Title: Sampling Design
1 2How do we gather data?
- Surveys
- Opinion polls
- Interviews
- Studies
- Observational
- Retrospective (past)
- Prospective (future)
- Experiments
3Population
- the entire group of individuals that we want
information about
4Census
- a complete count of the population
5How good is a census?Do frog fairy tale . . .
The answer is 83!
6Why would we not use a census all the time?
- Not accurate
- Very expensive
- Perhaps impossible
- If using destructive sampling, you would destroy
population - Breaking strength of soda bottles
- Lifetime of flashlight batteries
- Safety ratings for cars
Look at the U.S. census it has a huge amount of
error in it plus it takes a long time to compile
the data making the data obsolete by the time we
get it!
Suppose you wanted to know the average weight of
the white-tail deer population in Texas would
it be feasible to do a census?
Since taking a census of any population takes
time, censuses are VERY costly to do!
7Sample
- A part of the population that we actually examine
in order to gather information - Use sample to generalize to population
8Sampling design
- refers to the method used to choose the sample
from the population
9Sampling frame
- a list of every individual in the population
10Random Rectangles
- Estimate the average area of the rectangles
11Judgmental Sample
12Simple Random Sample (SRS)
Suppose we were to take an SRS of 100 THS
students put each students name in a hat.
Then randomly select 100 names from the hat.
Each student has the same chance to be selected!
Not only does each student have the same chance
to be selected but every possible group of 100
students has the same chance to be selected!
Therefore, it has to be possible for all 100
students to be juniors in order for it to be an
SRS!
- consist of n individuals from the population
chosen in such a way that - every individual has an equal chance of being
selected - every set of n individuals has an equal chance of
being selected
13Stratified random sample
Homogeneous groups are groups that are alike
based upon some characteristic of the group
members.
Suppose we were to take a stratified random
sample of 100 THS students. Since students are
already divided by grade level, grade level can
be our strata. Then randomly select 50 juniors
and randomly select 50 seniors.
- population is divided into homogeneous groups
called strata - SRSs are pulled from each strata
14Systematic random sample
Suppose we want to do a systematic random sample
of THS students - number a list of
students (There are approximately 2000 students
if we want a sample of 100, 2000/100 20) Select
a number between 1 and 20 at random. That
student will be the first student chosen, then
choose every 20th student from there.
- select sample by following a systematic approach
- randomly select where to begin
15Cluster Sample
Suppose we want to do a cluster sample of THS
students. One way to do this would be to
randomly select 10 classrooms during 2nd period.
Sample all students in those rooms!
- based upon location
- randomly pick a location sample all there
16Multistage sample
To use a multistage approach to sampling THS
students, we could first divide 2nd period
classes by level (AP, Honors, Advanced, etc.) and
randomly select 4 second period classes from each
group. Then we could randomly select 5 students
from each of those classes. The selection
process is done in stages!
- select successively smaller groups within the
population in stages - SRS used at each stage
17SRS
- Disadvantages
- Large variance
- May not be representative
- Must have sampling frame (list of population)
18Stratified
- Advantages
- More precise unbiased estimator than SRS
- Less variability
- Cost reduced if strata already exists
- Disadvantages
- Difficult to do if you must divide stratum
- Formulas for SD confidence intervals are more
complicated - Need sampling frame
19Systematic Random Sample
- Advantages
- Unbiased
- Ensure that the sample is distributed across
population - More efficient, cheaper, etc.
- Disadvantages
- Large variance
- Can be confounded by trend or cycle
- Formulas are complicated
20Cluster Samples
- Advantages
- Unbiased
- Cost is reduced
- Sampling frame may not be available (not needed)
- Disadvantages
- Clusters may not be representative of population
- Formulas are complicated
21Convenience Sample
- Advantages
- Sample individuals who are convenient
- Convenience
- Disadvantages
- Not representative of population
- Considered a bad sampling method
22Judemental Sample
- Advantages
- The approach is well understood and has been
refined by experience over many years - The auditor is given an opportunity to bring his
judgement and expertise into play.
