Transcript sampling design

Sampling Design
Steps in Sampling Process
1.Define the population
2.Identify the sampling frame
3.Select a sampling design
4.Determine the sample size
5.Draw the sample
Sampling Design Process
Define Population
Determine Sampling Frame
Determine Sampling Procedure
Non-Probability Sampling
Type of Procedure
Convenience
Judgmental
Quota
Probability Sampling
Type of Procedure
Simple Random Sampling
Stratified Sampling
Cluster Sampling
Determine Appropriate
Sample Size
Execute Sampling
Design
Terminology
Population
The entire body of units of interest to decision makers
in a situation.
Element (sampling unit)
one unit from a population
Sampling
The selection of a subset of the population
Sampling Frame
Listing of population from which a sample is chosen
Census
A polling of the entire population
Survey
A polling of the sample
SAMPLING
• Census -- the entire population
– most useful is the population ("n") is small
– or the cost of making an error are high
• Sample -- contacting a portion of the
population (e.g., 10% or 25%)
– best with a very large population (n)
– easiest with a homogeneous population
Terminology
Parameter
The variable of interest
Statistic
The information obtained from the sample about the
parameter
Goal
To be able to make inferences about the population
parameter from knowledge of the relevant statistic - to
draw general conclusions about the entire body of units
Critical Assumption
The sample chosen is representative of the population
Population Vs. Sample
Population of Interest
Population
Sample
Parameter
Statistic
Sample
We measure the sample using statistics in order to draw
inferences about the population and its parameters.
Characteristics of Good Samples
• Representative
• Accessible
• Low cost
…this (bad)…
Sample
Population
…or this (VERY bad)…
Sample
Population
Define the Population
• It addresses the question “Ideally, who do
you want to survey?”
• It involves
– defining population units
– setting population boundaries
Steps in the Sampling Process
1. Define the “population”
The Element ......
individuals
families
seminar groups
sampling Unit….
individuals over 20
families with 2 kids
seminar groups at ”new” uni
Extent ............
individuals who have bought “one”
families who eat fast food
seminar groups doing MR
Timing .......... bought over the last seven days
The Target population for a toy store can
be defined as all households with
children living in Calgary.
What’s wrong with this definition?
Sampling Frame
• Obtaining a “list” of population (how to reach sample)
Students eat at Maconalds?
young people at random in the street?
‘phone book
students union listing
Uni. mailing list
• Problems with lists
– omissions
– ineligibles
– duplications
• Random digit dialing (RDD)
Select “sample units”

