第六章 抽樣設計. σ2σ2 population 母體 sample 樣本 Ѕ2Ѕ2 parameter 參數 statistic...

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Page 1: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

第六章抽樣設計

Page 2: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

σ2

Population

母體Sample

樣本

Ѕ2

x

Parameter

參數Statistic

統計量

Sampling

抽樣

Generalization

推論

Page 3: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

Lower cost Greater accuracy of results Greater speed of data collection Availability of population elements Sample vs. Census

Why sample?

Page 4: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

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

Page 5: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

誤差 Differences between parameters and

statistics=error• sampling error 抽樣誤差• Systematic error 系統變異 (also called

measurement error)

Page 6: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

Target Population

group to which you wish to generalize the results of the study

should be defined as specifically as possible

Page 7: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

populationsamplingframe

sample

Sampling frame 抽樣主體• the list of elements from which the sample is

actually drawn

Page 8: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

Steps in sampling design

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?

Page 9: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

What is the population

Clearly define your population of interest Population vs. research subjects

Page 10: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

What are the parameters of Interest?

Summary of descriptors (mean, variance) of variables in the population

Issue of the scale of measurement

Page 11: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

What is the sampling frame?

the list of elements from which the sample is actually drawn

Page 12: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

What is the type of sample?

Probability sample vs. nonprobability sample

Page 13: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

What size sample is needed?

The larger, the better

Page 14: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

Sampling Techniques

Probability Sampling (random sampling) 隨機抽樣

Nonprobability Sampling (nonrandom sampling) 非隨機抽樣

Page 15: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

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)

Page 16: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

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

Page 17: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

Simple Random Sampling

every unit in the population has an equal and known probability of being selected as part of the sample ( 抽籤 )

Page 18: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

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

Page 19: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

亂數表1 2 3 4 5 6 7 8 9 10

1 49486 93775 88744 80091 92732 38532 41506 54131 44804 436372 94860 36746 04571 13150 65383 44616 97170 25057 02212 419303 10169 95685 47585 53247 60900 20097 97962 04267 29283 075504 12018 45351 15671 23026 55344 54654 73717 97666 00730 890835 45611 71585 61487 87434 07498 60596 36255 82880 84381 304336 89137 30984 18842 69619 53872 95200 76474 67528 14870 596287 94541 12057 30771 19598 96069 10399 50649 41909 09994 753228 89920 28843 87599 30181 26839 02162 56676 39342 95045 601469 32472 32796 15255 39636 90819 54150 24064 50514 15194 4145010 63958 47944 82888 66709 66525 67616 75709 56879 29649 07325

Page 20: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

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

Page 21: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

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

Page 22: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

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

Page 23: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

For example:

You want to obtain a sample of 100 from apopulation of 1,000. You would select every10th (or kth) person from the list.

k = 1000/100=10

Page 24: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

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)

Page 25: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

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)

Page 26: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

第一層

第二層

第三層.....

第 K 層

Sample

Page 27: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

Homogeneity is very high within the strata.

Heterogeneity is very high between the stratas

Page 28: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

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

Page 29: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

Potential disadvantages

Sometimes the exact composition of the population is often unknown

with multiple stratifying variables, sampling designs can become quite complex

Page 30: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

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

Page 31: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

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

Page 32: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

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

Page 33: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

For example:

Suppose a researcher plans to conduct a surveyregarding various attitudes of Agricultural College Students at Tunghai U. He wishes to compare perceptionsacross 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.

Page 34: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

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

Page 35: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

一班

三班

k 班

五班

二班

四班

二班

九班

Population Sample

Page 36: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

Example

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

Page 37: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

Why use cluster samples?

They're easier to obtain than a simple random or systematic sample of the same size

Page 38: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

Disadvantages of Cluster Sampling Less accurate than other sampling

techniques (selection stages, accuracy)

Generally leads to violation of an assumption that subjects are independent

Page 39: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

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

Page 40: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

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

Page 41: 第六章 抽樣設計. σ2σ2 Population 母體 Sample 樣本 Ѕ2Ѕ2 Parameter 參數 Statistic 統計量 Sampling 抽樣 Generalization 推論

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