第 5章 抽样技术
Sampling Technology
一、基本抽样问题
? 基本概念
? 制定抽样计划的步骤
? 抽样误差与非抽样误差
? 概率抽样方法
? 非概率抽样方法
本节概要（ 1）
? To understand the concept of sampling.
? To learn the steps in developing a sampling
plan.
? To understand the differences between
probability samples and nonprobability
samples.
? To understand the concepts of sampling
error and nonsampling error.
本节概要（ 2）
? To review the types of probability sampling
methods.
? To gain insight into nonprobability
sampling methods.
基本概念
? Population（总体）
– The total group of people from whom
information is needed.
? Census（普查）
– Data obtained from or about every member of
the population of interest.
? Sample（样本）
– A subset of the population of interest.
Steps in Developing a Sample Plan
设计一个抽样方案的步骤
Step 1,Define the
Population of
Interest
Step 2,Choose
Data Collection
Method
Step 3,Choose
Sampling Frames
Step 4,Select a
Sampling Method
Step 5,Determine
Sample Size
Step 6,Develop and
Specify Operational
Plan
Step 7,Execute
Operational Sampling
Plan
Steps in Developing a Sampling Plan
（ 1）
? Step 1,Defining the Population of Interest
– Bases for defining the population of interest
include,
? Geography
? Demographics
? Use
? Awareness
Steps in Developing a Sampling Plan
（ 2）
? Step 2,Choosing a Data Collection Method
– The selection of a data collection method has
implications for the sampling process.
? Step 3,Choosing a Sampling Frame
– Sampling frame
? List of population elements from which to select
units to be sampled.
Steps in Developing a Sampling Plan
（ 3）
? Step 4,Selecting the Sampling Method
– Probability samples
? Samples in which every element of the population
has a known,nonzero probability of selection.
– Nonprobability samples
? Include the selection of specific elements from the
population in a nonrandom manner.
Steps in Developing a Sampling Plan
（ 4）
? Step 4,Selecting the Sampling Method
(continued)
– Sampling error,The difference between the
sample value and the true value of the
population mean.
Steps in Developing a Sampling Plan
（ 5）
Advantages of
probability samples
Disadvantages of
probability samples
- The researcher can be sure of
obtaining information from a
representative cross section of the
population of interest.
- Sampling error can be computed.
- The survey results are projectable
to the total population,
- They are more expensive than
nonprobability samples of the
sample size in most cases,The
rules for selection increase
interviewing costs and professional
time must be spent in developing
the sample design,
- Probability samples take more time
to design and execute than non-
probability samples.
Steps in Developing a Sampling Plan
（ 6）
Advantages of
nonprobability samples
Disadvantages of
nonprobability samples
- Nonprobability samples cost less
than probability samples,This
characteristic of nonprobability
samples may have considerable
appeal in those situations where
accuracy is not of critical
importance.
- Nonprobability samples ordinarily
can be conducted more quickly
than probability samples.
- Sampling error cannot be computed.
- The researcher does not know the
degree to which the sample is
representative of the population
from which it was drawn.
- The results of nonprobability
samples cannot and should not be
projected to the total population.
Steps in Developing a Sampling Plan
（ 7）
? Step 5,Determine Sample Size
– Once the sampling method has been chosen,the
next step is to determine the appropriate sample
size.
? Step 6,Developing Operational Procedures
for Selecting Sample Elements
– Involves determining whether a probability or
nonprobability sample is being used.
Steps in Developing a Sampling Plan
（ 8）
? Step 7,Execution of the Sampling Plan
– The final step in the sampling process involves
execution of the operational sampling plan
discussed in the previous steps.
– It is important that this step include adequate
checking to make sure that specified procedures
are adhered to.
Classification of Sampling Methods
抽样方法分类
Sampling
Methods
Probability
Samples
Simple
RandomCluster
Systematic Stratified
Non-
probability
QuotaJudgment
Convenience Snowball
Probability Sampling Methods
概率抽样
? Simple Random Sampling（ 简单随机抽样 ）
– Is considered to be the purest form of
probability sampling,A probability sample is a
sample in which every element of the
population has a known and equal probability
of being selected into the sample.
