ARM Lecture 5

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Sampling Design

Lecture - 5 Lecture - 5

Advanced Research Methods (ARM) Advanced Research Methods (ARM)

(2)



_{What is difference between}

data and statistics?

(3)

Recall…



 _{Statistics is a tool for converting}_{Statistics is a tool for converting} _data_data _into_into

information information:: Data Data Statistics Statistics Information Information

But where then does

But where then does datadata _{come from? How is it gathered?}_{come from? How is it gathered?}

How do we ensure its accurate? Is

How do we ensure its accurate? Is the data reliable? Is itthe data reliable? Is it

representative of the population from which it was

(4)

Sampling



 _{Sampling is that part of}_Sampling _{is that part of statistical practice}_{statistical practice}

which is concerned with the selection of which is concerned with the selection of

individual observations intended to yield some individual observations intended to yield some knowledge about a population of concern,

knowledge about a population of concern, especially for the purposes of

especially for the purposes of statisticalstatistical inference.

(5)

…

Sampling

Sampling is the processis the process

of selecting a small number of elements

from a larger defined target group

of elements such that

the information gathered

from the small group will allow judgments

to be made about the larger groups

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What is a sample?

A sample is a portion of the

elements of a population. A sample

is chosen to make inferences about

the population by examining or

measuring the elements in the

sample.

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Reasons for Sampling

Researchers rarely survey the population for two Researchers rarely survey the population for two reasons(Adér, Mellenbergh, & Hand, 2008):

reasons(Adér, Mellenbergh, & Hand, 2008): (1)The cost is too high and

(1)The cost is too high and

(2)The population is dynamic, i.e., the component (2)The population is dynamic, i.e., the component of population could change over time. E.g.

of population could change over time. E.g. patients in a hospital

(8)

Advantages of sampling:

(1) The cost is lower, (1) The cost is lower,

(2) Data collection is faster, and (2) Data collection is faster, and (3) It is possible

(3) It is possible to ensure homogeneity and toto ensure homogeneity and to improve the accuracy and quality of the data improve the accuracy and quality of the data because the data set is smaller.

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Basics of Sampling Theory

Population Population Element Element Defined target Defined target population population Sampling unit Sampling unit Sampling frame Sampling frame

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Selection of Elements



_Population_Population 

_{Population Element}_{Population Element}  _Sampling_Sampling  _Survey_Survey   _Census_Census

(11)

Definitions



 _{Population: The target population is the collection of}_Population: _{The target population is the collection of}

elements or objects that possess the information sought elements or objects that possess the information sought by the researcher and about which inferences are to be by the researcher and about which inferences are to be

made.

made. The target The target population should population should be defined be defined in termsin terms of elements, sampling units, extent, and

of elements, sampling units, extent, and time.time. 

 An An elementelement is the object about which or from is the object about which or from whichwhich

the information is desired, e.g., the respondent. the information is desired, e.g., the respondent. 

 A A sampling unitsampling unit is an element, or a unit containingis an element, or a unit containing

the element, that is available for

the element, that is available for selection at someselection at some stage

stage of the of the sampling sampling process. process. E.g. orE.g. organizationganization 

 ExtentExtent refers to the geographical boundaries.refers to the geographical boundaries.



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Sampling frame



 _{Sampling frame (synonyms: "sample frame",}_{Sampling frame (synonyms: "sample frame",}

"survey frame") is the actual set of

"survey frame") is the actual set of units fromunits from which a sample has been drawn: in the case of a which a sample has been drawn: in the case of a

simple random sample, all units from the simple random sample, all units from the sampling frame have an equal chance to be sampling frame have an equal chance to be drawn and to occur in the sample.

drawn and to occur in the sample.



 _{In the ideal case, the sampling frame should}_{In the ideal case,}_{the sampling frame should}

coincide with the population of interest. coincide with the population of interest.

