Sampling Design

Sampling Terminology Sample Population or universe Population element A subset, or some part, of a larger population Population or universe Any complete group of entities that share some common set of characteristics Population element An individual member of a population Census An investigation of ALL the individual elements that make up a population

Why Sample? Sampling Cuts costs Reduces labor requirements Gathers vital information quickly Most properly selected samples give sufficiently accurate results

Table 12.1 Sample Versus Census

Target Population A.k.a., the Relevant population Operationally define All women still capable of bearing children vs. All women between the ages of 12 and 50 Comic book reader? Does this include children under 6 years of age who do not actually read the words?

A list of elements from which the sample may be drawn Sampling Frame A list of elements from which the sample may be drawn A.K.A., the working population Mailing lists - data base marketers Sampling services or list brokers

Two Major Categories of Sampling Probability sampling Known, nonzero, & equal probability of selection for every population element Nonprobability sampling Probability of selecting any particular member is unknown

Nonprobability Sampling Convenience Judgment Quota Snowball

Convenience Sampling Also called haphazard or accidental sampling The sampling procedure of obtaining the people or units that are most conveniently available

Judgment Sampling Also called purposive sampling An experienced individual selects the sample based on his or her judgment about some appropriate characteristics required of the sample member

Quota Sampling Ensures that the various subgroups in a population are represented on pertinent sample characteristics to the exact extent that the investigators desire It should not be confused with stratified sampling.

Snowball Sampling A variety of procedures Initial respondents are selected by probability methods Additional respondents are obtained from information (or referrals) provided by the initial respondents

Comparing the Nonprobability Techniques Strengths Weaknesses Convenience Sampling Least expensive Least time needed Most convenient Selection bias Not representative Judgmental Sampling Low expense Little time needed Convenient Subjective Does not allow generalizations Quota Sampling Can control sample characteristics Most likely not representative Snowball Sampling Can estimate rare characteristics Time consuming

Figure 12.8 Probability Sampling Techniques Most Commonly-Used Probability Sampling Techniques Figure 12.8 Probability Sampling Techniques Probability Sampling Techniques Simple Random Sampling Systematic Sampling Stratified Sampling

Simple Random Sampling A sampling procedure that ensures that each element in the population will have an equal chance of being included in the sample

Systematic Sampling A simple process Every nth name from the list will be drawn Periodicity Problem that occurs in systematic sampling when the original list has a systematic pattern (I.e., the original list is not random in character)

Stratified Sampling Probability sample Subsamples are drawn within different strata using simple random sampling Each stratum is more or less equal on some characteristic Do not confuse with quota sample

Comparing the Probability Techniques Strengths Weaknesses Simple Random Sampling Easily understood Can project results Expensive Difficult to construct sampling frame No assurance of representativeness Systematic Sampling Easier to implement than SRS Increased representativeness Sampling frame not necessary Can decrease representativeness Stratified Sampling Precision Includes all important subpopulations Selection of stratification variables difficult

What is the Appropriate Sample Design? Degree of accuracy Resources Time Advanced knowledge of the population National versus local Need for statistical analysis

Choosing Between Nonprobability & Probability Sampling Factor Nonprobability Probability Nature of Research Exploratory Conclusive Relative Magnitude of Sampling & Nonsampling Errors Nonsampling errors larger Sampling errors larger Population Variability Homogeneous (low variability) Heterogeneous (high variability) Statistical Considerations Unfavorable Favorable Operational Considerations

Internet Samples Recruited Ad Hoc Samples Opt-in Lists

Information Needed to Determine Sample Size Variance (standard deviation) Get from pilot study or rule of thumb (managerial judgment) Magnitude of error Managerial judgment or calculation Confidence level Managerial judgment

Sample Size Formula for Questions Involving Means

Sample Size Formula - Example Suppose a survey researcher is studying expenditures on lipstick Wishes to have a 95 percent confident level (Z) and Range of error (E) of less than $2.00. The estimate of the standard deviation is $29.00.

Sample Size Formula - Example

Sample Size Formula - Example Suppose, in the same example as the one before, the range of error (E) is acceptable at $4.00 (rather than the original $2.00), sample size is reduced.

Sample Size Formula - Example

Calculating Sample Size 99% Confidence [ ] 1389 = 265 . 37 2 53 74 ú û ù ê ë é ) 29 )( 57 ( n 347 6325 18 4

Sample Size for a Proportion

E pq z n = Where: n = Number of items in samples 2 E pq z n = Where: n = Number of items in samples Z2 = The square of the confidence interval in standard error units. p = Estimated proportion of success q = (1-p) or estimated the proportion of failures E2 = The square of the maximum allowance for error between the true proportion and sample proportion or zsp squared.

Sample Size for a Proportion: Example A researcher believes that a simple random sample will show that 60 percent of a population (p = .6) recognizes the name of an automobile dealership. Note that 40% of the population would not recognize the dealership’s name (q = .4) The researcher wants to estimate with 95% confidence (Z = 1.96) that the allowance for sampling error is not greater than 3.5 percentage points (E = 0.035)

Calculating Sample Size at the 95% Confidence Level 753 = 001225 . 922 ) 24 )(. 8416 3 ( 035 ( . 4 6 (. 96 1. n q p 2