Probability of Selection =
Sample Size
Population Size
Probability Sampling Methods
? Systematic Sampling（系统抽样）
– Probability sampling in which the entire
population is numbered,and elements are
drawn using a skip interval.
Skip Interval =
Population Size
Sample Size
Probability Sampling Methods
? Stratified Samples（分层抽样）
– Stratified samples are probability samples that
are distinguished by the following procedural
steps:
? First,the original or parent population is divided
into two or more mutually exclusive and exhaustive
subsets (e.g.,male and female).
? Second,simple random samples of elements from
the two or more subsets are chosen independently
from each other.
Probability Sampling Methods
? Cluster Samples（整群抽样）
– In the case of cluster samples,the sampling
units are selected in groups,There are two basic
steps in cluster sampling:
? First,the population of interest is divided into
mutually exclusive and exhaustive subsets.
? Second,a random sample of the subsets is selected.
Nonprobability Sampling Methods
非概率抽样方法
? Convenience Samples（便利样本）
– Nonprobability samples used primarily because
they are easy to collect.
? Judgment Samples（判断样本）
– Nonprobability samples in which the selection
criteria are based on personal judgment that the
element is representative of the population
under study.
Nonprobability Sampling Methods
? Quota Samples（配额样本）
– Nonprobability samples in which population
subgroups are classified on the basis of
researcher judgment.
? Snowball Samples（滚雪球样本）
– Nonprobability samples in which selection of
additional respondents is based on referrals
from the initial respondents.
本节小结（ 1）
? The population,or universe,is the total
group of people in whose opinions one is
interested.
? A census involves collecting desired
information from all the members of the
population of interest.
? A sample is simply a subset of a population.
本节小结（ 2）
? Probability sampling methods are selected
in such a way that every element of the
population has a known,nonzero
probability of selection.
? Nonprobability sampling methods include
all methods that select specific elements
from the population in a nonrandom
manner.
? 确定概率抽样的样本容量
? 确定样本容量的方法
? 抽样分布
二、确定样本含量
本节概要（ 1）
? To learn the financial and statistical issues
in the determination of sample size.
? To discover the methods for determining
sample size.
? To gain an appreciation of a normal
distribution.
本节概要（ 2）
? To understand population,sample,and
sampling distribution.
? To distinguish between point and interval
estimates.
? To recognize problems involving sampling
means and proportions,
Determining Sample Size for Probability Samples
确定概率抽样的样本容量
The process of determining sample size for
probability samples involves financial,statistical,
and managerial issues,Other things being equal,the
larger the sample,the less the sampling error,
Methods for Determining Sample Size
确定样本容量的方法
Budget Available
可支配预算
Rules of Thumb
单凭经验的做法
Number of
Subgroups to be
Analyzed
Often,sample size
for a project is
determined,at least
indirectly,by the
budget available
At times,the size of
a sample may boil
down to the use of
some type of rule of
thumb or a feel
Serious
consideration must
be given to the
number and
anticipated size of
various subgroups
of the total sample
Traditional Statistical Methods
传统的统计方法
Pieces of information required to make the necessary
calculations when using a sample result:
The desired level of
confidence that
the sample result
will fall within a
certain range
(result plus or minus
sampling error) of true
population value
An estimate of
the population
standard deviation
总体标准差估计
The acceptable
level of sampling
error
抽样的容许误差水平
The Normal Distribution
正态分布
? General Properties(一般特征 )
– The normal distribution is a continuous
distribution that is bell shaped and symmetrical
about the mean - mean,median,and mode are
equal,Sixty-eight percent of the observations
fall within plus or minus one standard deviation
of the mean,approximately 95 percent fall
within plus or minus two standard deviations,
and approximately 99.5 percent fall within plus
or minus three standard deviations.
The Normal Distribution
? 为什么要重视正态分布？
– First,many variables encountered by marketers
have probability distributions that are close to
the normal distribution.