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Example



 Consider, a survey aimed at establishing the number of potentialConsider, a survey aimed at establishing the number of potential customers for Easypaisa in the population of Islamabad City.

customers for Easypaisa in the population of Islamabad City. The research team has drawn 1000 numbers at random from a The research team has drawn 1000 numbers at random from a telephone directory for the city, made 200 calls each day from telephone directory for the city, made 200 calls each day from Monday to Friday from 8am to 5pm and asked some questions. Monday to Friday from 8am to 5pm and asked some questions.



 In this example, populationIn this example, population of interest is all inhabitants of the of interest is all inhabitants of the city; thecity; the sampling frame

sampling frame includes only those dwellers who satisfy all includes only those dwellers who satisfy all the followingthe following conditions:

conditions:



 has a telephone;has a telephone;



 the telephone number is included in the directory;the telephone number is included in the directory;



 likely to be at home from 8am to 5pm from Monday to Friday;likely to be at home from 8am to 5pm from Monday to Friday;



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Sampling Plans…



_A_{A sampling plan}_{sampling plan} _{is just a method or procedure}_{is just a method or procedure}

for specifying how a sample will be taken from a for specifying how a sample will be taken from a population.

(15)

What is a Good Sample?



_{Accurate: absence of bias}_{Accurate: absence of bias}



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Is sample unbiased?

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Types of Errors



 _{Sampling and}_{Sampling and} 

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Sampling Error



 Sampling error is any type of bias that isSampling error is any type of bias that is

attributable to mistakes in either drawing a sample or attributable to mistakes in either drawing a sample or determining the sample size

determining the sample size



 Sampling errors are caused by sampling design. ItSampling errors are caused by sampling design. It

includes: includes: (1)

(1) Selection errorSelection error: Incorrect selection probabilities: Incorrect selection probabilities are used.

are used. (2)

(2) Estimation errorEstimation error: Biased parameter estimate: Biased parameter estimate because of the elements in these samples.

(19)



 _{E.g. Two samples of size 10 of 1,000 households. If}_{E.g. Two samples of size 10 of 1,000 households. If}

we happened to get the highest income level data

points in our first sample and all the lowest income

levels in the second, this delta is due to sampling

error.



 _{Increasing the sample size}_{Increasing the sample size}_will_will _{reduce this type of}_{reduce this type of}

error.

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Non-sampling errors



 Nonsampling errorsNonsampling errors are more serious and are due to mistakesare more serious and are due to mistakes

made in the acquisition of data or due to

made in the acquisition of data or due to the sample observationsthe sample observations being selected improperly. Non-sampling errors are caused by the being selected improperly. Non-sampling errors are caused by the

mistakes in data processing. It includes: mistakes in data processing. It includes: (1)

(1) OvercoverageOvercoverage: Inclusion of data from outside of the: Inclusion of data from outside of the population.

population. (2)

(2) UndercoverageUndercoverage: Sampling frame does not : Sampling frame does not include elements ininclude elements in the population.

the population. (3)

(3) Measurement errorMeasurement error: The : The respondent misunderstanrespondent misunderstand thed the question.

question. (4)

(4) Processing errorProcessing error: Mistakes in data coding.: Mistakes in data coding. (5)

(21)



 Increasing the sample sizeIncreasing the sample size will not will not reduce this type of error.reduce this type of error. 

 Acquisition errors arise from the recording of incorrect Acquisition errors arise from the recording of incorrect

responses, due to:



 — incorrect measurements being taken because of faulty equipment,— incorrect measurements being taken because of faulty equipment,



 — mistakes made during transcription from primary sources,— mistakes made during transcription from primary sources,



 — inaccurate recording of data due — inaccurate recording of data due to misinterpretation of terms, orto misinterpretation of terms, or



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Sampling Methods

Probability Probability sampling sampling Nonprobability Nonprobability sampling sampling