- Disadvantages
- It is unscientific
- It is wasteful and usually too large samples are
selected - You cannot extrapolate the results to the
population as a whole as the samples are not
representative - Personal bias in selecting the sample is
unavoidable
23Identify the sampling design
- 1)The Educational Testing Service (ETS) needed a
sample of colleges. ETS first divided all
colleges into groups of similar types (small
public, small private, etc). Then they randomly
selected 3 colleges from each group.
Stratified random sample
24Identify the sampling design
- 2) A county commissioner wants to survey people
in her district to determine their opinions on a
particular law up for adoption. She decides to
randomly select blocks in her district and then
survey all who live on those blocks.
Cluster sampling
25Identify the sampling design
- 3) A local restaurant manager wants to survey
customers about the service they receive. Each
night the manager randomly chooses a number
between 1 10. He then gives a survey to that
customer, and to every 10th customer after them,
to fill it out before they leave.
Systematic random sampling
26Bias
- ERROR
- favors certain outcomes
Anything that causes the data to be wrong! It
might be attributed to the researchers, the
respondent, or to the sampling method!
27Sources of Bias
- things that can cause bias in your sample
- cannot do anything with bad data
28Voluntary response
- People chose to respond
- Usually only people with very strong opinions
respond
An example would be the surveys in magazines that
ask readers to mail in the survey. Other
examples are call-in shows, American Idol,
etc. Remember, the respondent selects themselves
to participate in the survey!
Remember the way to determine voluntary
response is Self-selection!!
29Convenience sampling
The data obtained by a convenience sample will be
biased however this method is often used for
surveys results reported in newspapers and
magazines!
- Ask people who are easy to ask
- Produces bias results
An example would be stopping friendly-looking
people in the mall to survey. Another example is
the surveys left on tables at restaurants - a
convenient method!
30Undercoverage
- some groups of population are left out of the
sampling process
Suppose you take a sample by randomly selecting
names from the phone book some groups will not
have the opportunity of being selected!
31Nonresponse
Because of huge telemarketing efforts in the past
few years, telephone surveys have a MAJOR problem
with nonresponse!
- occurs when an individual chosen for the sample
cant be contacted or refuses to cooperate - telephone surveys 70 nonresponse
People are chosen by the researchers, BUT refuse
to participate. NOT self-selected! This is
often confused with voluntary response!
One way to help with the problem of nonresponse
is to make a follow-up contact with the people
who are not home when you first contact them.
32Response bias
Suppose we wanted to survey high school students
on drug abuse and we used a uniformed police
officer to interview each student in our sample
would we get honest answers?
- occurs when the behavior of respondent or
interviewer causes bias in the sample - wrong answers
Response bias occurs when for some reason
(interviewers or respondents fault) you get
incorrect answers.
33Wording of the Questions
The level of vocabulary should be appropriate for
the population you are surveying
Questions must be worded as neutral as possible
to avoid influencing the response.
- wording can influence the answers that are given
- connotation of words
- use of big words or technical words
34Source of Bias?
1) Before the presidential election of 1936, FDR
against Republican ALF Landon, the magazine
Literary Digest predicting Landon winning the
election in a 3-to-2 victory. A survey of 10
million people. George Gallup surveyed only
50,000 people and predicted that Roosevelt would
win. The Digests survey came from magazine
subscribers, car owners, telephone directories,
etc.
Undercoverage since the Digests survey comes
from car owners, etc., the people selected were
mostly from high-income families and thus mostly
Republican! (other answers are possible)
352) Suppose that you want to estimate the total
amount of money spent by students on textbooks
each semester at SMU. You collect register
receipts for students as they leave the bookstore
during lunch one day.
Convenience sampling easy way to collect
data or Undercoverage students who buy books
from on-line bookstores are included.
363) To find the average value of a home in Plano,
one averages the price of homes that are listed
for sale with a realtor.
Undercoverage leaves out homes that are not for
sale or homes that are listed with different
realtors. (other answers are possible)
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