ARM Lecture 5

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Sampling Design

Lecture - 5

 What is difference between data and statistics?

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Recall… 

Statistics is a tool for converting data into information:: Statistics information

Data

Information

But where then does data come from? How is it gathered? How do we ensure its accurate? Is the data reliable? Is it representative of the population from which it was drawn?

Sampling Sampling is that part of statistical practice  which is concerned with the selection of  individual observations intended to yield some knowledge about a population of concern, especially for the purposes of statistical inference.

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… Sampling is 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

 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.

Reasons for Sampling Researchers rarely survey the population for two reasons(Adér, Mellenbergh, & Hand, 2008): (1)The cost is too high and (2)The population is dynamic, i.e., the component of population could change over time. E.g.  patients in a hospital

Advantages of sampling: (1) The cost is lower, (2) Data collection is faster, and (3) It is possible to ensure homogeneity and to improve the accuracy and quality of the data  because the data set is smaller.

Basics of Sampling Theory  Population Element Defined target population Sampling unit Sampling frame

Selection of Elements  Population

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 Population Element 

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 Sampling

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 Survey

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Census

Definitions 

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  A sampling unit is an element, or a unit containing the element, that is available for selection at some stage of the sampling process. E.g. organization organization  Extent refers to the geographical boundaries.  Time is the time period under consideration.

Sampling frame Sampling frame (synonyms: "sample frame", "survey frame") is the actual set of units from  which a sample has been drawn: in the case of a simple random sample, all units from the sampling frame have an equal chance to be drawn and to occur in the sample.  In the ideal case, the sampling frame should coincide with the population of interest. 

Example 

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

In this example, population example, population of interest is all inhabitants of the city; the sampling frame includes only those dwellers who satisfy all the following conditions:  has a telephone;  the telephone number is included in the directory;  likely to be at home from f rom 8am to 5pm from Monday to Friday;  not a person who refuses to answer all telephone surveys.

Sampling Plans…  A sampling plan is just a method or procedure  A sampling for specifying how a sample will be taken from a population.

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 What is a Good Sample?  Accurate: absence of bias

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Precise estimate: sampling error 

Is sample unbiased?

Types of Errors Sampling and  Non-Sampling Errors… 

Sampling Error 

Sampling error is any type of bias that is attributable to mistakes in either drawing a sample or determining the sample size

Sampling errors are caused by sampling design. It includes: (1) Selection error: error: Incorrect selection probabilities are used. (2) Estimation error: error: Biased parameter estimate  because of the elements in these samples.

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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.

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Increasing the sample size will reduce this type of  error.

Non-sampling errors 

Nonsampling errors are more serious and are due to mistakes made in the acquisition of data or due to the sample observations  being selected improperly. Non-sampling errors are caused by the mistakes in data processing. It includes: (1) Overcoverage Overcoverage:: Inclusion of data from outside of the population. (2) Undercoverage Undercoverage:: Sampling frame does not include elements in the population. (3) Measurement error: error: The respondent misunderstand misunderstand the question. error: Mistakes in data coding. (4) Processing error: (5) Non-response Non-response::

Increasing the sample size will size will not reduce this type of error.  Acquisition errors arise from the recording of incorrect responses, due to: 

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— incorrect measurements being taken because of faulty equipment, — mistakes made during transcription from primary sources, — inaccurate recording of data due to misinterpretation of terms, or — inaccurate responses to questions concerning sensitive issues.

Sampling Methods

Probability sampling

Nonprobability sampling

Steps in Sampling Design  What is the relevant population?  What are the parameters of interest?  What is the sampling frame? frame?  What is the type of sample?  What size sample is needed?  How much will it cost? 

Steps

Define the Population Determine the Sampling Frame Select Sampling Technique(s) Determine the Sample Size Execute the Sampling Process

Classification of Sampling Techniques Sampling Techniques

 Nonprobability Sampling Techniques

Convenience Sampling

Judgmental Sampling

Simple Random Sampling

Systematic Sampling

Probability Sampling Techniques

Quota Sampling

Stratified Sampling

Snowball Sampling

Cluster  Sampling

Other Sampling Techniques

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Non-Probability  Sampling Designs

Nonprobability Nonprobability 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 of others with like characteristics

Nonprobability Sampling Reasons to use  Procedure satisfactorily meets the sampling objectives  Lower Cost  Limited Time  Not as much human error as selecting a completely random sample  Total list population not available

Nonprobability Sampling Convenience Sampling  Purposive Sampling 

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Judgment Sampling Quota Sampling

 Snowball Sampling

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

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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

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

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test markets purchase engineers selected in industrial marketing research expert witnesses used in court

Quota Sampling Quota 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 composition Control Characteristic Sex Male Female

Sample composition

Percentage

Percentage

Number

48 52 ____ 100

48 52 ____ 100

480 520 ____ 1000

Snowball Sampling In snowball sampling, 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. 

