Dr. Mazharul Islam 1 Email: [email protected].

Dr. Mazharul Islam www.studyandjobs24.com 1

Email: [email protected]


SamplingSampling is a statistical procedure of drawing a small number of

elements from a population and drawing conclusion regarding the population.

Types of SamplingThere are two types of sample such as i) Non-probability sampling and ii) Probability samplingi) Non-probability SamplingNon-probability sampling is a non-random and subjective method of

sampling where the selection of the units depends on the personal judgment of the sampler.

ii) Probability Sample Probability or random sampling is a method where a sample is selected

according to the rules of probability.PopulationA population is the total collection of all the population elements, each

of which is a potential case.Example: All students in a college constitute a population of interest

and each student in the college questioned about his/her age, height, weight, or opinion on any issue is a population element.

Types of PopulationThere are two types of population such as:i) Finite Populationii) Infinite Population


i) Finite Population A finite population contains a countable number of sampling units.ii) Infinite Population An infinite population consists of an endless number of sampling

units.SampleAny representative part of population is called sample.SurveySurvey is a general term that refers to the collection of data by

means of interviews, questionnaires or observation.Census SurveyA census is an investigation or a count of all the population

elements.

Sample SurveyA sample survey is a study involving a subset (or sample) of

individuals selected from a larger population by accepted statistical methods.

Target PopulationA target population is the entire group about which information is

desired and conclusion is made. Sampled PopulationThe population, which we actually sample, is the sampled

population. It is also called survey population.


Sampling UnitA sampling unit or simply unit is a well-defined, distinct and identifiable element or group of elements on which observation is made.Sampling FrameA sampling frame is a list of units or group of units in the population to be sampled.Sample SizeSample size refers to the number of units contained in a sample.Population SizePopulation size is the number of units which constitute the population.ParameterThe numerical characteristics of population are called parameters.StatisticThe numerical characteristic of sample is called statistic.EstimatorsAn estimators is the method or formula for estimating the value of the parameter.EstimateAn estimate is the numerical value of the estimator obtained from the sample. BiasBias is a term which refers to how far the average value of the estimator lies from the parameter.


Sample Design Sample design refers to the plans and methods to be

followed in selecting sample from the target population and the estimation technique vis-à-vis formula for computing the sample statistics.

Survey design Survey design is the process of preparing a complete plan

of operations to be followed in conducting a survey and disseminating its intended results.

Importance of SamplingA sample is taken almost always to provide statistical data

on an extensive range of subjects for both research and administrative purposes. The following examples are designed to illustrate their importance of sampling in real life:

a) In opinion poll, a relatively small number of persons are interviewed, and their opinions on current issues are solicited in order to discover the attitude of the community as a whole.

b) Marketing and advertising agencies conduct countless inquiries to determine customers’ expectations, attitudes, buying habits, or shopping patterns. This information is useful to the manufacturers of goods for sales promotion.


c) Large lots of manufactured products are accepted or rejected by purchasing departments in business or government following inspection of a relatively small number of items drawn from these lots.

d) At border stations, customs officers enforce the laws by checking the effects of only a small number of travelers crossing the border.

e) A department store wishes to examine whether it is loosing or gaining customers by drawing a sample from its list of credit card holders by selecting every tenth name.

f) Auditors often judge the extent to which the proper accounting procedures have been followed by examining a small number of transactions, selected from a large number of such transactions taking place within a specified period of time.

g) Ministry of Health and Family Welfare might be interested to know the status of knowledge among the adult population in Dhaka city on the danger of environmental pollution by interviewing a few selected adults of the city.


Sampling with ReplacementIf the sample is taken with replacement from a

population, finite or infinite, the unit drawn is returned to the population and the number of units available for future drawing is not affected and consequently the probability of drawing any remaining unit in successive selections will remain unaltered. Sampling with replacement is sometimes referred to as an unrestricted sampling.

Sampling without ReplacementIn sampling without replacement, the unit drawn is not

returned to the population in subsequent drawings. Unlike sampling with replacement, the probability of drawing any remaining unit in successive selection will be increased.

