SAMPLING DESIGN

MEANING & NEED: A sample design is a definite plan for obtaining a sample from a given population. Difference between Census and sample. If one measures each and every element of a population for some characteristics of interest, the study is referred to as a Census. If one selects a small subset of the population for the study and then generalizes the results to the entire population, then it is referred to as sampling.

Sampling is an act, process, or technique of selecting a representative part of a population. The main aim is to draw inferences or determining the characteristics of the whole population. Second aim is to test a statistical hypothesis / research hypothesis relating to population.

Sampling Concepts Element: Unit of study individual or organization. Population: Total collection of elements under investigation. Sample: The subset of the elements of the population chosen for study. Sampling unit (elements): A sampling unit can be an individual element or a set of elements based on the sampling process used. Sampling frame: The sampling frame refers to a complete enumeration/list of the population as specified by the research problem. It is a list of all the sampling units.

Sampling Error: Error is defined as, an act, assertion (claim) or belief that intentionally deviates from what is correct, right, or true. The Difference between sample statistic and population parameter is known as sampling error. Error because of involvement human intelligence and the use of sampling methods which may be not be accurate.

It can be reduced (or eliminated) and the study findings can be assumed to be more reliable by increasing the sample size. Errors are of two types: Random Sampling Error & Non-Sampling Error. Random Sampling Error / sampling error is due to differences in sample and population - can be avoided through sample size Can be controlled through careful sample designs, large samples, etc.

Non-sampling Error: Systematic Error non-observational error measurement error. non-observational error due to non-coverage (due to probability chance) or non-response errors (occurs when data collected from the element actually selected into the sample non-cooperation due to refusal / language barriers (non-potential respondent)

Characteristics of Good Sample: Sample:1. Representativeness and Accuracy: In measurement terms, the sample must be valid. -Accurate sample hardly shows any difference between sample value and population value. (say, average). 2. Precision: (correctness) The sample must yield precise estimate. Precision can be measured by SE or SD. The smaller the SE or estimate, the higher is the precision of the sample. 3. Size: Good sample must be adequate in size in order to be reliable. The sample should be of such size that the inferences drawn from the sample are accurate to the given level of confidence.

Advantages & Limitations (of Sampling)1. 2. 3. Advantages Reduces the time and cost. Saves Labor. Better quality better interviewing, more thorough investigation, better supervision. Quicker results infinite population. 1. Limitations Demands thorough knowledge of sampling techniques. Characteristics cannot be defined with small samples. Complicated sampling plan requires more labor. Some differences exist between statistic and parameter.

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SAMPLING TECHNIQUES OR METHODS Sampling techniques are classified into two generic types: Probability or random sampling and Non-probability or Non- random sampling. Probability sampling is of following types: Simple random sampling. Stratified random sampling. Systematic random sampling. Multistage cluster sampling. Non -Probability sampling is of following types: Convenience sampling (accidental). Purposive sampling (judgmental). Quota sampling. Snow-ball sampling.

PROBABILITY SAMPLING METHODSMETHODSSIMPLE RANDOM SAMPLING: SAMPLING: This sampling technique gives each element an equal and independent chance of being selected. A equal chance means equal probability of selection. That is all elements should be included in the sample frame to draw a random sample. If the purpose of research is do arrive at conclusions/predictions affecting the population of the whole , then choice of this method is useful. Procedure: Enumeration of all elements in the population. Preparation of a list of all elements, giving them numbers in a serial order, 1, 2, 3, ----, so on. Drawing sample number by using lottery method. (computer facility) Example: Telephone directory OR Sample of 10 students from 50slips of paper, global container and shuffle. Two alternatives: with replacement/ without replacement.

SIMPLE RANDOM SAMPLING: 1. Suitable only when population is a homogeneous group with reference to characteristics. 2. Possible only when population is relatively small. 3. Possible only when complete list of all elements are present.

SIMPLE RANDOM SAMPLING1. 2. 3. 4. Advantages: Equal chance. Easiest to apply. Does not require prior knowledge of population. Sampling error can be easily be computed. 1. Disadvantages: Impractical non availability of population list migrants/nomadic life, etc. Wasteful fail to get full information about the population. Techniques does not ensure proportionate representation to various groups. Less precise method sampling error is large. Expensive in time and money.

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STRATIFIED RANDOM SAMPLING This is an improved type of random or probability sampling. The problems of simple random sampling gave rise to this new form. In this method, the population is sub-divided into homogeneous groups or strata, and from each stratum, random sample is drawn. Example: University students based on discipline OR employees of business undertaking may be divided into managers and non-managers based on salary/grade, etc.

Need for stratification: To increase a samples statistical efficiency. Provides adequate data for analyzing the various subpopulations and applying different methods to different strata. Ensures representation to all relevant sub-groups of the population. More efficient than simple random sampling. Essential when researcher wants to study the characteristics of population sub-groups, e.g., male and female employees, etc. Stratification is useful to apply different methods of data collection, example interviews for workers and selfadministered questionnaire for executives, etc.

