Download Probability Sampling and Sample Sizes

Chapter Nine
Sampling: Theory,
Designs and Issues in
Marketing Research
Copyright © 2006
McGraw-Hill/Irwin
Learning Objectives
1. Discuss the concept of sampling and list
reasons for sampling.
2. Identify and explain the different roles that
sampling plays in the overall information
research process.
3. Demonstrate the basic terminology used in
sampling decisions.
4. Understand the concept of error in the context
of sampling.
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Learning Objectives
5. Discuss and calculate sampling distributions,
standard errors, and confidence intervals and
how they are used in assessing the accuracy
of a sample.
6. Discuss the factors that must be considered
when determined sample size.
7. Discuss the methods of calculating appropriate
sample sizes.
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Value of Sampling in
Information Research
•
Discuss the concept of sampling
and list reasons for sampling
Sampling
•
Selection of a small number of elements from a
larger defined target group—information
gathered will allow judgments to be made about
the larger group
– Census
•
Includes data about every member of the
defined target population
– Sampling
•
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Used when it is impossible to conduct a
census of the population
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Value of Sampling in
Information Research
•
Identify and explain the different roles
that sampling plays in the overall
information research process
Role of Sampling
– Identifying, developing, and
understanding new marketing constructs
that need to be investigated
– Plays an indirect role in the design of the
questionnaire
– Enables the researchers to make
decisions using limited information
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Value of Sampling in
Information Research
•
Discuss the concept of sampling
and list reasons for sampling
Concept of Sampling
– Making the right decision in the selection
of items (i.e., people, products or
services)
– Feeling confident that data from the
sample can be transformed into accurate
information about the target population
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Overview: The Basics
of Sampling Theory
•
Discuss the concept of sampling
and list reasons for sampling
Basic Sampling Terminology
– Population
•
Defined target population
– Element
–
–
–
–
Must be unique
Must be countable
Target population
Identify correctly
– Sampling Units
– Sampling Frames
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Overview: The Basics
of Sampling Theory
•
Discuss the concept of sampling
and list reasons for sampling
Main Factors Underlying Sampling
Theory
– Sampling Discussions
– Logic Behind this Perspective
– Important Assumption
•
•
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Probability distribution
Sampling distribution
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Exhibit 9.2
McGraw-Hill/Irwin
Discuss the concept of sampling
and list reasons for sampling
9
Exhibit 9.3
McGraw-Hill/Irwin
Discuss the concept of sampling
and list reasons for sampling
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Overview: The Basics
of Sampling Theory
•
Discuss the concept of sampling
and list reasons for sampling
Central Limit Theorem
– for almost all target populations the
sampling distribution of the sample mean
or the percentage value derived from a
simple random sample will be
approximately normally distributed,
provided that the sample size is
sufficiently large ( i.e., when n is ≥ 30)
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Overview: The Basics
of Sampling Theory
•
Discuss the concept of sampling
and list reasons for sampling
With an understanding the basics of the central limit theorem,
the researcher can:
–
Draw representative samples from any target population
–
Obtain sample statistics from a random sample that serve as
accurate estimate of the target population’s parameters
–
Draw one random sample instead of many, reducing the costs
of data collection
–
Test more accurately the reliability and validity of constructs
and scale measurements
–
Statistically analyze data and transform them into meaningful
into meaningful information about the target population.
