Sampling: Design and Procedures - clsbe.lisboa.ucp.pt · Sampling: Design and Procedures ......

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1MBACATÓLICA Marketing Research week 6

MBACATÓLICAJAN/APRIL 2006

Fernando S. Machado

Marketing ResearchMarketing Research

Week 6

• Sampling: Design and Procedures

• Sampling: Sample Size Determination

• Data Preparation


Sampling: Design and Procedures

ü The Sampling Process

ü Sampling Techniques

ü Application: Shopping Center Sampling

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Identifying the Target Population

Determining the Sampling Frame

Selecting a Sampling Technique

Probability Sampling

Non-Probability Sampling

Determining the Relevant Sample Size

Execute Sampling

Data Collection From Respondents

Information for Decision-Making

Reconciling the Population, Sampling Frame Differences

Handling the Non-Response Problem

The Sampling Process


Sampling ProcessSampling Process

Determining Target Populationü Look to the research objectives ü Consider all alternativesü Know your marketü Consider the appropriate sampling unitü Consider convenience

Target Population: The collection of elements or objects that possess the information sought by the researcher and about which inferences are to be made.

Sampling Frame: representation of the elements ofthe target population. It consists of a list or set ofdirections for identifying the target population.

3


Selecting a Sampling Procedure• Decide whether to use probability or non probability sampling

Probability Samplingü All population members have a known probability of being in the sample

Non Probability Samplingü Costs and trouble of developing sampling frame are eliminatedü Results can contain hidden biases and uncertainties

Sampling Process (Contd.)


Sampling Techniques

Classification of Sampling Techniques

ConvenienceSampling

ProbabilitySampling Techniques

JudgmentalSampling

QuotaSampling

SnowballSampling

SystematicSampling

StratifiedSampling

ClusterSampling

Other samplingTechniques

Simple randomSampling

NonprobabilitySampling Techniques

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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

Procedures for Drawing Probability SamplesProcedures for Drawing Probability Samples

Simple Random Samplingü Each population member, and each possible sample, has equal probability of being selected


1. Select a suitable sampling frame

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

3. Determine the sample 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

Systematic Samplingü Involves systematically spreading the sample through the list of population membersü Commonly used in telephone surveys

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nh = nh=1

H

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

Stratified Sampling• The chosen sample is forced to contain units from each of the segments or strata of the population


Sampling Techniques Sampling Techniques (Contd.)(Contd.)

Types of Stratified Sampling

Proportionate Stratified Sampling

ü Number of objects/sampling units chosen from each group is proportional to number in population

ü Can be classified as directly proportional or indirectly proportional stratified sampling

Disproportionate Stratified Sampling

ü Sample size in each group is not proportional to the respective group sizes

ü Used when multiple groups are compared and respective group sizes are small

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Sampling TechniquesSampling Techniques (Contd.)(Contd.)

Cluster Sampling

ü Involves dividing population into subgroups

ü Random sample of subgroups/clusters is selected

ü For each selected cluster, either all the elements are included in the sample or a sample of elements is drawn probabilistically

Cluster Sampling is:

ü Very cost effectiveü Useful when subgroups can be identified that are representative of entire population


Freguesia nº Population Cumulative1 100 000 100 0002 50 000 150 0003 20 000 170 0004 150 000 320 0005 75 000 395 0006 5 000 400 0007 30 000 430 0008 25 000 455 0009 35 000 490 00010 10 000 500 000

An example of area samplingHow to select probabilistically a sample of 3 freguesias from a group of 10?

Solution: Randomly generate 3 numbers on the interval 1-500 000.Ex: 75 235, 232 974, 429 232 ⇒ select freguesias 1, 4 and 7

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Sampling efficiency improved by decreasing cost at a faster rate than accuracy

Sampling efficiency improved by increasing accuracy at a faster rate than cost

Random selection of groupsAll groups included

Heterogeneity within groupsHeterogeneity between groups

Homogeneity between groups

Homogeneity within groups

A Comparison of Stratified and Cluster Sampling Processes

Stratified Sampling Cluster Sampling


Sampling TechniquesSampling Techniques (Contd.)(Contd.)Types of Non Probability Sampling

Judgmental sampling

ü "Expert" uses judgement to identify representative samples

Snowball sampling

ü Form of judgmental sampling

ü Appropriate when reaching small, specialized populations

ü Each respondent, after being interviewed, is asked to identify one or more others in the appropriate group