– Second,the normal distribution is useful for a
number of theoretical reasons; one of the more
important of these relates to the central limit
theorem.
The Normal Distribution
? Central Limit Theorem（中心极限定理）
– A distribution of a large number of sample
means or sample proportions will approximate
a normal distribution regardless of the actual
distribution of the population from which they
were drawn.
– Standard Normal Distribution
? A normal distribution with a mean of zero and a
standard deviation of one.
Population,Sample,and Sampling Distribution
总体、样本与抽样分布
? Population Distribution（总体分布）
– A population distribution is a frequency
distribution of all of the elements of the
population.
? Sample Distribution（样本分布）
– A sample distribution is a frequency
distribution of all the elements of the
population.
Population,Sample,and Sampling
Distribution
? Sampling Distribution of the Sample Mean
（样本均数的抽样分布）
– A frequency distribution of the means of many
samples drawn from a particular population,It
is normally distributed.
Sampling Distribution of the Mean
? Standard Deviation（标准差）
– A measure of dispersion calculated by
subtracting the mean of a series from each
value in the series,squaring each result,
summing them,dividing the sum by the number
of items minus 1,and taking the square root of
this value.
– Standard Error of the Mean
（均数标准误）
? The standard deviation of a distribution of sample
means.
Sampling Distribution of the Mean
? Making Inference on the Basis of a Single
Sample（单样本的简单推断）
– Point Estimates（ 点估计 ）
? Inferences regarding the sampling error associated
with a particular estimate of a population value.
– Interval Estimates（区间估计）
? Inferences regarding the likelihood that a population
value will fall within a certain range.
Sampling Distribution of the Mean
? Making Inference on the Basis of a Single
Sample
– Confidence Level（置信水平）
? The probability that a particular confidence interval
will include the true population.
Sampling Distribution of the Proportion
比例的抽样分布
? General Properties（一般特征）
– A frequency distribution of the proportions of
many samples drawn from a particular
population,It is normally distributed.
? Preferences
– Marketing researchers have a tendency to prefer
dealing with sample size problems as problems
of estimating proportions rather than means.
Sample Size Distributions
样本容量的分布
? Problems Involving Means（ 均数估计的问题 ）
– The level of confidence (Z) and the amount of
error (E) to be used in calculating the required
sample size must be set by the researcher.
– In designing a sampling procedure,an
acceptable trade-off between accuracy,level of
confidence,and cost must be evaluated.
– The population standard deviation must be
estimated.
Sample Size Distributions
? Problems Involving Proportions
– The level of confidence (Z) and the amount of
error (E) to be used in calculating the required
sample size must be set by the researcher.
– Advantages Involving Proportions
? If there is no basis for estimating P,you can make
what is sometimes referred to as the most
pessimistic or worse case assumption regarding the
value of P.
Statistical Power
统计效能
? Type I Error（ I型错误）
– The error of concluding that there is a
difference when there is not a difference.
? Type II Error（ II型错误）
– The error of saying there is no difference when
there actually is a difference.
? Power（效能）
– The probability of not making a Type II error is
called power.
Power Example
Sample Size Required to Detect Differences Between Proportions from
Independent Samples at Different Levels of Power and Alpha Levels
Difference
to Detect Power
50 % 90 %80 %75 %70 %60 %
0.01
0.05
0.10
0.15
19,205
766
190
83
52,53039,23934,69730,85724,491
2,0941,5681,3841,231977
518389343305242
226169150133106
本节小结（ 1）
? Determining sample size involves financial,
statistical,and managerial considerations,
Other things being equal,the larger the
sample the less the sampling error.
? In turn,the cost of research grows with the
size of the sample.
本节小结（ 2）
? There are a number of traditional statistical
techniques for determining sample size.
? Crucial to statistical sampling theory is the
concept of the normal distribution.
? Power is the probability of not making a
Type II error,A Type II error is the mistake
of saying there is not a difference when
there is a difference.
本节小结（ 3）
? The standard deviation of a distribution of
sample means is called the standard error of
the mean.
? A researcher who is interested in estimating
proportions rather than means uses the
sampling distribution of the proportion.