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Steps in Sampling Design



_{What is the relevant population?}_{What is the relevant population?} 

_{What are the parameters of interest?}_{What are the parameters of interest?} 

_{What is the}_{What is the sampling frame}_{sampling frame??} 

_{What is the type of sample?}_{What is the type of sample?} 

_{What size sample is needed?}_{What size sample is needed?} 

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Steps

Define the Population Define the Population

Determine the Sampling Frame Determine the Sampling Frame Select Sampling Technique(s) Select Sampling Technique(s)

Determine the Sample Size Determine the Sample Size Execute the Sampling Process Execute the Sampling Process

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Classification of Sampling

Techniques

Sampling Techniques Sampling Techniques Nonprobability Nonprobability Sampling Techniques Sampling Techniques Probability Probability Sampling Techniques Sampling Techniques Convenience Convenience Sampling Sampling Judgmental Judgmental Sampling Sampling Quota Quota Sampling Sampling Snowball Snowball Sampling Sampling Systematic Systematic Sampling Sampling Stratified Stratified Sampling Sampling Cluster Cluster Sampling Sampling Other Sampling Other Sampling Techniques Techniques Simple Random Simple Random Sampling Sampling

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Non-Probability

Sampling Designs

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Nonprobabil

Nonprobability

ity Sampling Methods

Sampling Methods

Convenience sampling relies

upon convenience and access

Judgment sampling relies upon belief

that participants fit characteristics

Quota sampling emphasizes representation

of specific characteristics

Snowball sampling relies upon respondent

referrals

(28)

Nonprobability Sampling

Reasons to use Reasons to use



 _{Procedure satisfactorily meets the sampling}_{Procedure satisfactorily meets the sampling}

objectives objectives



 _{Lower Cost}_{Lower Cost} 

 _{Limited Time}_{Limited Time} 

 _{Not as much human error as selecting a}_{Not as much human error as selecting a}

completely random sample completely random sample



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Nonprobability Sampling



 _{Convenience Sampling}_{Convenience Sampling} 

_{Purposive Sampling}_{Purposive Sampling}



 Judgment SamplingJudgment Sampling



 Quota SamplingQuota Sampling



(30)

Convenience Sampling

Convenience sampling

Convenience sampling attempts to obtain a sample of attempts to obtain a sample of convenient

convenient elements. elements. Often, rOften, respondents espondents are are selectedselected because they happen to be in

because they happen to be in the right place at the rightthe right place at the right time.

time. 

 use of students, and members of social organizationsuse of students, and members of social organizations



 mall intercept interviews without qualifying themall intercept interviews without qualifying the

respondents respondents 

 department stores using charge account listsdepartment stores using charge account lists



(31)

Judgmental Sampling

Judgmental sampling

Judgmental sampling is a form of convenienceis a form of convenience sampling in which the population elements are

sampling in which the population elements are selectedselected based on the judgment of the researcher.

based on the judgment of the researcher. 

 test marketstest markets



 purchase engineers selected in industrial purchase engineers selected in industrial marketingmarketing

research research 

(32)

Quota Sampling

Quota sampling

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

sampling.



 The first stage consists of developing control categories, or quotas, of The first stage consists of developing control categories, or quotas, of

population elements. population elements.



 In the second stage, sample elements are selected based onIn the second stage, sample elements are selected based on

convenience or judgment. convenience or judgment.

P

Pooppuullaattiioonn SSaammppllee

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(33)

Snowball Sampling

In

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

is selected, usually at random. 

 After being interviewed, these respondents are asked After being interviewed, these respondents are asked

to identify others who belong to the target population to identify others who belong to the target population of interest.

of interest. 

 Subsequent respondents are selected based on theSubsequent respondents are selected based on the

referrals. referrals.

