Chapter 5Sampling and Sample Designs

• All items in any field of inquiry constitute a ‘Universe’ or ‘Population’.

• The word ‘Universe’ denotes the aggregate from which the sample is to be taken.

• A complete enumeration of all items in the ‘population’ is known as a Census inquiry.Merits of Census Method:

• Each and Every unit of the population is covered.

• Representative, accurate and reliable results.

• Appropriate method of obtaining information on rare events.

• Used as a basis for various surveys.Demerits of Census Method:

• Difficult to adopt in case the universe is infinite.

• Large amount of effort, money and time is required.Sampling:

• The process of understanding about the universe on the basis of a sample drawn.

• The selected respondents constitute a ‘sample’, the selection process is ‘sampling technique’, the survey is ‘sample survey’.

• From population size N, if a part of size n (< N) of the population is selected, the group consisting of these n units is ‘sample’.Sample Design:

• Is a definite plan for obtaining a sample from a given population.

• Technique or procedure involved in selecting items for the sample.

• Determines the size of the sample.

Sample( Selected Respondents)

Sampling( Selection Process/

Technique

Sample Design

Sample Survey( Survey of the selected respondents )

Sample Design…Understanding ???Sample Design…Understanding ???

Sample Design

Universe

Sampling Unit

Source List

Budget

Sample Size

Type of Universe: • Defining the set of objects to be studied.• Identifying the universe – finite or infinite.• Have an idea about the nature and number

of items in the universe.Sampling Unit:

• Determining the sampling unit before selecting the sample – geographical one, construction unit, social unit, individual etc.

• Important to decide one or more of such units that researcher has to select for study.

Source List:• Known as ‘sampling frame’ from which

sample is to be drawn.• Contains the names of all items of a finite

universe.• In case of non-availability, researcher has to

prepare the same.• List must be comprehensive, correct, reliable

and appropriate.Size of Sample:

• Refers to the number of items to be selected from the universe.

• Size of the sample should be optimum – representative, reliable and flexible.

• Based on the nature and size of the universe, nature of the problem to be studied, involvement of cost, etc.Budgetary Constraint:

• Cost considerations have a major impact upon the size and type of the sample.

• Can even lead to the use of a non-probability sample.

Characteristics of a Good Sample Design:• Must result in a truly representative sample.• Must be such which results in a small

sampling error.• Must be viable in the context of funds

available for the study.• Must be such that systematic bias can be

controlled.

Types of Sample Design

Element selection basisRepresentation basis

Probability(Random selection)

Non-Probability( Non-Random)

Restricted(Confined within)

Unrestricted(Element is drawn from

population at large)

Basic Sampling DesignBasic Sampling Design

Element Selection Technique

Representation basisProbability Sampling

Non-probability Sampling

Unrestricted Sampling

Simple RandomSampling

Haphazard Sampling or Convenience Sampling

Restricted Sampling

Complex Random Sampling

Systematic Sampling Stratified Sampling Cluster Sampling Multistage Sampling

Purposive Sampling orJudgment Sampling Quota Sampling

All respondents have an equal chance of being selected.Selection of items, matter of chance.Technique-Lottery Method or Table of Random Numbers.

Selecting one unit at random and then Additional units at evenly spaced Intervals.K=N/n ( K=Sampling Interval, N= Universe, n= Sample Size)

Simple Random

Systematic

Population is divided into different groups ( Strata)Sample is drawn from each stratum at random Formation of subgroups at first and a number of these subgroups (clusters )are randomly selected . All numbers in each cluster are surveyed Random selection is made of primary,intermediate and final units.Provinces Districts Towns items at random

StratifiedCluster

Multistage

Non-probability SamplingConvenience Sampling:

• Is obtained by selecting ‘convenient’ population units.

• Is also called as chunk, which refers to the fraction of population being investigated which is selected neither by probability nor by judgment but by convenience.

• Samples are prone to bias by their nature of selection.

• Used frequently for making pilot studies.

• Questions may be tested and preliminary information obtained by the chunk before the final sampling design is decided upon.Purposive Sampling:

• Type of non-random sampling, also known as judgment or deliberate sampling.

• Choice of sample items depends exclusively on the judgment of the researcher.

• Items selected are mostly typical (representative) of the universe with regard to the characteristics under investigation.

• Used in case of small size of the universe.• Sample units may be affected by the

personal prejudice or bias of the universe.Quota Sampling:

• Quotas are set up according to some specified characteristics (age, income, habitation..)

