11-2

Chapter Outline 4) A Classification of Sampling Techniques

i. Nonprobability Sampling Techniques

a. Convenience Sampling

b. Judgmental Sampling

c. Quota Sampling

d. Snowball Sampling

ii. Probability Sampling Techniques

a. Simple Random Sampling

b. Systematic Sampling

c. Stratified Sampling

d. Cluster Sampling

e. Other Probability Sampling Techniques

11-3

Chapter Outline

5. Choosing Nonprobability versus ProbabilitySampling

6. Uses of Nonprobability versus Probability Sampling

7. International Marketing Research

8. Ethics in Marketing Research

9. Internet and Computer Applications

10. Focus On Burke

11. Summary

12. Key Terms and Concepts

11-4

The Sampling Design ProcessFig. 11.1

Define the Population

Determine the Sampling Frame

Select Sampling Technique(s)

Determine the Sample Size

Execute the Sampling Process

11-5

Define the Target Population

The target population is the collection of elements or objects that possess the information sought by the researcher and about which inferences are to be made. The target population should be defined in terms of elements, sampling units, extent, and time.

An element is the object about which or from which the information is desired, e.g., the respondent.

A sampling unit is an element, or a unit containing the element, that is available for selection at some stage of the sampling process.

Extent refers to the geographical boundaries.

Time is the time period under consideration.

11-6

Define the Target Population

Important qualitative factors in determining the sample size

the importance of the decision the nature of the research the number of variables the nature of the analysis sample sizes used in similar studies incidence rates completion rates resource constraints

11-7Classification of Sampling TechniquesFig. 11.2

Sampling Techniques

NonprobabilitySampling

Techniques

ProbabilitySampling

Techniques

ConvenienceSampling

JudgmentalSampling

QuotaSampling

SnowballSampling

SystematicSampling

StratifiedSampling

ClusterSampling

Other SamplingTechniques

Simple RandomSampling

11-8

Convenience Sampling

Convenience sampling attempts to obtain a sample of convenient elements. Often, respondents are selected because they happen to be in the right place at the right time.

use of students, and members of social organizations

mall intercept interviews without qualifying the respondents

department stores using charge account lists

“people on the street” interviews

11-9

Judgmental Sampling

Judgmental sampling is a form of convenience sampling in which the population elements are selected based on the judgment of the researcher.

test markets purchase engineers selected in industrial

marketing research bellwether precincts selected in voting

behavior research expert witnesses used in court

11-10

Quota SamplingQuota sampling may be viewed as two-stage restricted judgmental sampling.

The first stage consists of developing control categories, or quotas, of population elements.

In the second stage, sample elements are selected based on convenience or judgment.

Population Samplecomposition composition

ControlCharacteristic Percentage Percentage NumberSex Male 48 48 480 Female 52 52 520

____ ____ ____100 100 1000

11-11

Snowball Sampling

In snowball sampling, an initial group of respondents is selected, usually at random.

After being interviewed, these respondents are asked to identify others who belong to the target population of interest.

Subsequent respondents are selected based on the referrals.

11-12

Simple Random Sampling

Each element in the population has a known and equal probability of selection.

Each possible sample of a given size (n) has a known and equal probability of being the sample actually selected.

This implies that every element is selected independently of every other element.

11-13

Systematic Sampling The sample is chosen by selecting a random starting

point and then picking every ith element in succession from the sampling frame.

The sampling interval, i, is determined by dividing the population size N by the sample size n and rounding to the nearest integer.

When the ordering of the elements is related to the characteristic of interest, systematic sampling increases the representativeness of the sample.

If the ordering of the elements produces a cyclical pattern, systematic sampling may decrease the representativeness of the sample. For example, there are 100,000 elements in the population and a sample of 1,000 is desired. In this case the sampling interval, i, is 100. A random number between 1 and 100 is selected. If, for example, this number is 23, the sample consists of elements 23, 123, 223, 323, 423, 523, and so on.

11-14

Stratified Sampling

A two-step process in which the population is partitioned into subpopulations, or strata.

The strata should be mutually exclusive and collectively exhaustive in that every population element should be assigned to one and only one stratum and no population elements should be omitted.

Next, elements are selected from each stratum by a random procedure, usually SRS.

A major objective of stratified sampling is to increase precision without increasing cost.

