第 13 章 抽樣.

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1 第 13 章 抽樣

2 學習目標 讀完本章你應該了解： 1. 抽樣理論所依據的兩大前提。 2. 衡量樣本效度時，準確度與精確度的特徵。
3. 發展抽樣計畫前，五個必答的問題。

3 學習目標（續） 讀完本章你應該了解： 4. 兩大類的抽樣技術，以及各類中多樣化的抽樣方法。 5. 不同抽樣方法的使用時機。

4 怎樣才算是足夠大的樣本數量？ 「在蓋洛普最近的民調中…當問到這民調根據哪種科學抽樣基礎時…大部分人會說，受測者高達1,500人至2,000人―對全國性的民調而言，這樣本數高於平均值―卻不能代表所有美國人的意見。」 蓋洛普公司的主編Frank Newport

5 抽樣的本質 抽樣（Sampling） 母體元素（Population Element） 母體（Population） 普查（Census）
抽樣清冊（Sampling frame） The basic idea of sampling is that by selecting some of the elements in a population, we may draw conclusions about the entire population. A population element is the individual participant or object on which the measurement is taken. It is the unit of study. It may be a person but it could also be any object of interest. A population is the total collection of elements about which we wish to make some inferences. A census is a count of all the elements in a population. A sample frame is the listing of all population elements from which the sample will be drawn.

6 為什麼要抽樣？ 母體元素 成本較低 的可用性 抽樣提供 資料蒐集 結果更準確 更快速
This slide lists the reasons researchers use a sample rather than a census. 資料蒐集 更快速 結果更準確

7 何時使用普查法？ 可行性 必要性 The advantages of sampling over census studies are less compelling when the population is small and the variability within the population is high. Two conditions are appropriate for a census study. A census is feasible when the population is small and necessary when the elements are quite different from each other.

8 怎樣才是一個好的樣本？ 準確度 精確度 The ultimate test of a sample design is how well it represents the characteristics of the population it purports to represent. In measurement terms, the sample must be valid. Validity of a sample depends on two considerations: accuracy and precision. Here a sample is being taken of water, using a can suspended on a fishing line. Accuracy is the degree to which bias is absent from the sample. When the sample is drawn properly, the measure of behavior, attitudes, or knowledge of some sample elements will be less than the measure of those same variables drawn from the population. The measure of other sample elements will be more than the population values. Variations in these sample values offset each other, resulting in a sample value that is close to the population value. For these offsetting effects to occur, there must be enough elements in the sample and they must be drawn in a way that favors neither overestimation nor underestimation. Increasing the sample size can reduce systematic variance as a cause of error. Systematic variance is a variation that causes measurements to skew in one direction or another. Precision of estimate is the second criterion of a good sample design. The numerical descriptors that describe samples may be expected to differ from those that describe populations because of random fluctuations inherent in the sampling process. This is called sampling error and reflects the influence of chance in drawing the sample members. Sampling error is what is left after all known sources of systematic variance have been accounted for. Precision is measured by the standard error of estimate, a type of standard deviation measurement. The smaller the standard error of the estimate, the higher is the precision of the sample.

9 研究程序中的抽樣設計 Exhibit 13-1 represents the several decisions the researcher makes when designing a sample. The sampling decisions flow from two decisions made in the formation of the management-research question hierarchy: the nature of the management question and the specific investigative questions that evolve from the research question.

10 樣本設計的類型 元素選擇 機率 非機率 不受限制的 簡單隨機抽樣(Simple random) 便利抽樣(Convenience) 受限制的
複雜隨機抽樣(Complex random) 立意抽樣(Purposive) 系統抽樣(Systematic) 判斷抽樣(Judgment) 集群抽樣(Cluster) 配額抽樣(Quota) 分層抽樣(Stratified) 雪球抽樣 (Snowball) 雙重抽樣(Double) Exhibit 13-2 The members of a sample are selected using probability or nonprobability procedures. Nonprobability sampling is an arbitrary and subjective sampling procedure where each population element does not have a known, nonzero chance of being included. Probability sampling is a controlled, randomized procedure that assures that each population element is given a known, nonzero chance of selection.

11 抽樣設計的步驟 目標母體為何？ 想知道的母體參數為何？ 抽樣清冊為何？ 什麼是合適的抽樣方法？ 需要的樣本大小為何？
This slide addresses the steps in sampling design.

12 何時使用較大的樣本規模？ 要求精確 子群體多 信賴水準高 母體變異大 誤差範圍小
The greater the dispersion or variance within the population, the larger the sample must be to provide estimation precision. The greater the desired precision of the estimate, the larger the sample must be. The narrower or smaller the error range, the larger the sample must be. The higher the confidence level in the estimate, the larger the sample must be. The greater the number of subgroups of interest within a sample, the greater the sample size must be, as each subgroup must meet minimum sample size requirements. Cost considerations influence decisions about the size and type of sample and the data collection methods. A cheese factory is pictured here. Ask students if taking a sample would require a large or small sample of the output and what would influence their answer.

13 簡單隨機抽樣 優點 隨機撥號易於執行 缺點 需有母體元素清冊 耗時 使用較大的樣本規模 產生較大的誤差 高成本
In drawing a sample with simple random sampling, each population element has an equal chance of being selected into the samples. The sample is drawn using a random number table or generator. This slide shows the advantages and disadvantages of using this method. The probability of selection is equal to the sample size divided by the population size. Exhibit 13-6 covers how to choose a random sample. The steps are as follows: Assign each element within the sampling frame a unique number. Identify a random start from the random number table. Determine how the digits in the random number table will be assigned to the sampling frame. Select the sample elements from the sampling frame.