Convenience sampling

ü Used to obtain information quickly and inexpensively

Quota sampling

ü Judgmental sampling where the sample includes a minimum number from each specified subgroup in the population

ü Often based on demographic data

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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

Strengths and Weaknesses of Basic Sampling TechniquesStrengths and Weaknesses of Basic Sampling Techniques


Application: Shopping Center SamplingApplication: Shopping Center Sampling

ü 20% of all questionnaires completed or interviews granted are store-intercept interviews

ü Bias is introduced by methods used to select the sample

Sources of Bias:• Selection of shopping center

• Point of shopping center from which respondents are drawn

• Time of day

• More frequent shoppers will be more likely to be selected

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Shopping Center SamplingShopping Center Sampling (Contd.)(Contd.)

Solutions to Bias:

ü Shopping Center Bias

• Use several shopping centers in different neighborhoods

• Use several diverse cities

ü Sample Locations Within a Center

• Stratify by entrance location

• Take separate sample from each entrance

• To obtain overall average, strata averages should be combined by weighing them to reflect traffic that is associated with each entrance


Shopping Center SamplingShopping Center Sampling (Contd.)(Contd.)

ü Time Sampling- Stratify by time segments- Interview during each segment- Final counts should be weighed according to traffic counts

ü Sampling people versus shopping visits- If the goal is to develop a sample that represents the total population, then we should attach a lower weight to more frequent shoppers.

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Sampling: Sample Size Determination

ü Statistical vs. Ad-hoc Methods of Sample Size Determinationü Sample Reliability, Sampling Distributions and Sample Sizeü Some Practical Rules for Determining Sample Sizeü Non-response Problems


Sample Size and Statistical TheorySample Size and Statistical TheoryDetermining the Sample Sizeü Use of statistical techniques or ad hoc methods ü Ad hoc methods used when researcher knows from

experience what sample size to adopt or when budgetary constraints dictate the size of the sample

A Sampling ProblemThe management of a local restaurant wants to determine the average monthly amount spent by households at fancy restaurants. Some households do not spend anything at all, whereas other households spend as much as 300€ per month. Management wants to be 95% confident of the findings and does not want the error to exceed plus or minus 5€. What sample size should be used to determine the average monthly household expenditure?

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Population Characteristics/parametersPopulation Mean (µ)ü Normally unknown; Determine its value as closely as possible

by taking a sample from population

Population Variance (σ2)ü Measure of population dispersion

ü Based on degree to which a response differs from population average response

Sample Characteristics/statisticsSample Mean (X)ü Is used to estimate the unknown population mean

Sample Variance (S2)ü Is used to estimate unknown population variance


Distribution of Sample Means (n=10)

0

5

10

15

20

25

30

<165 175 185 195 205 215 225 235 >235

Distribution of Sample Means (n=100)

0

5

10

15

20

25

30

<165 175 185 195 205 215 225 235 >235

Effect of Sample Size on Distribution of Sample Mean

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Effect of Population Variance on Distribution of Sample Mean

Distribution of Sample Means (n=10 , sigma=50)

0

5

10

15

20

25

30

<165 175 185 195 205 215 225 235 >235

Distribution of sample means (n=10 , sigma=20)

0

5

10

15

20

25

30

<165 175 185 195 205 215 225 235 >235


ü X will vary from sample to sample

ü As sample size (n) increases, variation in X will decrease ⇒ Standard error depends on sample size

ü As the population variation increases, variation in X will increase ⇒ Standard error depends on population variance

ü Assume that variation of X follows normal distribution - reasonable if population is normal or if sample size is large

ü Sampling distribution

• Indicates probability of getting a particular sample mean

Sample Reliability

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Sampling Distributions

( )XNX σµ,≈ ( )pNp σπ,≈

XX Sn

s

n=→=

σσ ( ) ( )

pp Sn

ppn

=−

→−

=11 ππ

σ

Standard error of sample mean:

Standard error of sampleproportion:


Variable Population Sample

Mean µ

Proportion π p

Variance σ2 S2

Standard Deviation σ S

Size N n

Standard error of the mean

Standard error of proportion σp Sp

Standardized variate (X-µ)/σ

XσX

S

SXX /)( −

X

Symbols for Population and Sample Variables

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Finding Probabilities Corresponding to Known Values

