Ch 4 - Designing
Studies
I can identify the population and
sample in a survey.
• Population - the entire group of
individuals about which we want
information.
• Sample - the part of the population from
which we actually collect information.
Sample Survey
• 1st - determine what population we
want to describe
• 2nd - determine exactly what we want to
measure (define our variables)
• The student government at a high
school surveys 100 of the students at a
the school to get their opinions about a
change to the bell schedule.
• What’s the population? Sample?
• What was being studied?
I can understand two types of bias
in sampling.
• Bias - when the design on a study will
favor certain outcomes
• Convenience Sample - choosing
individuals who are easiest to reach
• Voluntary Response - when the sample
chooses themselves by responding to a
general appeal.
Why do each lead to bias?
Convenience
Bias
Voluntary
Response Bias
•
unrepresentative of the entire population because answer will be
influence by where you are.
•
i.e. if you are surveying how people feel about the library tax and only
ask people who are at the library
•
When you identify the bias - also state
only people with strongly opinions (in either direction) will respond.
IN WHICH DIRECTION!
So, what’s a good method?
• SRS - simple random sample - n
individuals chosen from a population in
such a way that every set of n
individuals has an equal chance to be in
the sample actually selected.
from this class?
• Ideas: put all names in a hat, on equally
sized slips of paper and select 4 of them
• Assign everyone a number and use a
Random Digit Table (Table D) to select
the four people
How to use Table D
1. assign every individual in the population a
digit.
2. the number of digits have to equal the number
of digits in the population
3. start with 0 (or 00 or 000...)
4. decide what to do if you get a repeated digit or
a digit not in the range you need
5. pick a line to start at and read consecutive
groups of digits to select your sample
Day 2
Other Sampling Methods
Stratified Random
Sample
Cluster Sample
•
first, divide the population into
smaller groups (mirror the
population)
• next, choose a separate SRS
from each stratum
•
next, choose an SRS of the
clusters
• combine all SRSs to form the
full sample
•
all individuals in each cluster are
included in the sample
• first, classify population into
similar groups (strata)
• groups are homogeneous - like
the math class you’re in
groups are heterogenous - like CLC
groups
•
A manager of a beach-front hotel wants to survey guests in the hotel
to estimate overall customer satisfaction. The hotel has two towers, an
older one to the south and a newer one to the north. Each tower has
10 floors of standard rooms (40 rooms per floor) and 2 floors of suites
(20 suites per floor). Half of the rooms in each tower face the beach,
while the other half of the rooms face the street. There are a total of
880 rooms.
•
a) Explain how to select a simple random sample of 88 rooms.
•
b) Explain how to select a stratified random sample of rooms.
•
c) Explain how to select a cluster of rooms.
•
d) Explain why selecting 2 of the 24 different floors would not be a
good way to obtain a cluster sample.
Advantages & Disadvantages
SRS
Advantage
Disadvantage
simple to carry out
chance of over- or underrepresenting in the
sample
each individual in the population has the same chance
to be selected
no chance of over- or under-representing
Stratified
each individual in the population still has the same
chance of being selected
can be convenient when groups are already “created”
Clustering
each individual in the population still has the same
chance of being selected
a little more complicated
to execute
chance of over- or underrepresenting in the
sample
A Sample Free Response
•
In response to nutrition concerns raised last year about food served in school
cafeterias, the Smallville School District entered into a one-year contract with
the Healthy Alternative Meals (HAM) company. Under this contract, the
company plans and prepares meals for 2,500 elementary, middle, and high
school students, with a focus on good nutrition. The school administration
would like to survey the students in the district to estimate the proportion of
students who are satisfied with the food under this contract.
•
Two sampling plans for selecting the students to be surveyed are under
consideration by the administration. One plan is to take a simple random
sample of students in the district and then survey those students. The other
plan is to take a stratified random sample of students in the district and then
survey those students.
•
(a) Describe a simple random sampling procedure that the administrators
could use to select 200 students from the 2,500 students in the district.
•
(b) If a stratified random sampling procedure is used, give one example of an
effective variable on which to stratify in this survey. Explain your reasoning.
Answers to part A
Answers to part B
Answers to part C
What type of sampling is this?
• At a party there are 30 students over age 21
and 20 students under age 21. You choose at
random 3 of those over 21 and separately at
random 2 of those under 21 to interview about
attitudes towards alcohol. You have given
every student at the party the same chance to
be interviewed.
• What is that chance?
• What type of sampling procedure was this?
HINT: an SRS will allow for
a sample to have all of a
certain “group” or none of a
“groups
• One the west side of Rocky Mountain National Park,
many mature pine trees are dying due to infestation
by pine beetles. Scientists would like to use
sampling to estimate the proportion of all pine trees
in the area that have been infested.
• Why would an SRS not be practical?
• Could they just sample the pines along the road?
• Suppose the sampling was carried out randomly
and accurately and 35% of the pine trees sampled
were infested. Can they conclude 35% of all pine
trees are infested?
Day 3
Inference and what can go
wrong?
Why do we sample?
• to infer about a population
• surveying a population takes too much time and
money!
Can we trust it?
• YES - the law of probability allows for random
sampling to work!
• there are margins of error to account for the variability
between the sample and the population. Nothing was
wrong with the procedure!
What can go wrong?
• There are different types of bias to cause
sampling to go wrong:
•
Sampling Errors
•
Nonsampling Errors
Sampling
Nonsampling
• Voluntary Response
• Convenience Sample
• Undercoverage
• (we already know about voluntary and convenience- see day 1 notes)
• Nonresponse
• Response Bias
Undercoverage
• when some groups in the population are
left out of the process when choosing
the sample
• Example: if you were to go to people’s
houses and survey about the
unemployment rate - you are leaving
out all the homeless people and those
who have jobs and are not home.
Nonresponse
• when an individual chosen for the
sample can’t be contacted or refuses to
participate
• the is not voluntary response bias,
these individuals were chosen to be in
the sample and do not want to be
Response Bias
• when the individual gives the wrong answer
• this can be due to many factors
•
people know what the answer should be and
give that
•
what the interviewer looks like can influence
the response
•
recalling past events
Wording of Questions
• the most important influence on the
responses given. Never trust a survey
unless you have seen the questions!
•
•
Order of the Questions
Any prompts/cues given before the
question
Ch 4 Project
•
by yourself or with a partner
•
You will design and conduct an experiment to investigate the effects
of response bias in surveys
•
You can choose the topic, but you must design your experiment to
answer one of the following questions:
1.
Can the wording of a questions create response bias?
2.
Do the characteristics of the interviewer create response bias?
3.
Does anonymity change the responses to sensitive questions?
4.
Does manipulating the answer choices change the response?
Ch 4 Project
• see page 267 for what is required
• I will hand out a rubric - USE IT!
• Not only are you going to analyze the survey
results, you will analyze if the way the survey
was conducted biased the results
• due: October 31, 2013 (approved by Friday,
October 19)
• One class day to work on it - Friday, Oct. 26