14 系統抽樣 優點 設計簡便 比簡單隨機抽樣更易於執行 容易訂出抽樣分配的平均數或比率 缺點 母體本身的週期性，可能導致抽樣及結果的偏誤
若母體呈現單調上升或下降趨勢，可能導致結果偏誤 成本適中 In drawing a sample with systematic sampling, an element of the population is selected at the beginning with a random start and then every Kth element is selected until the appropriate size is selected. The kth element is the skip interval, the interval between sample elements drawn from a sample frame in systematic sampling. It is determined by dividing the population size by the sample size. To draw a systematic sample, the steps are as follows: Identify, list, and number the elements in the population Identify the skip interval Identify the random start Draw a sample by choosing every kth entry. To protect against subtle biases, the research can Randomize the population before sampling, Change the random start several times in the process, and Replicate a selection of different samples.

15 分層隨機抽樣 優點 可控制各分層的樣本規模 增加統計效率 可提供代表及分析各子群體的資料 各分層可使用不同的方法 缺點
若以不同的比例選出子群體，會提高結果的錯誤率 若將母體分層，特別昂貴 高成本 In drawing a sample with stratified sampling, the population is divided into subpopulations or strata and uses simple random on each strata. Results may be weighted or combined. The cost is high. Stratified sampling may be proportion or disproportionate. In proportionate stratified sampling, each stratum’s size is proportionate to the stratum’s share of the population. Any stratification that departs from the proportionate relationship is disproportionate.

16 集群抽樣 優點 若執行恰當，能提供母體參數的不偏估計值 比簡單隨機抽樣更經濟、有效率 每個樣本的平均成本最低 沒有母體清冊也容易執行 缺點
由於子群體具有同質性而非異質性，通常統計效率較低 成本適中 In drawing a sample with cluster sampling, the population is divided into internally heterogeneous subgroups. Some are randomly selected for further study. Two conditions foster the use of cluster sampling: the need for more economic efficiency than can be provided by simple random sampling, and 2) the frequent unavailability of a practical sampling frame for individual elements. Exhibit 13-7 provides a comparison of stratified and cluster sampling and is highlighted on the next slide. Several questions must be answered when designing cluster samples. How homogeneous are the resulting clusters? Shall we seek equal-sized or unequal-sized clusters? How large a cluster shall we take? Shall we use a single-stage or multistage cluster? How large a sample is needed?

17 分層與集群抽樣的比較表 Exhibit 13-7

18 區域抽樣（Area Sampling） Area sampling is a cluster sampling technique applied to a population with well-defined political or geographic boundaries. It is a low-cost and frequently used method.

19 雙重抽樣 優點 若第一階段結果有足夠的資料，將母體分層或集群化，則可降低成本 缺點 若隨意濫用，則成本上升
In drawing a sample with double (sequential or multiphase) sampling, data are collected using a previously defined technique. Based on the information found, a subsample is selected for further study.

20 非機率抽樣 無一般化的必要性 可行性 研究目的受限 時間 成本
With a subjective approach like nonprobability sampling, the probability of selecting population elements is unknown. There is a greater opportunity for bias to enter the sample and distort findings. We cannot estimate any range within which to expect the population parameter. Despite these disadvantages, there are practical reasons to use nonprobability samples. When the research does not require generalization to a population parameter, then there is no need to ensure that the sample fully reflects the population. The researcher may have limited objectives such as those in exploratory research. It is less expensive to use nonprobability sampling. It also requires less time. Finally, a list may not be available. 時間 成本

21 非機率抽樣的方式 便利抽樣 判斷抽樣 配額抽樣 雪球抽樣
Convenience samples are nonprobability samples where the element selection is based on ease of accessibility. They are the least reliable but cheapest and easiest to conduct. Examples include informal pools of friends and neighbors, people responding to an advertised invitation, and “on the street” interviews. Judgment sampling is purposive sampling where the researcher arbitrarily selects sample units to conform to some criterion. This is appropriate for the early stages of an exploratory study. Quota sampling is also a type of purposive sampling. In this type, relevant characteristics are used to stratify the sample which should improve its representativeness. The logic behind quota sampling is that certain relevant characteristics describe the dimensions of the population. In most quota samples, researchers specify more than one control dimension. Each dimension should have a distribution in the population that can be estimated and be pertinent to the topic studied. Snowball sampling means that subsequent participants are referred by the current sample elements. This is useful when respondents are difficult to identify and best located through referral networks. It is also used frequently in qualitative studies. 雪球抽樣

22 關鍵詞 區域抽樣（area sampling） 普查（census） 集群抽樣（cluster sampling）
便利樣本（convenience sample） 非比例分層抽樣（disproportionate stratified sampling） 雙重抽樣（double sampling） 判斷抽樣（judgment sampling） 多階抽樣（multiphase sampling） 非機率抽樣（nonprobability sampling） 母體（population） 母體元素（population element） 母體參數（population parameters） 母體的事件發生比例（population proportion of incidence） 機率抽樣（probability sampling）

23 關鍵詞（續） 比例分層抽樣（proportionate stratified sampling） 配額抽樣（quota sampling）
樣本清冊（sample frame） 樣本統計量（sample statistics） 抽樣（sampling） 抽樣誤差（sampling error） 逐次抽樣（sequential sampling） 簡單隨機抽樣（simple random sampling） 跳躍間隔（skip interval） 雪球抽樣（snowball sampling） 分層隨機抽樣（stratified random sampling） 系統抽樣（systematic sampling） 系統變異（systematic variance）