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Probability Sampling Designs

Probability Sampling Designs  Simple random sampling  Systematic sampling  Stratified sampling 

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Proportionate Disproportionate

Cluster sampling  Double sampling 

Simple Random Sampling 

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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.

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

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. 

Stratified Sampling 

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The elements within a stratum should be as homogeneous as possible, but the elements in different strata should be as heterogeneous as possible. 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.

Cluster Sampling 

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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, Ideally , each cluster should be a small-scale representation of the population. In probability proportionate to size sampling, 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.

Types of Cluster Sampling Fig. 11.3

One-Stage Sampling

Cluster Sampling

Two-Stage Sampling

Simple Cluster  Sampling

Multistage Sampling

Probability Proportionate to Size Sampling

Sample vs. Census

Type of Study

1. Budget

Sample Sizes Used in Marketing Research Studies Table 11.2

Type of Study

Problem identificat

Factors to Consider in Sample Design

Research objectives

Degree of accuracy

Resources

Time frame

Knowledge of  target population

Research scope

Statistical analysis needs

Determining Sample Size How many completed questionnaires do we need to have a representative sample?  Generally the larger the better, but that takes more time and money.  Answer depends on: 

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How different or dispersed the population is. Desired level of confidence. Desired degree of accuracy. a ccuracy.

Common Methods for Determining Sample Size 

Common Methods:    

Budget/time available Executive decision Statistical methods Historical data/guidelines

Factors Affecting Sample Size for Probability  Designs  Variability of the population characteristic under investigation  Level of confidence desired in the estimate  Degree of precision desired in estimating the population characteristic 

n = [N Z ]/[Ne + σ Z ] 2

2

2

2

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 Where  e is the specified error  σ is the SD of the population  N is the population  Z is the table value of Z-Table. For a 95% Confidence Interval, value of Z is 1.96

Probability Sampling and Sample Sizes

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

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Research Design

Measurement 

Selecting observable empirical events

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Using numbers or symbols to represent aspects of the events

 Applying a mapping rule to connect the observation to the symbol

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 What is Measured? 

Objects: Objects:  

Things of ordinary experience Some things not concrete

 Properties:  Properties: characteristics of objects

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Characteristics of Data Classification  Order  Distance (interval between numbers)  Origin of number series 

Data Types Order Interval Origin Nominal

none none none

Ordinal

yes

unequal

none

Interval yes equal or unequal Ratio yes equal zero

none

Sources of Measurement Differences Respondent  Situational factors  Measurer or researcher  Data collection instrument 

 Validity  

Content Validity

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Criterion-Related Validity  

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Predictive Concurrent

Construct Validity

Reliability  

Stability  

Test-retest

Equivalence 

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Parallel forms

Internal Consistency    

Split-half  KR20 Cronbach’s alpha

Practicality  

Economy 

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Convenience

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Interpretability 

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MEASUREMENT SCALES

 What is Scaling?  Scaling is assigning numbers to indicants of the properties of objects

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Types of Response Scales  Rating Scales  Ranking Scales  Categorization 

Types of Rating Scales Simple category   Multiple choice, single response  Multiple choice, multiple response  Likert scale  Semantic differential 

• Numerical • Multiple rating • Fixed sum • Stapel • Graphic rating

Rating Scale Errors to Avoid 

Leniency   

Negative Leniency  Positive Leniency 

Central Tendency   Halo Effect 

Types of Ranking Scales 

Paired-comparison

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Forced Ranking

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Comparative

Dimensions of a Scale 

Unidimensional

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Multidimensional

Scale Design Techniques  Arbitrary scaling  Consensus scaling  Item Analysis scaling  Cumulative scaling  Factor scaling 

Sarndal, Swenson, and Wretman (1992), Model  Assisted Survey Sampling, Springer-Verlag  Fritz Scheuren (2005). "What is a Margin of  Error?", Chapter 10, in "What is a Survey?",  American Statistical Association, Washington 

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Thank you for your kind attention Go forth and research…. ….but be careful out there.