CHAPTER 5: DATA COLLECTION AND
SAMPLING
Outline
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Population and sample
Sources of data
Sampling
Sampling plans
– Simple random sampling
– Stratified random sampling
– Cluster sampling
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POPULATION AND SAMPLE
• Parameter: summary measure about population, usually
unknown or known from some published sources
• Statistic: summary measure about sample
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SOURCES OF DATA
• Primary data:
– Data published (in printed form, on data tapes, disks,
and internet) the same organization that collected data
– Some government agencies:
http://www.census.gov/
http://www.statcan.ca/
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Sample data available from the Statistics Canada website
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Sample data available from the Statistics Canada website
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SOURCES OF DATA
• Secondary data:
– Data published by an
organization different
from the one that
originally collected
and published the
data
– A popular source of
the secondary data is
the Statistical Abstract
of the United States
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SOURCES OF DATA
• Observational and experimental studies:
– Observational study: data is collected and recorded
without controlling any factor like it is done in an
experimental study
– experimental study: if more than one factor may cause
the same outcome, it may be desirable to vary one
factor at a time and control (keep unchanged) the other
factors e.g.,
• aircraft primer paints are applied to improve finished
paint adhesion force which depends on
– primer application method: dripping and spraying
– type of primer paint: type 1, 2, 3
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SOURCES OF DATA
• an experiment was designed in which
– three specimens were painted with each primer
using each application method, a finish paint was
applied, and the adhesion force was measured.
The resulting data are shown below:
Adhesion Force Data
Primer Type
Dipping
1
4.0, 4.5, 4.3
2
5.6, 4.9, 5.4
3
3.8, 3.7, 4.0
Spraying
5.4, 4.9, 5.6
5.8, 6.1, 6.3
5.5, 5.0, 5.0
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SOURCES OF DATA
• Surveys:
– Personal interview
– Telephone interview
– Questionnaire survey
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SAMPLING
• Target population
– The population about which inference is desired
• Sampled population
– The actual population about which the sample has
been taken
• Self-selected samples
– The responders mail/call responses
– Such samples are usually biased
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SAMPLING PLANS
• Simple random sampling
• Stratified random sampling
• Cluster sampling
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SIMPLE RANDOM SAMPLING
• Suppose we have data about the annual incomes of 40
families in a spreadsheet file RANDSAMP.XLS.
• We want to choose a simple random sample of size 10
from this frame.
• How can this be done?
• And how do summary statistics of the chosen families
compare to the corresponding summary statistics of the
population?
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SIMPLE RANDOM
SAMPLING
The family income data
are shown on right
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SIMPLE RANDOM SAMPLING
• A simple random sample is a sample in which the
sampling units are chosen from the population by means
of a random mechanism such as a random number table
so that every possible sample with the same number of
observations is equally likely to be chosen.
• For example, let sample 1 consist of families 1, 2, 3, 4, 5,
6, 7, 8, 9, 10 and sample 2 consist of families 1, 2, 3, 4, 5,
6, 7, 8, 9, 11. If a simple random sample is chosen, then
Samples 1 and 2 will be equally likely to be chosen.
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SIMPLE RANDOM SAMPLING
• Solution: The idea is very simple. We first generate a
column of random numbers in column C. Then we sort the
rows according to the random numbers and choose the
first 10 families in the sorted rows.
• The following procedure produces the results.
– Random numbers. Enter the formula =RAND() in cell
C10 and copy it down column C.
– Replace with values. To enable sorting we must
“freeze” the random numbers - that is, replace their
formulas with values. To do this, select the range
C10:C49 use Edit/Copy and then use Edit/Paste
Special with the Values option.
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SIMPLE RANDOM SAMPLING
– Copy to a new range. Copy the range A10:C49 to the
range E10:G49.
– Sort. Select the range E10:G49 and use the Data/Sort
menu item. Sort according to the Random # column in
ascending order. Then the 10 families with the 10
smallest random numbers are the ones in the sample.
– Means. Use the AVERAGE, MEDIAN and STDEV
functions in row 6 to calculate summary statistics of the
first 10 incomes in column F.
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SIMPLE RANDOM
SAMPLING
The result of all the
operations are shown
on right
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STRATIFIED RANDOM SAMPLING
• Suppose we can identify various sub-populations within
the total population. We call these sub-populations strata.
• It makes sense to select a simple random sample from
the stratum instead of from the entire population. This is
called stratified sampling.
• This method is particularly useful when there is
considerable variation between the various strata but
relatively little variation within a given stratum.
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STRATIFIED RANDOM SAMPLING
• To obtain a stratified random sample we must choose a
total sample size n, and we must choose a sample size ni
for each stratum i.
• There are many ways to choose these numbers but the
most popular method is proportional sample sizes.
• The advantage of proportional sample sizes is that they
are very easy to determine. The disadvantage is that they
ignore differences in variability among the strata.
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STRATIFIED RANDOM SAMPLING
• Sears has data on all 1000 people in the city of Smalltown
who have Sears credit cards.
• Sears is interested in estimating the average number of
other credit cards these people own, as well as other
information about their use of credit.
• The company decides to stratify these customers by age,
select a stratified sample of size 100 with proportional
sample sizes, and then contact these 100 people by
phone.
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STRATIFIED RANDOM SAMPLING
• First, Sears must decide exactly how to stratify by age.
• The reasoning is that different age groups probably have
different attitudes and behavior regarding credit.
• After preliminary investigation they decide to have three
age categories: 18-30, 31-62, and 63-80.
• Number of customers in each category are as follows:
Category
Number of Customers
18 to 30
132
31 to 62
766
63 to 80
102
1000
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STRATIFIED RANDOM SAMPLING
• In a stratified random sampling with proportional sample
sizes, the total sample size of 100 is distributed in 3
categories as follows:
Category
Number of Customers
Sample Size
18 to 30
132
132*100/100013
31 to 62
766
766*100/100077
63 to 80
102
102*100/100010
1000
100
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CLUSTER SAMPLING
• Suppose a company is interested in various
characteristics of households in a particular city. The
sampling units are households.
• We could proceed with the sampling methods discussed
but it would be more convenient another way.
• We could divide the city into city blocks as sampling units
and then sample all the households in the chosen blocks.
• In this case the city blocks are called clusters and the
sampling is called cluster sampling.
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CLUSTER SAMPLING
• The advantage of cluster sampling is sampling
convenience (and possibly less cost).
• It is straightforward to select a cluster sample. The key is
to define the sampling units as the clusters, then select a
simple random sample of clusters. Then sample all the
population members in each selected cluster.
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