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Overview: The Basics
of Sampling Theory
•
Understand the concept of error in
the context of sampling
Types of Errors
•
Classified as being either sampling
or non-sampling
– Random sampling errors
– Sampling Error
•
Any type of bias that is attributable to
mistakes in either drawing a sample or
determining sample size
– Central Limit Theorem—sampling error can be
reduced by increasing the size of the sample
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Exhibit 9.4
McGraw-Hill/Irwin
Discuss the concept of sampling
and list reasons for sampling
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Overview: The Basics
of Sampling Theory
•
Understand the concept of error in
the context of sampling
Nonsampling Error
– A bias that occurs in a research study
regardless of whether a sample or
census is used
•
•
•
•
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Population frame error
Measurement error
Response error
Errors in gathering and recording data
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Overview: The Basics
of Sampling Theory
•
Discuss and calculate sampling
distributions, standard errors, and
confidence intervals
Statistical Precision
– Critical Level of Error
– General Precision
– Precise Precision
•
Estimated standard Error
– Measure of the sampling error and an
indication of how far the sample result
lies from the actual target population
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Estimating Standard Error-General Precision
Sx s/ n
[( p)(q )]
Sp 
n
• Standard error of the sample mean=Estimated standard
deviation of the sample mean divided by the square root
of the Sample size
• Standard error of the sample percentage value
= square root of [(the % of the sample possessing the
characteristic times the % of the sample NOT possessing
the characteristic) divided by the Sample size]
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Estimating Standard Error-General Precision
Sx s/ n
•
•
•
•
•
•
•
[( p)(q )]
Sp 
n
A) Calculate the Standard error for the sample mean if 900 people were interviewed
with a estimated sample deviation of 12.5
The sample mean was 36
B) Calculate the Standard error of sample percentage if 65% of the sample of 489
people have VCR’s q=(100-p)
The sample proportion was
A) = +- .406
B) = +- 2.16%
We can then use estimated standard error to construct a confidence interval
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Confidence Interval
•
Confidence Interval
–
Statistical range of values within which the true
value of the defined target population parameter
is expected to be
_
-
Confidence Intervals
range from almost zero to almost 100 percent,
but the most commonly used confidence levels
are the 90, 95, and 99 percent levels
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Confidence Interval for population
mean and proportions
CI   x  ( Sx )( ZB, CL )
CI p  p  ( Sp )( ZB, CL )
•
•
•
•
•
Critical Z Value for 90% is 1.65, 95% is 1.96, 99% is 2.58
Calculate the Confidence interval for the population mean if the sample
mean is 25 and the Standard error of the sample mean is 2 with a 90%
confidence level
Answer = 25 +- 3.3
Calculate the Confidence interval for a population proportion if the sample
proportion is 75% and the Estimated standard error of the sample
proportion is 5% with a confidence level of 95%
75% +- 9.8%
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Probability Sampling and Sample Sizes
• Determining Sample Size
– 3 Factors in Determining Sample Sizes
• Variability of the population characteristic under
investigation
 u or  p
• Standard deviation
• Level of confidence desired in the estimate
• Degree of precision desired in estimating the population
characteristic
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Probability Sampling
and Sample Sizes
Discuss the methods of calculating
appropriate sample size
• When estimating a population mean
n = (Z2B,CL)(σ2/e2)
• When estimates of a population proportion are
of concern
n = (Z2B,CL)([P x Q]/e2)
Estimate the sample size having a 95% confidence
level, a estimate population standard deviation of
5 and a 3% tolerance level of error
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Probability Sampling
and Sample Sizes
Discuss the methods of calculating
appropriate sample size
• There is a direct relationship between the desired CL
(90% 95%, 99%) and the require sample size
– CL are directly associated with corresponding
critical z-values
– The higher the level of confidence required the
larger the sample size
• Acceptable tolerance level of error—amount of
precision desired (2%, 5%, or 10%)
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Probability Sampling
and Sample Sizes
Discuss the methods of calculating
appropriate sample size
• Sample Size
– Not a product of the population size, it is
not a direct factor in determining sample
size
• Finite Correction Factor
• Should be used if the sample size is
greater than 5% of the population
_
FCF = √N-n/N-1
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Probability Sampling
and Sample Sizes
Discuss the methods of calculating
appropriate sample size
1.
Determine if the sample size is more than 5% of the
population by taking the calculated sample size and
dividing it by the known defined target population size
2.
If it is, then calculate the appropriate finite correction
factor and multiply the originally calculated sample size
by it to adjust the required sample size
3.
If the target population size is ≤500 should consider
doing a census
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Sample Sizes Versus
Usable Observations for
Data Analysis
Discuss the methods of calculating
appropriate sample size
• Sample Size
– Researchers can estimate the number of sampling
units that must be surveyed
• Not all initial responses are usable
– Inactive mailing addresses
– Telephone number no longer in service
– Incomplete responses
– Factors to consider in drawing a sample
• Reachable rate RR
• Who is qualified to be included in the survey Overall
Incidence Rate OIR
• Expected completion rate ECR
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Calculating the Number of Contacts
n
Number of Contacts 
( RR) * (OIR) * ( ECR)
• Calculate the number of contacts you require if need a
sample 1500 students but only 90% answer the phone
and you have determine that 20% of students are taking
marketing and do not qualify. Finally you estimate that
only 90% will answer all the questions in the survey.
• Number of Contacts is 2315
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Summary
•
•
•
•
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Value of Sampling in Marketing Research
Overview: The Basics of Sampling Theory
Probability Sampling and Sample Sizes
Nonprobability Sampling and Sample Size
Sample Sizes versus Usable Observations
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