. This is a good design,
as long as the parents in the class respond. There should be
follow-up to get the opinions of parents who do not respond.
Chapter 12 Part II Answers
12. In a large city school system with 20 elementary schools, the school
board is considering
the adoption of a new policy that would require elementary students to
pass a test in order to be promoted to the next grade. The PTA wants to
find out whether parents agree with this plan. Listed below are some of
the ideas proposed for gathering data. For each, indicate what kind of
sampling strategy is involved and what (if any) biases might result.
d) Go through the district’s enrollment records, selecting every 40th
parent. PTA volunteers will go to those homes to interview the people
chosen.
This is systematic sampling. As long s a starting point is
randomized, this method should produce reliable data.
Chapter 12 Part II Answers
23. Anytime we conduct a survey we must take care to avoid
undercoverage. Suppose we plan to select 500 names form the city phone
book, call their homes between noon and 4p.m., and interview whoever
answers, anticipating contacts with at least 200 people.
a) Why is it difficult to use a simple random sample here?
A SRS is difficult in this case because there is an issue with
undercoverage. People with unlisted phone numbers and
those without phones are not in the sampling frame. People
who are at work, or otherwise away from home, are included
in the sampling frame. However, these people could never be
in the sample itself.
Chapter 12 Part II Answers
23. Anytime we conduct a survey we must take care to avoid
undercoverage. Suppose we plan to select 500 names form the city phone
book, call their homes between noon and 4p.m., and interview whoever
answers, anticipating contacts with at least 200 people.
b) Describe a more convenient, but still random, sampling strategy.
One possibility is to generate random phone numbers and
call at random times, although obviously not in the middle
of the night. This would take care of the undercoverage of
people at work during the day, as well as people with
unlisted numbers, although there is still a problem avoiding
undercoverage of people without phones.
Chapter 12 Part II Answers
23. Anytime we conduct a survey we must take care to avoid
undercoverage. Suppose we plan to select 500 names form the city phone
book, call their homes between noon and 4p.m., and interview whoever
answers, anticipating contacts with at least 200 people.
c) What kinds of households are likely to be included in the eventual
sample of opinion? Who will be excluded?
Under the original plan, those families in which one person
stays home are more likely to be included. Under the second
plan, many more are included. People without phones are
still excluded.
Chapter 12 Part II Answers
23. Anytime we conduct a survey we must take care to avoid
undercoverage. Suppose we plan to select 500 names form the city phone
book, call their homes between noon and 4p.m., and interview whoever
answers, anticipating contacts with at least 200 people.
d) Suppose, instead, that we continue calling each number, perhaps in the
morning or evening, until an adult is contacted and interviewed. How
does this improve the sampling design?
Follow-up of this type greatly improves the chance that a
selected household is included, increasing the reliability of
the survey.
Chapter 12 Part II
Answers
23. Anytime we conduct a survey we must take care to avoid
undercoverage. Suppose we plan to select 500 names form the city phone
book, call their homes between noon and 4p.m., and interview whoever
answers, anticipating contacts with at least 200 people.
e) Random digit dialing machines can generate the phone calls for us.
How would this improve our design? Is anyone still excluded?
Random dialers allow people with unlisted phone numbers to
be selected, although they may not be the most willing
participants. There is a reason that the phone number is
unlisted. Time of day will still be an issue, as will people
without phones.
Chapter 12 Part II Answers
28. A manufacturing company employs 14 project managers, 48
foremen, and 377 laborers. In an effort to keep informed about any
possible sources of employee discontent, management wants to conduct
job satisfaction interviews with a sample of employees every month.
a) Do you see any danger of bias in the company’s plan? Explain.
A small sample will probably consist mostly of laborers,
with few foremen, and maybe no project managers. Also,
there is a potential for response bias based on the interviewer
if a member of management asks directly about discontent.
Workers who want to keep their jobs will likely tell the
management that everything is fine.
Chapter 12 Part II Answers
28. A manufacturing company employs 14 project managers, 48
foremen, and 377 laborers. In an effort to keep informed about any
possible sources of employee discontent, management wants to conduct
job satisfaction interviews with a sample of employees every month.
b) Propose a sampling strategy that uses a simple random sample.
Assign a number 001 to 439 to each employee. Use a
random number table to select the sample.
Chapter 12 Part II
Answers
28. A manufacturing company employs 14 project managers, 48
foremen, and 377 laborers. In an effort to keep informed about any
possible sources of employee discontent, management wants to conduct
job satisfaction interviews with a sample of employees every month.
c) Why do you think a simple random sample might not provide the
representative opinion the company seeks?
Chapter 12 Part II
Answers
28. A manufacturing company employs 14 project managers, 48
foremen, and 377 laborers. In an effort to keep informed about any
possible sources of employee discontent, management wants to conduct
job satisfaction interviews with a sample of employees every month.
d) Propose a better sampling strategy.
A better strategy would be to stratify the sample by job type.
Sample a certain percentage of each job type.
Chapter 12 Part II Answers
28. A manufacturing company employs 14 project managers, 48
foremen, and 377 laborers. In an effort to keep informed about any
possible sources of employee discontent, management wants to conduct
job satisfaction interviews with a sample of employees every month.
e) Listed below are the last names of the project managers. Use random
numbers at the bottom to select two people to be interviewed. Be sure
Random Number Table
to explain your method carefully.
28914 26687 49104
01Barrett
06Bowman 11Chen
48827 42036
02DeLara
07DeRoos
12Grigorov
03Maceli
08Mulvaney 13Pagliarulo
04Rosica
09Smithson 14Tadros
05Williams 10Yamamoto
Use two-digits and Ignore 15-99 and 00
Base on these pre-assigned two-digit numbers and the random
number table shown
Yamamoto and Maceli would be selected.
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