• Within the quotas, selection of sample items depends on personal judgment.

• Probability of missing representative samples due to personal prejudice and bias.

Random Sampling MethodsSimple Random Sampling

• Each and every unit of the population has an equal opportunity of being selected in the sample.

• Selection of items in the sample is a matter of chance.

• All n items of the sample are selected independently of one another and all N items in the population have the same chance of being included in the sample.

• To ensure randomness of selection – Lottery method or table of random numbers.

• Lottery Method: A blindfold selection of the number of slips (sample size) is made out of the items of the universe.

• Slips should be of identical size, shape and color and should be mixed thoroughly.

• Limited practical utility in case the size of universe is large.Table of Random Numbers:

• Several standard tables of Random Numbers are available – Tippett (1927), Fisher and Yates (1938), Kendall and Smith (1939), Rao, Mitra and Mathai (1966).

• Tippett’s (1927) random number tables consisting of 41,600 digits grouped into 10,400 sets of four-digited random numbers.

• The first forty sets from Tippett’s table are:2952 6641 3992 9792 7969 5911 3170 56244167 9524 1545 1396 7203 5356 1300 26932370 7483 3408 2762 3563 1089 6913 76910560 5246 1112 6107 6008 8125 4233 87762754 9143 1405 9025 7002 6111 8816 6446

• For selecting 10 items out of 5000, the first ten numbers up to 5000 should be selected.

• If the size of the universe is less than 1000, for selecting 10 items out of 900, the numbers from 0001 to 0900 will be selected.

• If the size of the universe is less than 100, for selecting 10 items out of 90, after writing down the number in pairs and reading either horizontally or vertically and ignoring the numbers greater than 90, the items may be selected.

• Sample depends entirely on chance, hence no possibility of personal bias affecting the results.

• Difficult to have up-to-date lists of all the items of the population to be sampled.

• Difficulty involved in studying samples having widely dispersed geographically.

Complex Random Sampling DesignsSystematic Sampling:

• Is formed by selecting one unit at random and then selecting additional units at evenly spaced intervals until the sample has been formed.

• Required a complete list of the population from which sample is to be drawn.

• After the first item, subsequent items are selected by taking every k th item from the list.

• ‘k’ refers to the sampling interval or sampling ratio, i.e., the ratio of population to the size of the sample.

• k = N / n, N = universe size and n = sample size.

• Is relatively a simple technique and more efficient than simple random sampling.

• Also referred to as quasi-random sampling method.

• An element of randomness is introduced to pick up the unit with which to start and the reminder of the items for the sample are pre-determined by the sampling interval.

• Compared to simple random sample, systematic sample spreads more evenly over the entire population.

• In case of a fractional value of k, if it is < 0.5 it should be omitted, if it is > 0.5 it should be taken as 1, and if it is 0.5 it should be omitted if the number is even and taken as 1 if the number is odd.

• Example: If the number of households in a village will be 102, 115 and 110 and the sample size will be 20, thenk = 102 / 20 = 5.1 or 5k = 115 / 20 = 5.75 or 6k = 110 / 20 = 5.5 or 6

• The first household will be selected at random between 1 to k and then every k th household will be selected for the study.

Stratified Sampling:• Population is divided into different groups

called strata.• Sample is drawn from each stratum at

random.• Accepted in obtaining a representative

sample from the heterogeneous universe by:1. making as great homogeneity as possible within each stratum, and2. as marked a difference as possible between the strata.

• Stratified sample may be either proportional or disproportionate.

• Proportional – number of items drawn from each stratum is proportional to the size of the stratum.Example: If a province is divided into five parts and the percentages of population of the respective five parts to the total population are 10, 15, 20, 25 and 30 per cent, to draw a sample of 500 households as per the proportional stratified sample:

From Stratum (part) one : 500 (0.10) = 50From Stratum (part) two : 500 (0.15) = 75From Stratum (part) three : 500 (0.20) = 100From Stratum (part) fourth : 500 (0.25) = 125From Stratum (part) five : 500 (0.30) = 150

• The total sample will be 50 + 75 + 100 + 125 + 150 = 500.

• Disproportionate – An equal number of cases is taken from each stratum regardless of how the stratum is represented in the universe.

• A more representative sample, as little possibility of any essential group of the population being completely excluded.

Cluster Sampling: • Divide the area into a number of smaller

non-overlapping areas.• Randomly select a number of these smaller

areas (clusters).• The ultimate sample consisting of all (or

samples of) units in these small areas or clusters.