11-15

Stratified Sampling The elements within a stratum should be as

homogeneous as possible, but the elements in different strata should be as heterogeneous as possible.

The stratification variables should also be closely related to the characteristic of interest.

Finally, the variables should decrease the cost of the stratification process by being easy to measure and apply.

In proportionate stratified sampling, the size of the sample drawn from each stratum is proportionate to the relative size of that stratum in the total population.

In disproportionate stratified sampling, the size of the sample from each stratum is proportionate to the relative size of that stratum and to the standard deviation of the distribution of the characteristic of interest among all the elements in that stratum.

11-16

Cluster Sampling The target population is first divided into mutually

exclusive and collectively exhaustive subpopulations, or clusters.

Then a random sample of clusters is selected, based on a probability sampling technique such as SRS.

For each selected cluster, either all the elements are included in the sample (one-stage) or a sample of elements is drawn probabilistically (two-stage).

Elements within a cluster should be as heterogeneous as possible, but clusters themselves should be as homogeneous as possible. Ideally, each cluster should be a small-scale representation of the population.

In probability proportionate to size sampling, the clusters are sampled with probability proportional to size. In the second stage, the probability of selecting a sampling unit in a selected cluster varies inversely with the size of the cluster.

11-17

Types of Cluster SamplingFig. 11.3 Cluster Sampling

One-StageSampling

MultistageSampling

Two-StageSampling

Simple ClusterSampling

ProbabilityProportionate

to Size Sampling

11-18

Technique Strengths WeaknessesNonprobability Sampling Convenience sampling

Least expensive, leasttime-consuming, mostconvenient

Selection bias, sample notrepresentative, not recommended fordescriptive or causal research

Judgmental sampling Low cost, convenient,not time-consuming

Does not allow generalization,subjective

Quota sampling Sample can be controlledfor certain characteristics

Selection bias, no assurance ofrepresentativeness

Snowball sampling Can estimate rarecharacteristics

Time-consuming

Probability sampling Simple random sampling(SRS)

Easily understood,results projectable

Difficult to construct samplingframe, expensive, lower precision,no assurance of representativeness.

Systematic sampling Can increaserepresentativeness,easier to implement thanSRS, sampling frame notnecessary

Can decrease representativeness

Stratified sampling Include all importantsubpopulations,precision

Difficult to select relevantstratification variables, not feasible tostratify on many variables, expensive

Cluster sampling Easy to implement, costeffective

Imprecise, difficult to compute andinterpret results

Table 11.3

Strengths and Weaknesses of Basic Sampling Techniques

11-19Procedures for Drawing Probability SamplesFig. 11.4

Simple Random Sampling

1. Select a suitable sampling frame

2. Each element is assigned a number from 1 to N (pop. size)

3. Generate n (sample size) different random numbers between 1 and N

4. The numbers generated denote the elements that should be included in the sample

11-20Procedures for DrawingProbability SamplesFig. 11.4 cont. Systematic

Sampling

1. Select a suitable sampling frame

2. Each element is assigned a number from 1 to N (pop. size)

3. Determine the sampling interval i:i=N/n. If i is a fraction, round to the nearest integer

4. Select a random number, r, between 1 and i, as explained in simple random sampling

5. The elements with the following numbers will comprise the systematic random sample: r, r+i,r+2i,r+3i,r+4i,...,r+(n-1)i

11-21

1. Select a suitable frame

2. Select the stratification variable(s) and the number of strata, H

3. Divide the entire population into H strata. Based on the classification variable, each element of the population is assigned to one of the H strata

4. In each stratum, number the elements from 1 to Nh (the pop. size of stratum h)

5. Determine the sample size of each stratum, nh, based on proportionate or disproportionate stratified sampling, where

6. In each stratum, select a simple random sample of size nh

Procedures for DrawingProbability SamplesFig. 11.4 cont.

nh = n

h=1

H

Stratified Sampling

11-22Procedures for DrawingProbability SamplesFig. 11.4 cont.

Cluster Sampling

1. Assign a number from 1 to N to each element in the population2. Divide the population into C clusters of which c will be included in the sample3. Calculate the sampling interval i, i=N/c (round to nearest integer)4. Select a random number r between 1 and i, as explained in simple random sampling5. Identify elements with the following numbers: r,r+i,r+2i,... r+(c-1)i6. Select the clusters that contain the identified elements7. Select sampling units within each selected cluster based on SRS or systematic sampling8. Remove clusters exceeding sampling interval i. Calculate new population size N*, number of clusters to be selected C*= C-1, and new sampling interval i*.

