第六章
抽樣設計
Population
母體
Sample
樣本

Sampling
σ2
抽樣
x
Ѕ2
Generalization
推論
Parameter
參數
Statistic
統計量
Why sample?





Lower cost
Greater accuracy of results
Greater speed of data collection
Availability of population elements
Sample vs. Census
What is a good sample

Accuracy
• Systematic variance 系統變異
• The variation in measures due to some known or unknown
influences that “cause” the scores (results) to lean in one
direction more than another

Precision
• Sampling error 抽樣誤差
• the degree to which a given sample differs from the underlying
population
• sampling error tends to be high with small sample sizes and
will decrease as sample size increases
誤差

Differences between parameters and
statistics=error
• sampling error 抽樣誤差
• Systematic error 系統變異 (also called
measurement error)
Target Population

group to which you wish to generalize the
results of the study

should be defined as specifically as possible
population

sampling
frame
sample
Sampling frame 抽樣主體
• the list of elements from which the sample is
actually drawn
Steps in sampling design
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What is the population?
What are the parameters of interest?
What is the sampling frame?
What is the type of sample?
What size sample is needed?
How much will it cost?
What is the population


Clearly define your population of interest
Population vs. research subjects
What are the parameters of Interest?


Summary of descriptors (mean, variance) of
variables in the population
Issue of the scale of measurement
What is the sampling frame?

the list of elements from which the sample
is actually drawn
What is the type of sample?

Probability sample vs. nonprobability
sample
What size sample is needed?

The larger, the better
Sampling Techniques

Probability Sampling (random sampling) 隨
機抽樣

Nonprobability Sampling (nonrandom
sampling) 非隨機抽樣
Probability Sampling

sample should represent the population

using random selection methods

members of the population have a known
and non-zero chance of being selected
(EPSEM: Equal Probability of SElection
Method)
Types of Probability Sampling

Simple random sampling簡單隨機抽樣

Systematic sampling系統式抽樣

Stratified sampling 分層隨機抽樣

Cluster sampling 部落抽樣

Double sampling 雙重抽樣
Simple Random Sampling

every unit in the population has an equal
and known probability of being selected as
part of the sample (抽籤)
Random Numbers Table 亂數表

a table of random digits arranged in rows
and columns

after assigning an identification number to
each member of the population, numbers in
the random numbers table are used to select
those who will be in the sample
亂數表
1
2
3
4
5
6
7
8
9
10
1
49486 93775 88744 80091 92732 38532 41506 54131 44804 43637
2
94860 36746 04571 13150 65383 44616 97170 25057 02212 41930
3
10169 95685 47585 53247 60900 20097 97962 04267 29283 07550
4
12018 45351 15671 23026 55344 54654 73717 97666 00730 89083
5
45611 71585 61487 87434 07498 60596 36255 82880 84381 30433
6
89137 30984 18842 69619 53872 95200 76474 67528 14870 59628
7
94541 12057 30771 19598 96069 10399 50649 41909 09994 75322
8
89920 28843 87599 30181 26839 02162 56676 39342 95045 60146
9
32472 32796 15255 39636 90819 54150 24064 50514 15194 41450
10
63958 47944 82888 66709 66525 67616 75709 56879 29649 07325
Characteristics of simple random
sampling

Unbiased: 母體內每一個體被抽到的機會
均等

Independence : 母體內某一個個體被抽到
不會影響其他個體被抽到的機會
Limitations of simple random
samples

not practical for large populations

Simple random sampling becomes difficult
when we don’t have a list of the population
Systematic Sampling系統性抽樣

a type of probability sampling in which
every kth member of the population is
selected

k=N/n
N = size of the population
n = sample size
For example:
You want to obtain a sample of 100 from a
population of 1,000. You would select every
10th (or kth) person from the list.
k = 1000/100=10
Advantages/disadvantages of
systematic sampling

Assuming availability of a list of population
members

Randomness of the sample depends on
randomness of the list
• periodicity bias: 當母體個體排序出現某一週
期性或規則時, systematic sampling 會有週期
性誤差(periodicity bias)
Stratified Random Sample分層隨機
抽樣

Prior to random sampling, the population is
divided into subgroups, called strata, e.g.,
gender, ethnic groups, professions, etc.依母
體特性將個體分層(Strata) & 每一個體只
屬一層

Subjects are then randomly selected from
each strata再從每一層中隨機抽取樣本
(using simple random sampling)
第一層
第二層
第三層
..
..
.
第K層
Sample

Homogeneity is very high within the strata.

Heterogeneity is very high between the stratas
Why use stratified samples?

permits examination of subgroups by ensuring
sufficient numbers of subjects within subgroups
確保樣本包含母體中各種不同特性的個體，增
加樣本的代表性

generally more convenient than a simple random
sample
Potential disadvantages

Sometimes the exact composition of the
population is often unknown

with multiple stratifying variables, sampling
designs can become quite complex
Types of Stratified Sampling

Proportionate Stratified Random Sampling
比例分層隨機抽樣

Disproportionate Stratified Random
Sampling非比例分層隨機抽樣
Proportionate Sampling

strata sample sizes are proportional to
population subgroup sizes按母體比例抽取
樣本
• e.g., if a group represents 15% of the
population, the stratum representing that group
will comprise 15% of the sample
Disproportionate Sampling

strata sample sizes are not proportional to
population subgroup sizes每層抽出之樣本
數不能與母體之特徵比例相呼應

may be used to achieve equal sample sizes
across strata
For example:
Suppose a researcher plans to conduct a survey
regarding various attitudes of Agricultural College
Students at Tunghai U. He wishes to compare perceptions
across 4 major groups but finds some of the groups are
quite small relative to the overall student population.
As a result, he decides to over-sample minority students.
For example, although Hospitality students only represent
10% of the Agricultural student population, he uses a
disproportional stratified sample so that Hospitality
students will comprise 25% of his sample.
Cluster Sampling部落抽樣


used when subjects are randomly sampled
from within a “unit” or “group” (e.g.,
classroom, school, country, etc)
將母體分為若干部落 (cluster)，在自所有
部落中隨機抽取若干部落樣本並對這些
抽取的部落作抽查
一班
二班
二班
三班
四班
九班
五班
k班
Population
Sample
Example

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台中市民眾對連戰出訪大陸的看法
將台中市依“里”為部落分成許多里
隨機抽取3個里然後對此3個里的居民作
全面性的訪問
Compare using cluster sampling technique
and simple sampling technique
Why use cluster samples?

They're easier to obtain than a simple
random or systematic sample of the same
size
Disadvantages of Cluster
Sampling

Less accurate than other sampling
techniques (selection stages, accuracy)

Generally leads to violation of an
assumption that subjects are independent
Double sampling 雙重抽樣法


運用兩種不同的抽樣方法進行抽樣
Systematic sample + cluster/stratified
sample
Nonprobability sampling

Convenience sampling 簡便抽樣法
• getting people who are most conveniently available
• fast & low cost

Purposive sampling 計畫抽樣法
• Judgment sampling
• Quota sampling

Snowball sampling 滾雪球抽樣法
Characteristics of nonprobability
samples

members of the population do not have a
known chance of being selected

do not represent any known population

results cannot be generalized beyond the
group being tested