Non-probability SamplingThere are some non-probability sampling methods such

as i) Convenience Sampling ii) Accidental Samplingiii) Judgment Sampling iv) Quota Sampling v) Snowball Sampling


i) Convenience SamplingNon-probability samples that are unrestricted are known as

convenience samples. Researchers or field workers have the freedom to choose whomever they find; thus the name convenience. The convenience sample may consist of respondents living in an easily accessible locality. Undoubtedly, it is the simplest and least reliable form of non-probability sampling. The primary virtue is its low cost.

ii) Accidental SamplingAn accidental type sampling is one in which the selection of

the cases is made whatever happens to be available instantly. In such sampling, individuals are selected as they appear in a process. If it is decided that only diabetic patients or patients with abdominal pain, will be chosen from a queue in front of a hospital counter, the resulting sample will fall under accidental sampling procedure.

iii) Judgment SamplingIn judgment sampling, individuals are selected who are

considered to be most representative of the population as a whole. It is a judgment sampling because choice of the individual units depends entirely on the sampler, who, on his own judgment, decides the sample to be selected that conforms to some criteria. In study of labor problem, you may decide to talk only with those who have experienced discrimination while they were in job.


iv) Quota SamplingQuota sampling is a non-probability sampling, in which the

interviewers are told to contact and interview a certain number of individuals from certain sub-groups or strata of the population to make up the total sample. The formation of the strata is usually based on such characteristics as sex, age, social status, region of residence. These characteristics which are used to form strata, are termed ‘quota control’. The technique is widely used by market researchers, political opinion seekers and many others to avoid the cost problems of interviewing the individuals.

V) Snowball SamplingSnowball sampling is the colorful name for technique of

building up a list or a sample of a special population. Some recent authors have referred to snowball sampling as chain referral or network sampling.

Snowball sampling is conducted in stages. In the first stage, a few persons possessing the requisite characteristic are identified and interviewed. These persons are used as informants to identify others who qualify for inclusion in the sample. The second stage involves interviewing these persons who can be interviewed in the third stage and so on. For example, consider the selection of beggars for which no frame is available. This can be best done by asking an initial group of beggars to supply the names of other beggars they come across.


Probability SamplingThe different types of probability sampling are following:a) Simple Random Sampling;b) Stratified Sampling;c) Systematic Sampling;d) Cluster Sampling.

a) Simple Random Sampling Simple random sampling is a procedure that gives each of

the sampling units in the population an equal and drawn non-zero probability of being selected. Selection a simple random sample is accomplished with the aid of computer software, a table of random numbers, or a scientific calculator. The following 8-step procedure may be followed in drawing a simple random sample of n units using random numbers from a population of N units.

i. Assign serial numbers to the units in the population from 1 through N.

ii. Decide on the random number table to be used.iii. Choose and N-sized random number from any point in the

random number table.


iv. If this random number is less than or equal to N, this is your first selected unit.

v. Move on to the next random number not exceeding N, Vertically horizontally or in any other direction systematically and choose your second unit.

vi. If at any stage of your selection, the random number chosen exceeds N, discard it and choose the next random number.

vii. If, further, any random number is repeated, it must also be discarded and be replaced by a fresh random number appearing next.

viii. The process stops once you arrive at your desired sample size.

Example: Draw a simple random sample of size 5 from a population comprising 150 units.

Solution: Here n=5 and N=150. Assign serial numbers 001, 002, …, 150 to the 150 units in the population. Since 150 is a three-digit number, we merely read three-digit random numbers presented in the random number table. Suppose we start from the leftmost digit of first row of the random number table and proceed downward until we achieve a sample of 5. The random numbers were as follows:


277 130 802 108 541 603 497 786 666440

414 945 416 502 413 258 061 608 809 195493 063 609 923 779 381 396 840 474

433642 668 724 210 953 407 582 895 154

121Note that we choose only those numbers, which lie in the

range 001-150. Any number lying outside this range is omitted, since they do not correspond to any unit in the

population. The process stops once we arrive at five numbers. Note that the selected numbers are 130, 108,

61, 63 and 121. These numbers are underlined with bold faces. All these numbers are distinct. If a random

number occurs twice, the second occurrence is omitted, and another number is selected as its

replacement.Example: Assume that there are N=1000 records of daily

wages of the employees of a pharmaceutical industry. Draw a sample of 25 records using the random

numbers shown in the Appendix.Solution: The first step is to arrange the wages of 1000

employees assigning a number from 000 to 999. That is, we have 1000 three-digit numbers where 001

represents the first record, 999 the 999th record and 000 the 1000th. We may use the first column dropping the last 7 digits of each random number. We see that

the first selected number is 611, the second is 154, the is 945 and so on. Proceeding further down the column,

the following random numbers are chosen:


611 154 945 424 235 044 005 359 598460

321 692 195 451 948 980 331 809 797180

740 541 116 483 690If the wage records of the employees are actually numbered, we

merely choose the records with the corresponding numbers and these records represent a simple random sample of size n=25 from N=1000.