Suitable for large heterogeneous groups. Stratification Process: Three major decisions: Stratification base to be decided for study size of firm, or block, etc. Number of strata larger the representative ness, the better need go for sub-population groups cost of stratification to be considered. Strata sample sizes may be proportionate to stratas share of total population proportionate / disproportionate.

Proportionate Stratified sampling: sampling: Involves drawing a sample from each stratum in proportion to the latters share in the total population. For example: Final year PG students of a university consist of specializations such as :

Specialization stream

No. of students

Proportion of each stream

Production Finance Marketing Rural Development

40 20 30 10 100

0.4 0.2 0.3 0.1 1.0

Total

Proportionate Stratified sampling If a researcher wants to draw an overall sample of sample of 30. Then the strata sample size would be:Strata Sample Size (number of samples *Proportion)

Production Finance Marketing Rural Development

30 X 0.4 30 X 0.2 30 X 0.3 30 X 0.1

12 6 9 3 30

Total

STRATIFIED RANDOM SAMPLING (Proportionate) Proportionate) Advantages: Proportionate sampling gives proper representation to each stratum and its statistical efficiency is generally higher. Very popular method. Easy to carry the method. Population mean can be estimated simply by calculating the sample mean. 1. Disadvantages: Prior knowledge and characteristics is essential to adopt this method about the population. Expensive in time and money. Greater efficiency may require additional cost. Identification of the strata might lead to classification errors. Some may be included in wrong strata. Wrong interpretation.

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Disproportionate Stratified sampling: sampling: This method does not give proportionate representation to strata. Involves over representation of some strata and under representation to others. This type of technique is desired when there is more mixed elements of a stratum if need for larger sample - cost per sampling is expected to be more in some strata selections. Usage: Appropriate when population contains some small but important sub-groups. When certain sub-groups are heterogeneous, while others are homogeneous. When expected that there is appreciable differences in the response rates of sub-groups., etc. It cannot be used if there is unknown characteristics of the population or sub-groups.

Grade

Enrol lment

Sample number (average)

Proportio nate sample fraction

Disproportio nate sample fraction

Weighting

Weighted sample number

Disproportionate sample

1

50

10

27.8%(50/180*10 0)

20.0%(10/50*100)

1.67(33.3/20.0)

16.7(1.67*10)

17

2

40

10

22.2%(40/180*10 0)

25.0%(10/40*100)

1.33(33.3/25.0)

13.3(1.33*10)

13

3 4 5 6 Total

30 30 20 10 180

10 10 10 10

16.7% 16.7% 11.1% 5.6% 100.0%

33.3% 33.3% 50.0% 100.0% 33.3%

1.00 1.00 0.67 0.33 1.00

10.0 10.0 6.7 3.3 60.0

10 10 7 3 60

60

STRATIFIED RANDOM SAMPLING (Disproportionate) Disproportionate)Advantages: 1. Less time consuming compared with proportionate sampling. 2. Gives importance to particular groups which needs more important. Disadvantages: 1. Does not give each stratum the equal importance or representation. 2. Requires prior knowledge of the composition of the population. 3. Subject to classification errors.

SYSTEMATIC SAMPLINGMeaning and Process: Systematic sampling is also called Fixed Interval Method. This is an alternative to random sampling. It consists of taking every kth item in the population after a random start with an item from 1 to k. Example: Suppose to select the sample of 20 students from the list of 300 students divide the sample number with total - find quotient (15). Select a number at random between 1 and 15 using lottery method/random number tables if suppose it is 9, add 9+15, - 24 is the second sample, 24+15 is third sample and so on. Interval between sample is fixed.

Applications of systematic sampling: sampling: Pseudo-random (randomness cum nonprobability sampling) characteristics. Applicable to students in a class, Houses in a street, Telephone directory, Customer of a bank, Members of a association, etc. Statistically more efficient than simple random sample. Better representative.

SYSTEMATIC SAMPLINGAdvantages1. Much simpler than random sampling. Easy to use. 2. Easy to instruct the field investigators to use this method. 3. Requires less time and less money.. 4. Limited time schedule will prefer this method. 5. Easy to check the kth sample. 6. Spread evenly over the population

Disadvantages1. Ignores all elements between two kth elements selected. Cannot be considered as probability sampling. 2. Cannot be said as random. 3. Generalizations will be inaccurate. 4. Biased sampleno representative of the group.

MULTISTAGE CLUSTER SAMPLING When the population elements are scattered over a wider area and list of population elements is not available - simple or stratified random sampling method not possible. Cluster sampling is usually adopted. Meaning: Cluster sampling means random selection of sampling units consisting of population elements. (Cluster happens to be some geographic subdivisions. Clusters need not be homogeneous in characteristics). Each such sampling unit is a cluster of population elements. From each sampling unit, a sample of population elements is drawn by either simple random selection or stratified random selection.

Determining the number of stages in cluster sampling depends upon the geographical area of study, size of population and the consideration of costs. If number of stages are more than two, it is called as multi stage sampling. Example: Investigating the working efficiency of nationalized banks in India. Only few banks to be taken for study. Single stage select a large sampling unit states in a country (random selection of few banks). Two stage certain districts (two stage sampling- census of all banks within the districts); Three stage - certain towns and interview all banks in the chosen town. Four stage chosen town and randomly take sample banks. If we select randomly at all stages, it is called in multi stage random sampling design.