Z Scaleµ-3σ µ-2σ µ-1σ µ µ+1σ µ+2σ µ+3σ

35

-3

40

-2

45

-1

50

0

55

+1

60

+2

65

+3

(µ=50, σ =5)

Z Scale

Area is 0.3413Area between µ and µ + 1σ = 0.3431Area between µ and µ + 2σ = 0.4772Area between µ and µ + 3σ = 0.4986


Area is 0.475Area is 0.475

X 50X Scale

-Z 0Z Scale

Area is 0.025

Finding Values Corresponding to Known Probabilities: Confidence Interval

Area is 0.025

-Z

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95% Confidence Interval for the 95% Confidence Interval for the Population MeanPopulation Mean

XL

_XU

_X_

0.475 0.475

nX

σσ 22 =nX

σσ 22 =

For a given n we can be 95% confident that µ lies in the interval

[ ]UL XX ,

nerrorsampling

σ2=


Size of Interval EstimateSize of Interval Estimate and and Confidence Confidence LevelLevel

ü Precision level: when estimating a population parameter by using a sample statistic, the precision level is the desired size of the interval(maximum permissible difference between the sample statistic and the population parameter)

ü Confidence level: probability that a confidence interval will include the population parameter

Sample size

To determine sample size we need to specify:

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Sample Size Question

ü Size of the sampling error that is desired (D)

ü Confidence level ⇒ Z

ü Use an estimate (s) of unknown population st. dev. (σ)

ü Sample size n = Z2 s2 /D2

Determining the Population Standard Deviation• Use a sample standard deviation obtained from a previous comparable survey or from a pilot survey

• Estimate the population standard deviation subjectively

Z Dn

σ=


Sample Size When Proportions Are UsedSample Size When Proportions Are Used

n = z2 p(1 - p)/(sampling error)2

( )n

ZDerrorsamplingππ −

==1

üFor a 95% confidence level (Z=1,96), sampling error is maximised when π=0.5 ⇒ π(1- π)=0.25. Using 1s t expression we can obtain:

n erro100 9,8%250 6,2%500 4,4%750 3,6%

1000 3,1%

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Steps M e a n s Proportions 1. Specify the level of precision

D = ±$5.00

D = p - ∏ = ± .05

2. Specify the confidence level (CL)

CL = 95%

CL = 95%

3. Determine the z value associated with CL

z value is 1.96

z value is 1.96

4. Determine the standard deviation of the population

Estimate σ : σ = 5 5

Estimate ∏ : ∏ =

0.64 5. Determine the sample size using the formula for the standard error

n = σ 2 z2/D2 = 465

n = ∏ (1 -∏ ) z 2/D 2 =

355 7. If necessary, reestimate the confidence interval by employing s to estimate σ

= X ± z SX

= p ± z sp

8. If precision is specified in relative rather than absolute terms, determine the sample size by substituting for D.

D = R µ

n = C2z

2/R

2

D = R ∏

n = z2(1-∏ )/(R 2∏ )

Sample Size Determination for Means and Proportions


The management of a local restaurant wants to determine the average monthly amount spent by households at fancy restaurants. Some households do not spend anything at all, whereas other households spend as much as 300€ per month. Management wants to be 95% confident of the findings and does not want the error to exceed plus or minus 5€.

i) What sample size should be used to determine the average monthly household expenditure?

ii) After the survey was conducted, the average expenditure was found to be 90.30€ and the standard deviation was 45€. Construct a 95% confidence interval. What can be said about the level of precision?

A Sampling Problem

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Variable Mean Household Monthly Expense On

Departm.store shopping Clothes Gifts Confidence level

95%

95%

95%

z value

1.96

1.96

1.96

Precision level (D)

$5

$5

$4

Standard deviation of the population (σ)

$55

$40

$30

Required sample size (n)

465

246

217

Sample Size For Estimating Multiple Parameters


Rules of ThumbRules of Thumbü Sample should be large enough, so that when it is

divided into groups, each group will have a minimum sample size of 100 or more

ü If analysis involves comparison between subgroups, sample size in each subgroup should be 20 to 50

ü Use disproportionate sampling if one of groups of population is relatively small

ü Researcher must decide whether sample size dictated by budget constraints allows a worthwhile study to be conducted

ü Find similar studies and use their sample sizes as a guide

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Type of Study

Minimum Size Typical Range

Problem identification research (e.g. market potential)