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Probability Sampling

Designs

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Probability Sampling Designs



_{Simple random sampling}_{Simple random sampling} 

_{Systematic sampling}_{Systematic sampling} 

_{Stratified sampling}_{Stratified sampling}



 ProportionateProportionate



 DisproportionateDisproportionate



 _{Cluster sampling}_{Cluster sampling} 

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Simple Random Sampling



 _{Each element in the population has a}_{Each element in the population has a known and equal}_{known and equal}

probability of selection. probability of selection.



 _{Each possible sample of a given size (n) has a known and}_{Each possible sample of a given size (n) has a known and}

equal probability of being the sample actually selected. equal probability of being the sample actually selected.



 _{This implies that every element is}_{This implies that every element is selected independently}_{selected independently}

of every other element. of every other element.

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Systematic Sampling



 The sample is chosen by selecting a random starting point andThe sample is chosen by selecting a random starting point and

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

frame.



 _{The sampling interval, i, is}_{The sampling interval, i, is determined by dividing the population}_{determined by dividing the population}

size N by the sample size n and rounding to the nearest integer. size N by the sample size n and rounding to the nearest integer.



 _{When the ordering of the elements}_{When the ordering of the elements is related to the}_{is related to the characteristic}_{characteristic}

of interest, systematic sampling

of interest, systematic sampling increases the representativenessincreases the representativeness of the sample.

of the sample.



 _{For example, there are 100,000 elements in the population and a}_{For example, there are 100,000 elements in the population and a}

sample of 1,000

sample of 1,000 is desired. is desired. In this case In this case the sampling the sampling interval, i, iinterval, i, iss 100.

100. A A random random number number between 1 between 1 and 10and 100 is 0 is selected. selected. If, forIf, for example, this number is 23, the sample consists of elements 23 example, this number is 23, the sample consists of elements 23,, 123, 223, 323, 423, 523, and so on.

(38)

Stratified Sampling



 _{A two-step process in which the population is partitioned}_{A two-step process in which the population is partitioned}

into subpopulations, or strata. into subpopulations, or strata.



 _{The strata should be mutually exclusive and collectively}_{The strata should be mutually exclusive and collectively}

exhaustive in that every population element should be exhaustive in that every population element should be assigned to one and only one stratum and no population assigned to one and only one stratum and no population elements should be omitted.

elements should be omitted.



 _{Next, elements are selected from each stratum by a}_{Next, elements are selected from each stratum by a}

random procedure, usually SRS. random procedure, usually SRS.



 _{A major objective of stratified sampling is to increase}_{A major objective of stratified sampling is to increase}

precision without increasing cost. precision without increasing cost.

(39)

Stratified Sampling



 _{The elements within a stratum should be as homogeneous as}_{The elements within a stratum should be as homogeneous as}

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

heterogeneous as possible.



 _{Finally, the variables should decrease the cost of the stratification}_{Finally, the variables should decrease the cost of the stratification}

process by being easy to measure and apply. process by being easy to measure and apply.



 _{In proportionate stratified sampling, the size of the sample drawn}_{In proportionate stratified sampling, the size of the sample drawn}

from each stratum is proportionate to the relative size of that from each stratum is proportionate to the relative size of that stratum in the total population.

stratum in the total population.



 _{In disproportionate stratified sampling, the size of the sample from}_{In disproportionate stratified sampling, the size of the sample from}

each stratum is proportionate to the relative size of that stratum and each stratum is proportionate to the relative size of that stratum and to the standard deviation of the distribution of the characteristic of to the standard deviation of the distribution of the characteristic of interest among all the elements in that stratum.

(40)

Cluster Sampling



 _{The target population is first}_{The target population is first divided into mutually exclusive and}_{divided into mutually exclusive and}

collectively exhaustive subpopulations, or clusters. collectively exhaustive subpopulations, or clusters.



 _{Then a random sample of clusters is selected, based on a}_{Then a random sample of clusters is selected, based on a probability}_probability

sampling technique such as SRS. sampling technique such as SRS.



