Sampling DesignSampling Design

Sampling Terminology

• Sample– 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

Sample vs. Census

CONDITIONS FAVORING THE USE OF

Sample Census

1. Budget Small Large

2. Time available Short Long

3. Population size Large Small

4. Variance in the characteristic Small Large

5. Cost of sampling error Low High

6. Cost of nonsampling errors High Low

7. Nature of measurement Destructive Nondestructive

8. Attention to individual cases Yes No

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?

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

Technique 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

•Selection bias

•Most likely not representative

Snowball Sampling •Can estimate rare characteristics

•Time consuming

•Most likely not representative

Most Commonly-UsedProbability Sampling Techniques

Probability Sampling Techniques

Simple RandomSampling

StratifiedSampling

SystematicSampling

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

Technique 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

•Expensive

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 Favorable Unfavorable

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

2

Ezs

n

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.

2

E

zsn

2

00.2

00.2996.1

2

00.2

84.56

242.28 808

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

2

E

zsn

2

00.4

00.2996.1

2

00.4

84.56

221.14 202

Sample Size Formula - Example

99% ConfidenceCalculating Sample Size

1389

265.372

253.74

2

2)29)(57.2(n

2

347 6325.18 2

453.74

2

4)29)(57.2(n

2

2

2

EpqZ

n

Sample Size for a Proportion

2

2

Epqz

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.

001225

)24)(.8416.3(

)035( .

)4)(.6(.)96 1. (n

4.q

6.p

2

2