Applications of multi stage cluster sampling: The applications of cluster samplings are extensive, particularly in farm management surveys, socio-economic surveys, demographic studies, ecological studies, public opinion polls, attitude surveys, and so on. Advantages: Easier and more convenient; cost is less; convenience for field work; units can be substituted for other units within the same random; flexible. Disadvantages: Bias in cluster size; sampling error is greater; statistically less efficient; wrong representative ness will led to wrong inferences.

NONNON-PROBABILITY SAMPLING METHODSCONVENIENCE or ACCIDENTAL SAMPLING: Non-probability sampling selecting sample units in a just hit and miss fashion interviewing people whom we happen to meet conveniently accidental meetings. Usefulness: Testing ideas or rough impression on the subject. Use when data collection is not possible. Advantages: Cheapest and simplest; Does not require list of population; Does not require any statistical expertise. Disadvantages: Highly biased; less reliable; findings cannot be generalized.

PURPOSIVE or JUDGEMENT SAMPLING: This method means deliberate selection of sample units that conform to some pre-determined criteria. This is also known as judgment sampling. This involved selection of cases which we judge as the most appropriate ones for the given study. Does not aim at securing a cross section of a population. Subjective knowledge of the researcher helps in judgment. Usefulness: This method is appropriate when there is a typical and specific relevance of the sampling units to be studied. Advantages: Less costly and more convenient; guarantees inclusion of relevant elements in the sample, where as probability does not. Disadvantages: Does not ensure representative ness; less efficient in generalization of statements; requires prior extensive information about the population to be studied; is not useful for inferential statistics, only useful for descriptive statistics.

QUOTA SAMPLING A convenient sampling technique involving selection of quota groups (OR) a method of stratified sampling in which selection within strata is non-random. Example: The number of respondents (quota) that are to be drawn from each several categories is specified in advance and the final selection of respondents is left to the interview who proceeds until the quota for each category is filled. Similar like stratified sampling, but the judgment of selection is left to the interviewer. Applications: Used in studies like marketing surveys, opinion polls, leadership surveys which do not aim at precision, but quick results.

QUOTA SAMPLING Advantages: Less costly and less time; no list of population no sampling frame; field work can be organized, no strict supervision required. Disadvantages: No precise representative sample; impossible to estimate sampling error,; findings cannot be generalized; interviewers may ignore the core respondents in slums for example; difficult to look if more variables has to be considered; high degree of classification error (heterogeneous samples).

SNOWBALL SAMPLING It is a sample collected by building up a list of special population by using an initial set of its members as informants (chain system of referrals) . Example: Problems faced by Indians Collect some name from Indian embassy ask for some more to supply names and the procedure leds to exhaustive list of samples or to make a census survey. OR feedback on the quality products, etc. Advantages: Useful to study social groups, informal groups in an formal organization; useful for smaller populations where no frame are determined, etc. Disadvantages: Does not allow the use of probability statistical methods; difficult to apply when population is large; does not ensure the inclusion of all elements in the list.

Probability Vs Non Probability Sampling Probability Characteristics Non Probability Characteristics 1. Does not ensure a selection chance to each population unit. 2. Selection probability is unknown. 3. A non-probability sample may not be a representative one. 4. Does not led to inferences some times. 5. Distort results. 6. It is done when data collection is not feasible. (large and cost). And not aim at generalizing the findings. 1. Every population has a chance of being selected. 2. Probability sampling yields a representative sample. 3. Findings are generalized. 4. Cost and time required are large. 5. Benefits derived should justify the cost.

STEPS IN SAMPLING PROCESSSeven steps in a sampling process: 1.Defining the target population. 2.Specifying the sampling frame. 3.Specifying the sampling unit. 4.Selection of the sampling method. 5.Determination of sample size. 6.Specifying the sampling plan. 7.Selecting the sample.

Defining the Target Population: Target population example: Kitchen appliances ovens sampling unit to be defined - women age working income group - location. Well defined population. Specifying the sampling frame (list of elements from which the sample may be drawn): Ideal sampling frame database telephone directories, list of credit cards, mobile phone users, etc. OR Private players provide database various demographic and economic variables, etc.

Specifying the sampling Unit : Sampling unit is a basic unit that contains a single element or a group of elements of the population to be sampled. In above example: Household is sampling unit women in household is the sampling element OR each individual element would be a sample unit. Sampling methods: Probability and nonprobability techniques. Sample Size: Crucial role in sampling process. various techniques to determine the sample size.

Sample Size: Crucial role in sampling process. various techniques to determine the sample size. In non-probability sampling procedures allocation of budget, number of subgroups, etc . In probability procedures formulas are used to calculate the sample size after the levels of acceptable error and level of confidence are specified. Example: Toro Yemane formula.

Specifying the sampling plan: Decisions and implementation of the research process are outlined. Steps taken for modus operandi. If systematic sampling of a household, - if vacant, what steps to be taken to collect, etc. Work will be easy if field work is done and plan is a guideline. Selecting the sample: select the required samples and proceed for business research.