 _{For each selected cluster, either all the elements are included in the sample}_{For each selected cluster, either all the elements are included in the sample}

(one-stage) or a sample

(one-stage) or a sample of elements is drawn probabilistically (two-stage).of elements is drawn probabilistically (two-stage).



 _{Elements within a cluster should be as heterogeneous as possible, but}_{Elements within a cluster should be as heterogeneous as possible, but}

clusters themselves should

clusters themselves should be as be as homogeneous as homogeneous as possible. possible. IdeallyIdeally, , eacheach cluster should be a small-scale representation of the population.

cluster should be a small-scale representation of the population.



 _In_{In probability proportionate to size}_{probability proportionate to size sampling}_{sampling, the clusters are}_{, the clusters are}

sampled with probability proportional to

sampled with probability proportional to size. size. In the In the second stage, thesecond stage, the probability of selecting a sampling unit

probability of selecting a sampling unit in a selected in a selected cluster varies inversely cluster varies inversely with the size of the cluster.

(41)

Types of Cluster Sampling

Fig. 11.3

Fig. 11.3 _{Cluster Sampling}_{Cluster Sampling}

One-Stage One-Stage Sampling Sampling Multistage Multistage Sampling Sampling Two-Stage Two-Stage Sampling Sampling Simple Cluster Simple Cluster Sampling Sampling Probability Probability Proportionate Proportionate to Size Sampling to Size Sampling

(42)

Sample vs. Census

Type of Study

1. Budget

(43)

Sample Sizes Used in Marketing Sample Sizes Used in Marketing

Research Studies Research Studies Table 11.2 Table 11.2

Type of Study

Problem identificat

(44)

Factors to Consider in Sample Design

R

Reesseeaarrcch h oobbjjeeccttiivveess DDeeggrreee e oof f aaccccuurraaccyy

R

Reessoouurrcceess TTiimme e ffrraammee Knowledge of

Knowledge of target population

target population Research scopeResearch scope Statistical analysis needs

(45)



 _{How many completed questionnaires do we need}_{How many completed questionnaires do we need}

to have a

to have a representative sample?representative sample?



 _{Generally the larger the better, but that takes}_{Generally the larger the better, but that takes}

more time and money. more time and money.



_{Answer depends on:}_{Answer depends on:}



 How different or dispersed the population is.How different or dispersed the population is.



 Desired level of confidence.Desired level of confidence.



 Desired degree of aDesired degree of accuracy.ccuracy.

Determining Sample Size

(46)



 _{Common Methods:}_{Common Methods:}



 Budget/time availableBudget/time available



 Executive decisionExecutive decision



 Statistical methodsStatistical methods



 Historical data/guidelinesHistorical data/guidelines

Common

Methods

for

Determining

Sample Size

(47)

Factors Affecting Sample Size for Probability

Designs



_{Variability of the population characteristic}_{Variability of the population characteristic}

under investigation under investigation



 _{Level of confidence desired in the estimate}_{Level of confidence desired in the estimate} 

 _{Degree of precision desired in}_{Degree of precision desired in estimating the}_{estimating the}

population characteristic population characteristic

(48)

n = [N

22

Z

22

]/[Ne

22

+ σ

22

Z

22

]

Where Where



 _{e is the specified error}_{e is the specified error} 

 _{σ is the SD of the population}_{σ is the SD of the population} 

 _{N is the population}_{N is the population} 

 _{Z is the table value}_{Z is the table value of Z-Table. For a 95%}_{of Z-Table. For a 95%}

Confidence Interval, value of Z is 1.96 Confidence Interval, value of Z is 1.96

(49)

For a simple sample size calculator, click

For a simple sample size calculator, click here:here: http://www.surveysystem.com/sscalc.htm

http://www.surveysystem.com/sscalc.htm

Probability Sampling and

Sample Sizes

(50)

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Research Design

(51)

Measurement



 _{Selecting observable empirical events}_{Selecting observable empirical events}



 _{Using numbers or symbols}_{Using numbers or symbols to represent aspects}_{to represent aspects}

of the events of the events



_{Applying a}_{Applying a mapping rule}_{mapping rule to connect the}_{to connect the}

observation to the symbol observation to the symbol

(52)

What is Measured?