500

1,000-2,500

Problem-solving research (e.g. pricing)

200 300-500

Product tests

200 300-500

Test marketing studies

200 300-500

TV, radio, or print advertising (per commercial or ad tested)

150 200-300

Focus groups

2 groups 4-12 groups

Sample Sizes Used in Marketing Sample Sizes Used in Marketing Research StudiesResearch Studies


Non Response ProblemsNon Response Problems

ü Sample size has to be large enough to allow for non response

ü Those who respond may differ from non respondents in a meaningful way, creating biases

ü Seriousness of nonresponse bias depends on extent of non response

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Methods of ImprovingResponse Rates

Solutions to Nonresponse Problem -Improving Response RatesImproving Response Rates

ReducingRefusals

ReducingNot-at-Homes

PriorNotification

MotivatingRespondents

Incentives Questionnaire Designand Administration

Follow-Up OtherFacilitators

Callbacks


üAttempt to estimate the nonresponse bias (assess whether there are significant differences between respondents and non-respondents)

üAdjust to non-response bias- Sub-sampling of nonrespondents (contact a sub-sample of non-respondents in a mail survey by telephone)

- Replacement (contact nonrespondents from an earlier, similar survey)

- Substitution (divide the sample into sub-groups that are internally homogeneous in terms of respondent characteristics but heterogeneous in terms of response rates)

- Weighting (Potitz approach: attach higher weight to respondents who are less often at home)

Solutions to Nonresponse Problem (Contd)

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Data Preparation

ü Editing the Data

ü Coding the Data

ü Transcribing the Data

ü Cleaning the Data

ü Statistically Adjusting the Data


Prepare Preliminary Plan of Data Analysis

Data Preparation ProcessData Preparation Process

Edit

Code

Transcribe

Statistically Adjust the Data

Clean Data

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Preparing the Data for AnalysisPreparing the Data for Analysis (Contd.)(Contd.)

Data Editingü A review of the questionnaires with the objective of

increasing accuracy and precision.

Problems Identified With Data Editingü Interviewer Error (incorrect instructions from interviewers)ü Omissions (respondents may fail to answer a question or a whole section of the questionnaire)ü Ambiguity (responses may not be legible or may be unclear)ü Inconsistencies (preliminary check of obvious inconsistencies)ü Lack of Cooperation (ex: respondent who checks always the same response category in every item of a Likert scale)ü Ineligible Respondent



Treatment of unsatisfactory responses

ü Return questionnaire to the field in order to be completed

ü Assign missing values

ü Discard unsatisfactory respondents

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Codingü Coding closed-ended questions involves specifying how

the responses are to be entered

ü Open-ended questions are difficult to code• Lengthy list of possible responses is generated

Coding and Transcribing Different Types of Variables

ü Categorical data on sex, age, income, etc

ü Categorical data with possibility to choose multiple categories

ü Rank-ordered data


Preparing the Data for Analysis (Contd.)

Data cleaningü Consistency checks

• Out-of-range values• Extreme values• Logical inconsistencies

ü Treatment of missing responses• Casewise deletion• Pairwise deletion (“different sample” for each

calculation)• Substitute a neutral value• Substitute an imputed response (the researcher

attempts to infer from the available data the responses the individuals would have given if they had answered).

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Statistically Adjusting the Data: Weighting

ü Each response is assigned a number according to a pre-specified rule

ü Makes sample data more representative of target population on specific characteristics

ü Modifies number of cases in the sample that possess certain characteristics

ü Adjusts the sample so that greater importance is attached to respondents with certain characteristics


Population(N=10 000)

Sample(n=100)

Primary 5 000 40

Secondary 3 000 20

Higher 2 000 40

WeightingAn example:

Weight in population

Weight in sample

Weight

Primary 50% 40% 1.25

Secondary 30% 20% 1.5

Higher 20% 40% 0.5

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Statistically Adjusting the Data: Variable Re-specification

ü Existing data is modified to create new variablesthat are consistent with study objectives

• Recoding of a variable

• Large number of variables collapsed into fewer variables

• One categorical variable with d categories transformed into d-1 dummy variables



Statistically Adjusting the Data: Scale Transformation

ü Scale values are manipulated to ensure comparability with other scales

ü Standardization allows the researcher to compare variables that have been measured using different types of scales

ü Variables are forced to have a mean of zero and a standard deviation of one

ü Can be done only on interval or ratio scaled data

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