Sampling Technology
一、基本抽样问题
? 基本概念
? 制定抽样计划的步骤
? 抽样误差与非抽样误差
? 概率抽样方法
? 非概率抽样方法
本节概要（ 1）
? To understand the concept of sampling.
? To learn the steps in developing a sampling
plan.
? To understand the differences between
probability samples and nonprobability
samples.
? To understand the concepts of sampling
error and nonsampling error.
本节概要（ 2）
? To review the types of probability sampling
methods.
? To gain insight into nonprobability
sampling methods.
基本概念
? Population（总体）
– The total group of people from whom
information is needed.
? Census（普查）
– Data obtained from or about every member of
the population of interest.
? Sample（样本）
– A subset of the population of interest.
Steps in Developing a Sample Plan
设计一个抽样方案的步骤
Step 1,Define the
Population of
Interest
Step 2,Choose
Data Collection
Method
Step 3,Choose
Sampling Frames
Step 4,Select a
Sampling Method
Step 5,Determine
Sample Size
Step 6,Develop and
Specify Operational
Plan
Step 7,Execute
Operational Sampling
Plan
Steps in Developing a Sampling Plan
（ 1）
? Step 1,Defining the Population of Interest
– Bases for defining the population of interest
include,
? Geography
? Demographics
? Use
? Awareness
Steps in Developing a Sampling Plan
（ 2）
? Step 2,Choosing a Data Collection Method
– The selection of a data collection method has
implications for the sampling process.
? Step 3,Choosing a Sampling Frame
– Sampling frame
? List of population elements from which to select
units to be sampled.
Steps in Developing a Sampling Plan
（ 3）
? Step 4,Selecting the Sampling Method
– Probability samples
? Samples in which every element of the population
has a known,nonzero probability of selection.
– Nonprobability samples
? Include the selection of specific elements from the
population in a nonrandom manner.
Steps in Developing a Sampling Plan
（ 4）
? Step 4,Selecting the Sampling Method
(continued)
– Sampling error,The difference between the
sample value and the true value of the
population mean.
Steps in Developing a Sampling Plan
（ 5）
Advantages of
probability samples
Disadvantages of
probability samples
- The researcher can be sure of
obtaining information from a
representative cross section of the
population of interest.
- Sampling error can be computed.
- The survey results are projectable
to the total population,
- They are more expensive than
nonprobability samples of the
sample size in most cases,The
rules for selection increase
interviewing costs and professional
time must be spent in developing
the sample design,
- Probability samples take more time
to design and execute than non-
probability samples.
Steps in Developing a Sampling Plan
（ 6）
Advantages of
nonprobability samples
Disadvantages of
nonprobability samples
- Nonprobability samples cost less
than probability samples,This
characteristic of nonprobability
samples may have considerable
appeal in those situations where
accuracy is not of critical
importance.
- Nonprobability samples ordinarily
can be conducted more quickly
than probability samples.
- Sampling error cannot be computed.
- The researcher does not know the
degree to which the sample is
representative of the population
from which it was drawn.
- The results of nonprobability
samples cannot and should not be
projected to the total population.
Steps in Developing a Sampling Plan
（ 7）
? Step 5,Determine Sample Size
– Once the sampling method has been chosen,the
next step is to determine the appropriate sample
size.
? Step 6,Developing Operational Procedures
for Selecting Sample Elements
– Involves determining whether a probability or
nonprobability sample is being used.
Steps in Developing a Sampling Plan
（ 8）
? Step 7,Execution of the Sampling Plan
– The final step in the sampling process involves
execution of the operational sampling plan
discussed in the previous steps.
– It is important that this step include adequate
checking to make sure that specified procedures
are adhered to.
Classification of Sampling Methods
抽样方法分类
Sampling
Methods
Probability
Samples
Simple
RandomCluster
Systematic Stratified
Non-
probability
QuotaJudgment
Convenience Snowball
Probability Sampling Methods
概率抽样
? Simple Random Sampling（ 简单随机抽样 ）
– Is considered to be the purest form of
probability sampling,A probability sample is a
sample in which every element of the
population has a known and equal probability
of being selected into the sample.