 _Objects::_Objects



 Things of ordinary experienceThings of ordinary experience



 Some things not concreteSome things not concrete



(53)

Characteristics of Data

  _{Classification}_{Classification}   _Order_Order 

 _{Distance (interval between numbers)}_{Distance (interval between numbers)} 

(54)

Data Types

O

Orrd

deerr IIn

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va

all O

Orriig

giin

n

N

Noommiinnaall nnoonnee nnoonnee nnoonnee O

Orrddiinnaall yyeess uunneeqquuaall nnoonnee IInntteerrvvaall yyeess eeqquuaal l oorr nnoonnee

unequal unequal R

(55)

Sources of Measurement

Differences

  _Respondent_Respondent 

 _{Situational factors}_{Situational factors} 

 _{Measurer or researcher}_{Measurer or researcher} 

(56)

Validity



 _{Content Validity}_{Content Validity}



 _{Criterion-Related Validity}_{Criterion-Related Validity}



 PredictivePredictive



 ConcurrentConcurrent



(57)

Reliability

  _Stability_Stability   Test-retestTest-retest Equivalence Equivalence 

 Parallel formsParallel forms



 _{Internal Consistency}_{Internal Consistency}



 Split-half Split-half



 KR20KR20



(58)

Practicality

  _Economy_Economy   _Convenience_Convenience   _{Interpretability}_{Interpretability}

(59)

MEASUREMENT

SCALES

(60)

What is Scaling?



_Scaling_{Scaling is assigning numbers to indicants of the}_{is assigning numbers to indicants of the}

properties of objects properties of objects

(61)

Types of Response Scales



_{Rating Scales}_{Rating Scales} 

_{Ranking Scales}_{Ranking Scales} 

(62)

Types of Rating Scales



 _{Simple category}_{Simple category} 

 _{Multiple choice,}_{Multiple choice,}

single response single response



 _{Multiple choice,}_{Multiple choice,}

multiple response multiple response



 _{Likert scale}_{Likert scale} 

 _{Semantic differential}_{Semantic differential}

•

• Numerical

Numerical

•

• _{Multiple rating}

_{Multiple rating}

•

• Fixed sum

Fixed sum

•

• _Stapel

_Stapel

•

(63)

Rating Scale Errors to Avoid



 _Leniency_Leniency



 Negative Leniency Negative Leniency



 Positive Leniency Positive Leniency



 _{Central Tendency}_{Central Tendency} 

(64)

Types of Ranking Scales



 _{Paired-comparison}_{Paired-comparison}



 _{Forced Ranking}_{Forced Ranking}



(65)

Dimensions of a Scale

  _{Unidimensional}_{Unidimensional}   _{Multidimensional}_{Multidimensional}

(66)

Scale Design Techniques



_{Arbitrary scaling}_{Arbitrary scaling} 

 _{Consensus scaling}_{Consensus scaling} 

 _{Item Analysis scaling}_{Item Analysis scaling} 

 _{Cumulative scaling}_{Cumulative scaling} 

(67)



 _{Sarndal, Swenson, and Wretman (1992), Model}_{Sarndal, Swenson, and Wretman (1992), Model}

Assisted Survey Sampling,

Assisted Survey Sampling, Springer-VerlagSpringer-Verlag



 _{Fritz Scheuren (2005). "What is a Margin of}_{Fritz Scheuren (2005). "What is a Margin of}

Error?", Chapter 10, in "What is a

Error?", Chapter 10, in "What is a Survey?",Survey?", American Statistical Association,

(68)

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Thank you for your

kind attention

Go forth and research….

….but be careful out there.