Individuals

Household

Streets

Telephone numbers

Companies
Selecting a Sampling Design
 Probability sampling
–
–
–
–
simple random sampling
systematic sampling
stratified sampling
cluster sampling
 Non-probability sampling
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–
–
–
convenience sampling
judgement sampling
snowball sampling
quota sampling
Probability Sampling
• An objective procedure in which the
probability of selection is nonzero and is
known in advance for each population unit.
• It is also called random sampling.
Simple Random Sampling (SRS)
• Population members are selected directly from
the sampling frame
• Equal probability of selection for every
member
• Use random number table or random number
generator
Simple Random Sampling
N = the number of cases in the
sampling frame
n = the number of cases in the
sample
NCn
= the number of combinations
(subsets) of n from N
f = n/N = the sampling fraction
Objective: To select n units out of N
such that each NCn has an equal
chance of being selected
Procedure: Use a table of random
numbers, a computer random number
generator, or a mechanical device to
select the sample
Systematic Sampling
• Order all units in the sampling frame based
on some variable and number them from 1 to
N
• Choose a random starting place from 1 to N
and then sample every k units after that
systematic random sample
number the units in the population
from 1 to N
decide on the n (sample size) that you
want or need
k = N/n = the interval size
randomly select an integer between 1
to k
then take every kth unit
Stratified Sampling (I)
• The chosen sample is forced to contain units from
each of the segments, or strata, of the population
• Steps:
– Population is divided into strata based on an
appropriate population characteristic.
– Simple random samples are then drawn from each
stratum.
Stratified Random Sampling
Stratified Sampling (II)
• Direct Proportional Stratified Sampling
– The sample size in each segment is proportional to the
segment size in the population
• Disproportional Stratified Sampling
– The sample size in each segment is NOT proportional
to the segment size in the population
– Used if
1) some segments are too small
2) some segments are more important than others
3) some segments are more diversified than others
Cluster Sampling
• Clusters of population units are selected at random
and then all or some randomly chosen units in the
selected clusters are studied.
• Steps:
– Population is divided into subgroups, or clusters.
Ideally, each cluster adequately represents the
population.
– A simple random sample of a few clusters is
selected.
– All or some randomly chosen units in the selected
clusters are studied.
cluster or area random sampling
divide population into
clusters (usually along
geographic boundaries)
randomly sample clusters
measure all units within
sampled clusters
When to use stratified sampling
• If primary research objective is to compare
groups
• Using stratified sampling may reduce sampling
errors
When to use cluster sampling
• If there are substantial fixed costs associated
with each data collection location
• When there is a list of clusters but not of
individual population members
Non-Probability Sampling
• Subjective procedure in which the
probability of selection for some
population units are zero or unknown
before drawing the sample.
Types of Non-Probability
Sampling (I)
• Convenience Sampling
– A researcher's convenience forms the basis
for selecting a sample.
• Judgement Sampling
– A researcher exerts some effort in selecting a
sample that seems to be most appropriate for
the study.
Types of Non-Probability
Sampling (II)
• Snowball Sampling
– Selection of additional respondents is based on
referrals from the initial respondents.
– Used to sample from low incidence or rare
populations.
• Quota Sampling
– The population is divided into cells on the basis of
relevant control characteristics.
– A quota of sample units is established for each cell.
– A convenience sample is drawn for each cell until
the quota is met.
(similar to stratified sampling)
Quota Sampling
Let us assume you wanted to interview tourists coming to a
community to study their activities and spending. Based on
national research you know that 60% come for
vacation/pleasure, 20% are VFR (visiting friends and relatives),
15% come for business and 5% for conventions and meetings.
You also know that 80% come from within the province. 10%
from other parts of Canada, and 10% are international. A total
of 500 tourists are to be intercepted at major tourist spots
(attractions, events, hotels, convention centre, etc.), as you
would in a convenience sample . The number of interviews
could therefore be determined based on the proportion a given
characteristic represents in the population. For instance, once
300 pleasure travellers have been interviewed, this category
would no longer be pursued, and only those who state that one
of the other purposes was their reason for coming would be
interviewed until these quotas were filled.
Alberta
Canada
International
Totals
Pleasure
.48
.06
.06
.60
Visiting
.16
.02
.02
.20
Business
.12
.015
.015
.15
Convention
.04
.005
.005
.05
Totals
.80
.10
.10
100
Probability Vs. NonProbability Sampling
• Non-probability sampling is less time
consuming and less expensive.
• Theoretically speaking, quantitative
generalizations about population can only be
done under probability sampling.