Probability of Selection =
Sample Size
Population Size
Probability Sampling Methods
? Systematic Sampling（系统抽样）
– Probability sampling in which the entire
population is numbered,and elements are
drawn using a skip interval.
Skip Interval =
Population Size
Sample Size
Probability Sampling Methods
? Stratified Samples（分层抽样）
– Stratified samples are probability samples that
are distinguished by the following procedural
steps:
? First,the original or parent population is divided
into two or more mutually exclusive and exhaustive
subsets (e.g.,male and female).
? Second,simple random samples of elements from
the two or more subsets are chosen independently
from each other.
Probability Sampling Methods
? Cluster Samples（整群抽样）
– In the case of cluster samples,the sampling
units are selected in groups,There are two basic
steps in cluster sampling:
? First,the population of interest is divided into
mutually exclusive and exhaustive subsets.
? Second,a random sample of the subsets is selected.
Nonprobability Sampling Methods
非概率抽样方法
? Convenience Samples（便利样本）
– Nonprobability samples used primarily because
they are easy to collect.
? Judgment Samples（判断样本）
– Nonprobability samples in which the selection
criteria are based on personal judgment that the
element is representative of the population
under study.
Nonprobability Sampling Methods
? Quota Samples（配额样本）
– Nonprobability samples in which population
subgroups are classified on the basis of
researcher judgment.
? Snowball Samples（滚雪球样本）
– Nonprobability samples in which selection of
additional respondents is based on referrals
from the initial respondents.
本节小结（ 1）
? The population,or universe,is the total
group of people in whose opinions one is
interested.
? A census involves collecting desired
information from all the members of the
population of interest.
? A sample is simply a subset of a population.
本节小结（ 2）
? Probability sampling methods are selected
in such a way that every element of the
population has a known,nonzero
probability of selection.
? Nonprobability sampling methods include
all methods that select specific elements
from the population in a nonrandom
manner.
? 确定概率抽样的样本容量
? 确定样本容量的方法
? 抽样分布
二、确定样本含量
本节概要（ 1）
? To learn the financial and statistical issues
in the determination of sample size.
? To discover the methods for determining
sample size.
? To gain an appreciation of a normal
distribution.
本节概要（ 2）
? To understand population,sample,and
sampling distribution.
? To distinguish between point and interval
estimates.
? To recognize problems involving sampling
means and proportions,
Determining Sample Size for Probability Samples
确定概率抽样的样本容量
The process of determining sample size for
probability samples involves financial,statistical,
and managerial issues,Other things being equal,the
larger the sample,the less the sampling error,
Methods for Determining Sample Size
确定样本容量的方法
Budget Available
可支配预算
Rules of Thumb
单凭经验的做法
Number of
Subgroups to be
Analyzed
Often,sample size
for a project is
determined,at least
indirectly,by the
budget available
At times,the size of
a sample may boil
down to the use of
some type of rule of
thumb or a feel
Serious
consideration must
be given to the
number and
anticipated size of
various subgroups
of the total sample
Traditional Statistical Methods
传统的统计方法
Pieces of information required to make the necessary
calculations when using a sample result:
The desired level of
confidence that
the sample result
will fall within a
certain range
(result plus or minus
sampling error) of true
population value
An estimate of
the population
standard deviation
总体标准差估计
The acceptable
level of sampling
error
抽样的容许误差水平
The Normal Distribution
正态分布
? General Properties(一般特征 )
– The normal distribution is a continuous
distribution that is bell shaped and symmetrical
about the mean - mean,median,and mode are
equal,Sixty-eight percent of the observations
fall within plus or minus one standard deviation
of the mean,approximately 95 percent fall
within plus or minus two standard deviations,
and approximately 99.5 percent fall within plus
or minus three standard deviations.
The Normal Distribution
? 为什么要重视正态分布？
– First,many variables encountered by marketers
have probability distributions that are close to
the normal distribution.
– Second,the normal distribution is useful for a
number of theoretical reasons; one of the more
important of these relates to the central limit
theorem.