Example: Draw a simple random sample of size 5 from a population comprising 150 units.

Solution: The population from which sample of 5 has to be chosen, contains 150 units. For selecting a unit from 001-150, follow the steps below:

i. Choose a random number between 001 and 150. The number is 277.

ii. Divide 277 by 150. The remainder is 127, The unit labeled 127 in the population is your first selected unit.

iii. To select the second unit, choose the next random number. This number is 130, which is less than 150. We directly choose this number as our second unit in the sample.

iv. The next random number is 802, which results in a remainder of 52 when divided by 150. The unit corresponding to this number is our third selected unit.

v. Continuing this process, we arrive at the next two numbers. These are 108 and 91.

vi. The random numbers thus chosen are 52, 91, 108, and 130.


b) Stratified Random SamplingA restricted sampling design, which can be more

efficient than simple random sampling is the stratified random sampling. The procedure requires that we have prior knowledge of the population. The process of stratification involves dividing the population into several non-overlapping groups or classes called strata. Specifically, the stratification process possesses the following salient features:

i. The entire population is divided into several distinct sub-populations, called strata;

ii. Within each stratum, a separate and independent sample is selected.

iii. For each individual stratum, stratum mean, proportion, variance and other statistics are computed;

iv. These estimates are then properly weighted to form a combined estimate for the entire population.


c) Systematic SamplingIn discussing simple random sampling and stratified

sampling designs we have noted that both these designs require somewhat very laborious work in the sample selection process. For both the Simple Random Sampling and Stratified Random Sampling, an adequate sampling frame must be available and the sampling units thereof must be numbered or otherwise identified so that a randomization device, such as a random number table, can be used for selection of the specific units. In such instances, a more simplified and versatile form of probability sampling design, known as systematic sampling, can be employed. If employed with care, the systematic sampling design simplifies much of the work involved in simple random sampling or stratified sampling. In addition to its being operationally more convenient than simple random sampling, it ensures for each unit an equal probability of inclusion in the sample.

In selecting a sample of n units from a population of N

units when N=nk using systematic sampling approach, we follow the following steps:


i. List the units giving a serial number from 1 to N.ii. Determine the sampling interval k dividing N by n:

k=N/n.iii. Select a random number between 1 and k inclusive.

Say this is r. Your first selected unit is r.iv. Add k to r. Your second selected unit bears the serial

number r+k.v. Nest add 2k to r so that your third selected unit

bears the serial number r+2k.vi. Continue the process and finally the n-th unit will

bear the serial number r+(n-1)k. Example1: Suppose population consists of 15 units,

numbered serially from 01 to 15. Select a random sample of 3 units using systematic random sampling.

Solution: Here N=15, n=3 and the sampling interval, k=N/n = 15/3=5. We now select at random one of the first five units, 01 to 05, and then every 5th unit in the sequence. For example, if the first unit is 03, then the sample will consist of units 03, 08, and 13; if first unit is 01, the sample will consist of units 01, 06, and11.


d) Cluster SamplingDiametrically opposite to stratified sampling is cluster sampling. It consists of first selecting, at random, groups called clusters of individual items from the population, and then choosing all or a sub-sample of the items within each cluster to make up the overall sample. In order to get best results in cluster sampling design, differences between clusters are made as small as possible, while differences among individual items within each cluster are made as large as possible. Ideally, each fluster should be a miniature of the entire population, and thus a single cluster would be a satisfactory sample.


Example1: Select a random sample of size, n=200 households from a population of N=8000 households of a city.Solution: Since there dose not exist any good list of the households, it would be a difficult job to sample the individual households. It would be at the same time too expensive to prepare such a list. Instead, we can obtain a sample of blocks by dividing the entire area into a number of blocks and then selecting 200/8000=2.5% of the blocks. Suppose we make 80 blocks each with 100 households. Then 2.5% of 80 blocks implies80*2.5%=2 sample blocks. These 2 blocks contain 200 households. These households located within the boundaries of the sample blocks comprise the sample.

Dr. Mazharul Islam 1 Email: [email protected].

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