11-23Procedures for Drawing Probability Samples

Repeat the process until each of the remaining clusters has a population less than the sampling interval. If b clusters have been selected with certainty, select the remaining c-b clusters according to steps 1 through 7. The fraction of units to be sampled with certainty is the overall sampling fraction = n/N. Thus, for clusters selected with certainty, we would select ns=(n/N)(N1+N2+...+Nb) units. The units selected from clusters selected under PPS sampling will therefore be n*=n- ns.

Cluster Sampling

Fig. 11.4 cont.

11-24Choosing Nonprobability vs. Probability Sampling

Conditions Favoring the Use of

Factors

Nonprobability sampling

Probability sampling

Nature of research

Exploratory

Conclusive

Relative magnitude of sampling and nonsampling errors

Nonsampling errors are larger

Sampling errors are larger

Variability in the population

Homogeneous (low)

Heterogeneous (high)

Statistical considerations

Unfavorable Favorable

Operational considerations Favorable Unfavorable

Table 11.4 cont.

What is sampling? If all members of a population were identical, the

population is considered to be homogenous.

That is, the characteristics of any one individual in the population would be the same as the characteristics of any other individual (little or no variation among individuals).

So, if the human population on Earth was homogenous in characteristics, how many people would an alien need to abduct in order to understand what humans were like?

What is sampling? When individual members of a population are different from

each other, the population is considered to be heterogeneous (having significant variation among individuals).

How does this change an alien’s abduction scheme to find out more about humans?

In order to describe a heterogeneous population, observations of multiple individuals are needed to account for all possible characteristics that may exist.

What is Sampling?

Population

Sample

Using data to say something (make an inference) with confidence, about a whole (population) based on the study of a only a few (sample).

Sampling Frame

Sampling Process

What you want to talk

about

What you actually

observe in the data

Inference

What is Sampling?

Sampling is the process of selecting observations (a sample) to provide an adequate description and robust inferences of the population The sample is representative of the population.

There are 2 types of sampling: Non-Probability sampling (Thurday’s lecture) Probability sampling

Random Selection or Assignment

Selection process with no pattern; unpredictable Each element has an equal probability of being selected for a study Reduces the likelihood of researcher bias Researcher can calculate the probability of certain outcomes Variety of types of probability samples—we’ll touch on soon

Why Random Assignment? Samples that are assigned in a random fashion are most likely to be

truly representative of the population under consideration.

Can calculate the deviation between sample results and a population parameter due to random processes.

Simple Random Sampling (SRS) The basic sampling method which most others are based on.

Method: A sample size ‘n’ is drawn from a population ‘N’ in such a way that every possible

element in the population has the same chance of being selected. Take a number of samples to create a sampling distribution

Typically conducted “without replacement”

What are some ways for conducting an SRS? Random numbers table, drawing out of a hat, random timer, etc.

Not usually the most efficient, but can be most accurate! Time & money can become an issue What if you only have enough time and money to conduct one sample?

Systematic Random Sampling (SS) Method:

Starting from a random point on a sampling frame, every nth element in the frame is selected at equal intervals (sampling interval).

Sampling Interval tells the researcher how to select elements from the frame (1 in ‘k’ elements is selected). Depends on sample size needed

Example: You have a sampling frame (list) of 10,000 people and you need a sample of

1000 for your study…What is the sampling interval that you should follow? Every 10th person listed (1 in 10 persons)

Empirically provides identical results to SRS, but is more efficient. Caution: Need to keep in mind the nature of your frame for SS to

work—beware of periodicity.

In Simple Random Sampling

The gap, or period between successive elements is random, uneven, has no particular pattern.

In Systematic Sampling

Gaps between elements are equal andConstant There is periodicity.

Stratified Sampling (StS) Method:

Divide the population by certain characteristics into homogeneous subgroups (strata) (e.g., UI PhD students, Masters Students, Bachelors students).

Elements within each strata are homogeneous, but are heterogeneous across strata.

A simple random or a systematic sample is taken from each strata relative to the proportion of that stratum to each of the others.

Researchers use stratified sampling When a stratum of interest is a small percentage of a population

and random processes could miss the stratum by chance. When enough is known about the population that it can be easily

broken into subgroups or strata.