• Clusters should be as small as possible.• Number of sampling units in each cluster

should approximately be same.

• Reduces Cost by concentrating surveys in selected clusters.

• Certainly less precise than random sampling – not as much information in ‘n’ observations within a cluster as there happens to be in ‘n’ randomly drawn observations.

• Mostly used for the economic advantage it possesses; estimates based on cluster samples are usually more reliable per unit cost.

• Better known as Area sampling, if clusters happen to be some geographic subdivisions.

Multi-stage Sampling:• Is a further development of the principle of

cluster sampling.• Random selection is made of primary,

intermediate and final units from a given population or stratum.

• Example: A study on working of commercial banks in Cambodia:First Stage: To select large primary sampling unit such as Provinces in the country.

Second stage: To select certain districts and study all banks in the chosen districts.(Represents a two-stage sampling design)Third stage: To select certain towns and study all banks in the chosen towns.(Represents a three-stage sampling design)Fourth stage: To select randomly sample banks from each selected towns.(Represents a four-stage sampling design)

• Selection made at all stages randomly referred to as ‘multi-stage random sampling design’.

Selection of Appropriate Methodof Sampling

• A single method can not be considered as best under all situations.

• Normally, simple random sampling should be preferred because of its non-biasness.

• Purposive sampling is more appropriate when the universe happens to be small and a known characteristics of it is to be studied intensively.

• Nature of problem, size of universe, size of the sample, availability of funds, time etc. influence the selection of a method.

Characteristics of Sample• A sample should be so selected that it truly

represents universe. (Representativeness)• To ensure representativeness the random

method of selection should be used.• The size of sample should be adequate to

represent the characteristics of the universe. (Adequacy)

• There should not be any difference in the nature of units of the universe and sample. (Homogeneity)

• All items of the sample should be selected independently of one another. (Independence)

• All items of the universe should have the same chance of being selected in the sample.Sampling and Non-sampling Errors

• Error arising due to drawing inferences about the population on the basis of few observations – Sampling Error.

• Sampling Error in this sense is non-existent in complete enumeration survey. (whole population is surveyed).

• Error arising at the stages of ascertainment and processing of data – non-sampling errors.

• Non-sampling errors are common both in complete enumeration and sample surveys.

• Will be of large magnitude in census than in sample survey due to increase in the number of units.Sampling Errors

• Two types: Biased and unbiased• Biased Errors: Arise from any bias in

selection, estimation etc.

• It forms a constant component of error which does not decrease as the number in the sample increases.

• Commonly known as cumulative or non-compensating error.

Causes of Bias• Faulty selection process of sample• Faulty work during collection of information• Faulty methods of analysis

Faulty selection process of sample:• Deliberate selection of sample: Adopting

purposive sampling to select sample to obtain a pre-determined results.

• Substituting/ Replacing chosen sample: Replacing a chosen sample to a convenient sample without any proper plan.

• Non-response: If all the items to be included in the sample are not covered, even though no substitution has been attempted. (mostly occurs in mailed Questionnaires)

Faulty collection of DataBiased observations may result from:

• Poorly designed Questionnaire• Ill-trained interviewer• Failure of a respondent’s memory• Unorganized collection procedure• Faulty editing and coding of responses

Bias in Analysis• Acceptance of wrong methods of analysis• Improper way of interpretation of data

• Unbiased Errors: Arise due to chance differences between the members of population included in the sample and those not included.

• Random sampling error decreases as the size of sample increases.

• Also known as non-cumulative or compensating error.Non-sampling Errors

• Occur at every stage of planning and execution of the census or survey.

• Errors involved in observation, processing of data, tabulation errors etc.

Factors for Non-sampling Errors:• With respect to the objectives of the census

or survey, if data specification being inadequate and inconsistent.

• Inappropriate statistical unit.• Inaccurate methods of interview, observation

with inadequate or ambiguous schedules, definitions or instructions.

• Lack of trained and experienced investigators.

• Errors due to non-response (incomplete coverage in respect of units).

• Errors in data processing operations – editing, coding, classification etc.

• Errors during presentation and printing of tabulated results.Control of Sampling Errors

• Sample should be drawn either entirely at random or at random subject to restrictions.

• Size of the sample should be increased for increasing the accuracy level.Control of Non-sampling Errors

• Having adequate training before conduction of the survey.

• Employing better statistical techniques in processing and analysis of data.

• Pre-testing or conducting a pilot survey.• Undertaking complete and thorough editing

work.• Effective follow-up of non-response cases.