The Normal Distribution
? Central Limit Theorem（中心极限定理）
– A distribution of a large number of sample
means or sample proportions will approximate
a normal distribution regardless of the actual
distribution of the population from which they
were drawn.
– Standard Normal Distribution
? A normal distribution with a mean of zero and a
standard deviation of one.
Population,Sample,and Sampling Distribution
总体、样本与抽样分布
? Population Distribution（总体分布）
– A population distribution is a frequency
distribution of all of the elements of the
population.
? Sample Distribution（样本分布）
– A sample distribution is a frequency
distribution of all the elements of the
population.
Population,Sample,and Sampling
Distribution
? Sampling Distribution of the Sample Mean
（样本均数的抽样分布）
– A frequency distribution of the means of many
samples drawn from a particular population,It
is normally distributed.
Sampling Distribution of the Mean
? Standard Deviation（标准差）
– A measure of dispersion calculated by
subtracting the mean of a series from each
value in the series,squaring each result,
summing them,dividing the sum by the number
of items minus 1,and taking the square root of
this value.
– Standard Error of the Mean
（均数标准误）
? The standard deviation of a distribution of sample
means.
Sampling Distribution of the Mean
? Making Inference on the Basis of a Single
Sample（单样本的简单推断）
– Point Estimates（ 点估计 ）
? Inferences regarding the sampling error associated
with a particular estimate of a population value.
– Interval Estimates（区间估计）
? Inferences regarding the likelihood that a population
value will fall within a certain range.
Sampling Distribution of the Mean
? Making Inference on the Basis of a Single
Sample
– Confidence Level（置信水平）
? The probability that a particular confidence interval
will include the true population.
Sampling Distribution of the Proportion
比例的抽样分布
? General Properties（一般特征）
– A frequency distribution of the proportions of
many samples drawn from a particular
population,It is normally distributed.
? Preferences
– Marketing researchers have a tendency to prefer
dealing with sample size problems as problems
of estimating proportions rather than means.
Sample Size Distributions
样本容量的分布
? Problems Involving Means（ 均数估计的问题 ）
– The level of confidence (Z) and the amount of
error (E) to be used in calculating the required
sample size must be set by the researcher.
– In designing a sampling procedure,an
acceptable trade-off between accuracy,level of
confidence,and cost must be evaluated.
– The population standard deviation must be
estimated.
Sample Size Distributions
? Problems Involving Proportions
– The level of confidence (Z) and the amount of
error (E) to be used in calculating the required
sample size must be set by the researcher.
– Advantages Involving Proportions
? If there is no basis for estimating P,you can make
what is sometimes referred to as the most
pessimistic or worse case assumption regarding the
value of P.
Statistical Power
统计效能
? Type I Error（ I型错误）
– The error of concluding that there is a
difference when there is not a difference.
? Type II Error（ II型错误）
– The error of saying there is no difference when
there actually is a difference.
? Power（效能）
– The probability of not making a Type II error is
called power.
Power Example
Sample Size Required to Detect Differences Between Proportions from
Independent Samples at Different Levels of Power and Alpha Levels
Difference
to Detect Power
50 % 90 %80 %75 %70 %60 %
0.01
0.05
0.10
0.15
19,205
766
190
83
52,53039,23934,69730,85724,491
2,0941,5681,3841,231977
518389343305242
226169150133106
本节小结（ 1）
? Determining sample size involves financial,
statistical,and managerial considerations,
Other things being equal,the larger the
sample the less the sampling error.
? In turn,the cost of research grows with the
size of the sample.
本节小结（ 2）
? There are a number of traditional statistical
techniques for determining sample size.
? Crucial to statistical sampling theory is the
concept of the normal distribution.
? Power is the probability of not making a
Type II error,A Type II error is the mistake
of saying there is not a difference when
there is a difference.
本节小结（ 3）
? The standard deviation of a distribution of
sample means is called the standard error of
the mean.
? A researcher who is interested in estimating
proportions rather than means uses the
sampling distribution of the proportion.