POPULATION

STRATA 1 STRATA 2

n = 1000; SE = 10%

n= 500; SE=7.5% n = 500; SE=7.5%

equal intensity

POPULATION

STRATA 1

STRATA 2

n =1000, SE = 10%

n = 600SE=5.0%

n =400SE=7.5%

proportional to size

Sample equal intensity vs.? proportional to size ?

What do you want to do? Describe the population, or describe each strata?

Cluster sampling Some populations are spread out (over a state or

country).

Elements occur in clumps (towns, districts)—Primary sampling units (PSU).

Elements are hard to reach and identify.

Trade accuracy for efficiency.

You cannot assume that any one clump is better or worse than another clump.

Cluster sampling Used when:

Researchers lack a good sampling frame for a dispersed population.

The cost to reach an element to sample is very high.

Each cluster is as varied heterogeneous internally and homogeneous to all the other clusters.

Usually less expensive than SRS but not as accurate Each stage in cluster sampling introduces sampling error—

the more stages there are, the more error there tends to be.

Can combine SRS, SS, stratification and cluster sampling!!

Examples of Clusters and Strata

Recreation Research: Strata: weekday-weekend; gender; type of

travel; season; size of operation; etc. What are some others?

Clusters: counties; entry points (put-in and take-outs); time of day, city blocks, road or trail segments.

What are some others?

12 - 41

• Population: The entire group about which information is desired.

• Sample: A proportion or part of the population - usually the proportion from which information is gathered.

Populations and Samples

12 - 42

Target Population

• The participants to whom the answer to the question pertains.

• The target population definition has two aspects:

• Conceptual

• Operational

12 - 43

Sampling

• In its broadest sense, sampling is a procedure by which one or more members of a population are picked from the population.

• The objective is to make certain observations upon the members of the sample and then, on the basis of these results, to draw conclusions about the characteristics of the entire population.

More complex sampling methods

Stratified sampling

• When to use– Population with distinct subgroups

• Procedure – Divide (stratify) sampling frame into homogeneous

subgroups (strata) e.g. age-group, urban/rural areas, regions, occupations

– Draw random sample within each stratum

Stratified sampling

• Advantages– Can acquire information about whole

population and individual strata– Precision increased if variability within strata is

smaller (homogenous) than between strata

• Disadvantages– Sampling error is difficult to measure– Different strata can be difficult to identify– Loss of precision if small numbers in individual

strata (resolved by sampling proportional to stratum population)

Cluster sampling

• Principle

– Whole population divided into groups e.g. neighbourhoods

– A type of multi-stage sampling where all units at the lower level are included in the sample

– Random sample taken of these groups (“clusters”)

– Within selected clusters, all units e.g. households included (or random sample of these units)

– Provides logistical advantage

Cluster sampling

• Advantages– Simple as complete list of sampling units within

population not required– Less travel/resources required

• Disadvantages– Cluster members may be more alike than those in

another cluster (homogeneous)– this “dependence” needs to be taken into account in

the sample size and in the analysis (“design effect”)

Selecting a sampling method

• Population to be studied– Size/geographical distribution– Heterogeneity with respect to variable

• Availability of list of sampling units• Level of precision required• Resources available

Simple random sampling

• Principle– Equal chance/probability of each unit

being drawn

• Procedure– Take sampling population– Need listing of all sampling units (“sampling frame”)– Number all units– Randomly draw units

Simple random sampling

• Advantages– Simple– Sampling error easily measured

• Disadvantages– Need complete list of units– Units may be scattered and poorly accessible– Heterogeneous population

important minorities might not be taken into account

Systematic sampling

• Principle– Select sampling units at regular intervals

(e.g. every 20th unit)

• Procedure– Arrange the units in some kind of sequence– Divide total sampling population by the designated sample size

(eg 1200/60=20) – Choose a random starting point (for 20, the starting point will be

a random number between 1 and 20)– Select units at regular intervals (in this case, every 20th unit), i.e.

4th, 24th, 44th etc.

Systematic sampling

• Advantages– Ensures representativity across list

– Easy to implement

• Disadvantages– Need complete list of units

– Periodicity-underlying pattern may be a problem (characteristics occurring at regular intervals)

Definition of sampling

Procedure by which some members

of a given population are selected as

representatives of the entire population

in terms of the desired characteristics