• However, in practice, marketing researchers
also apply statistics to study non-probability
samples.
The sampling process
1. Determine the target population
who are the people you want information on?
age, gender, product use
2. Determine the sampling frame
how will you get the names, phone numbers or
addresses?
– existing lists, phone book, random digit dialing
The sampling process
3. Select a sampling procedure:
A. Probability (random) sample
– equal chance of being included in the sample
– random number table, even-odd, etc.
B. Stratified
– equalizing "important" variables
• year in school, geographic area, product use, etc.
The sampling process
C. Nonprobability sampling
– convenience sample
• people in my classes
– "snowball" sample
• friends of friends
– "quota" sampling
• 50 women, 50 men
– mall intercepts
• Market Mall
Generalization
• You can only generalize to the population
from which you sampled
– U of L students not college students
• geographic, different majors, different jobs, etc.
– College students not Canadian population
• younger, poorer, etc.
– Canadians not people everywhere
• less traditional, more affluent, etc.
Drawing inferences from samples
• Population estimates
– % who smoke, buy your product, etc
• 25% of sample
• what % of population?
– very dangerous with a non-representative
sample or with low response rates
Drawing inferences from
samples
• Relationships
– e.g., exposure to ads and liking for the product
– relationships (qualitatively different)
– less dangerous with a non-representative sample
Errors in Survey
Sampling Error
– random error
– the level of it is controlled by sample size
– a larger sample size leads to a smaller
sampling error.
Non-sampling Error
– systematic Error
– the level of it is NOT controlled by sample size.
Non-Sampling Errors (I)
• The basic types of non-sampling error
– Non-response error
– Response or data error
• A non-response error occurs when units selected
as part of the sampling procedure do not respond
in whole or in part
– If non-respondents are not different from those that
did respond, there is no non-response error
Non-Sampling Errors (II)
• A response or data error is any systematic
bias that occurs during data collection,
analysis or interpretation
– Respondent error (e.g., lying, forgetting, etc.)
– Interviewer bias
– Recording errors
– Poorly designed questionnaires
Determine sample size
ze Everything?
Is Si
Typical Statistics estimate requires:
Population variance
Acceptable sample error
Level of confidence (coefficient of confidence)
Sample Confidence
“Probability” we can take results as “accurate
representation” of universe
(i.e. that “sample statistics” are generalisable to the real
“population parameters”)
Typically a 95% probability
(i.e. 19 times out of 20 we would expect results in this
range)
Example:
We can be 95% sure
that, say, 65%
of a target market
will name Martini’s “V2” vodka
in an unprompted recall test
plus or minus 4%
We can be 95% sure (level of confidence)
that, say, 65% (predicted result)
of a target market (of a given total population)
will name Martini’s “V2” vodka
in an unprompted recall test
plus or minus 4% (to a known margin of error)
95% confidence
If we do the same test 20 times then it is
statistically probable that the results will fall
between 61-69 %, at least 19 times
If we lower the probability then we lower the
sample error
e.g.. at a 90% confidence level, result might be
believe between 64% - 66%
(a tighter range but we are less sure the sample
is representative of the real population)
Sample Size Issues
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Accuracy
Resources / Budget
Time
Reachability
Statistical Analysis
Sub Group Size
Cost of research
sample
size
cost
Determining sample size
Balance between financial and statistical issues
1. What can I afford
2. Rule of thumb
past experience
historical precedence
gut feeling
some consideration of sample error
3. Make up of sub-groups (cells)
What statistical inferences do you hope make between sub groups
(rare to fall between 20 for a sub group)
4. Statistical Methods
Implications for sample size
(Given reliability and validity hold)
Above a certain size little extra information is
gathered by increasing the sample size.
Generally, there is no relationship between the size of a
population and the size of sample needed to estimate a
particular population parameter, with a particular
error range and level of confidence.
We can choose an error range (e.g. + 5%)
We can set a confidence level (e.g. 95%)
But
Without knowing the spread of results (i.e. the standard
deviation for the population) we cannot work out the
sample size required
So
If you need a statistical assessment, estimate spread of
responses (population variance /standard deviation)
with:
• pilot tests................
• guess......................
• previous experience
Sample Size Determination
• 3 Statistical Determinants of Sample Size
 DEGREE OF CONFIDENCE
– Statistical Confidence
– 95% Confidence or .05 Level of Significance

DEGREE OF PRECISION
– Accuracy in Estimating Population Proportion
–
+/- $5.00 versus +/- $1.00
–
+/- 10% versus +/- 5%

VARIABILITY IN THE POPULATION
– To What Degree do the Sampling Units Differ
Size
The tough question
?
Too big - it’s a waste of money
Too small - you cannot make a BI
G decision
Sample Size Determination
TO BE
MORE CONFIDENT
MORE PRECISE
IF MORE VARIABLE
SAMPLE SIZE MUST INCREASE