Presentation on Probability Samples

8/3/2019 Presentation on Probability Samples

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Types of Probability Samples

Simple Random Sampling Systematic Random Sampling Stratified Random Sampling

Multi-stage Random Sampling Cluster Sampling Area Sampling


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Simple Random Sampling

It is the most common and familiar type of probability sampling. It isalso known as unrestricted random sampling. In this techniqueeach and every unit of the universe has the same chance of beingincluded in the sample. The selection of the units depends on theelement of chance and it is not affected by investigators bias.

Methods of Random Sample:

i. Lottery method

ii. Use of tables of random numbers

iii. Selection from sequential listiv. Grid system


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Methods of Random Samplei. Lottery Method: It is simple method of drawing a random sample.

This consists in identifying each and every unit of the population

with a distinct number which is recorded on a ticket, chit or token. Ifthe units drawn are not replaced, then it is known as simple randomsampling without replacementand if unit selected is replaced then itis called simple random with replacement.

ii. Use of Tables of Random Numbers: a random number is an

arrangement of digit 0 to 9, where each position is filled with one ofthese digits. A table of random numbers is constructed in such amanner that all numbers 0,1,2.9 appear independent of eachother.

Some of tables of random numbers which are commonly used:

a) Tippets Random Number Tablesb) Fisher and Yates Tables

c) Kendall and Smiths Tables

d) Rand Corporations Random Number Tables

e) Table of Random Numbers by C.R. Rao, Mitra and Mathai


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Methods of Random Sample

iii. Selection from Sequential List:Under this method the namesare, first of all, arranged serially according to alphabetical,geographical or in serial order. Then out of this list of the universeevery 10th or any other number may be included in the sample

selected.iv. Grid System:This technique is generally used for selecting a

sample of an area. In this method a map of entire area is drawn.Then a screen with squares is placed on the map and some of thesquares are selected at random. After that the areas falling within

the selected squares are taken as samples.


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Simple Random Sampling Advantages

i.Everyunit has equal chanceof being selected and chances ofindividual bias are less.

ii. This method saves time and money in studying a problem.

iii. It is possible to check the accuracy of sample by examininganother sample from the same universe.

Disadvantages

i.Sometimes only a few items are to be included in sample. Herethis method is not possible.

ii. If the universe includes heterogeneous unitsthen this method isnot of much use.

iii. Investigator has less control over selection of units. Sometimesthe selected units are spread over wide area and it is difficult tocontrol all of them.


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Stratified Random Sampling

This is the most commonly used method among the

various techniques of sampling. Here the population(universe) is divided into a number of groups called

strata. It is called stratified sampling because it dealswith strata. When the universe includesheterogeneousunits, then the application of stratifiedsampling technique is useful. Under this method theuniverse is divided into sub-groups and sample is takenfrom each subgroup. If N is taken as the total populationthen N1, N2, N3 Nkare its sub-group. Thus N= N1+ N2+..Nk.


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1. The universe is divided into sub-groups and from sub-group therequired items are selected.

2. The stratification is done in such a manner that the items in onestratum are similar to each other.

3. Each and every unit in the universe belongs to one stratum only.

4. For selection of items on random basis the size of each stratum in

the universe should be large.5. Size of the sample from each strata may be either proportional or

disproportional to the size of each stratum.

Procedures for DrawingProbability Samples Stratified

Sampling


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Stratified Random Sampling Advantages

i. Compared with simple random sampling this method providesmore efficient estimates with lesser degree of variability in eachstratum.

ii. Since sample size can be small therefore stratified samplingsaves time and cost of data collection.

iii. It ensures administrative convenience by dividing the universeinto homogeneous strata.

Disadvantages

i. It is difficult task to divide the universe into homogeneousgroups. If stratification is faulty, accurate results cannot be

obtained.ii. Disproportionate stratification needs assignment of weights to

different strata and the faulty weighting will make the sampleunrepresentative.

iii.If the strata are overlapping, disproportionate or unsuitable thenthe selection of samples may not be representative.


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Systematic Random Sampling

Systematic random sampling is slightly different from the simple randomsampling. Under this method a sample is taken from a list prepared on asystematic arrangement such as alphabetical, chronological,geographical order or on house number or any other method. In thismethod only the first unit is selected with the help of random numbersand the remaining units get selected automatically according to some

definite pattern at equal spacing from one another. First of all populationis arranged in serial order from 1 to N and the size of the sample isdetermined by dividing the population by the size of the sample i.e.

N= nk Where N= size of population

or k=N n= size of sample

n k=interval of sample

Systematic sampling dals with selecting any unit at random from thefirst unit and the subsequent units are selected at equal or regular

intervals.


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Systematic Random Sampling

Advantagesi. This method is simple to understand, very easy to operate and

checking can also be done quickly.

ii. This method is faster and less prone to error than simple randomsampling

iii.In comparison with simple and stratified random sampling

techniques, this method saves a lot of time, energy and finance.

Disadvantagesi. If the complete and upto-data frame is not available and the units

are not randomly arranged, this method will not work efficiency

and the estimation of standard error of sample mean will becomecomplex.

ii.Any hidden periodicity in the list will adversely affect therepresentative character of the sample and may contribute bias tothe estimate of population mean.


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Multistage Random Sampling

As the name indicates, sampling is done in stages. In multistagesampling the material to be sampled is composed of a numberof first stage sampling units, each of which in its turn, is madeup of a number of third-stage units, and so on, on until wereach the ultimate sampling unit in which we are interested.The sampling is done in stages.

At the first stage sampling units are sampled by some suitablerandom method.

At the second stage units is selected from each of the selectedfirst stage units, again by some suitable random method.

Further stages may be added, if necessary, to get a sample ofthe ultimate sampling units.

For example, to get a sample of crop-fields growing wheat inPunjab, we first of all get a sample of districts, then a sampleof village from each selected district and finally sample of

wheat crop-fields from each selected unit.


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Multistage Random Sampling

Advantages

i. This method is flexible in comparison with others.

ii. It ensures great saving in operational cost, especially if the area tobe covered is very large because the existing division and sub-divisions of the material can be taken as sampling units at differentstages.

iii. This method is more reliable and satisfactory.

iv. Under this method survey can be conducted with speed.

Disadvantages

i. In general this method is less efficient than single sample techniques.

ii. Errors are likely to be larger in this method as compared with othermethods of sampling.

iii. It involves listing of first stage units, second stage units etc. thoughcomplete listing is not required which means a costly affair.


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Cluster Sampling

It is a technique of selection in which the items for thesample are selected from the population in groups orcluster. Under this method, the universe is divided intosome sub-divisions which are termed as clusters and a

simple random sample of these clusters is drawn andthen the data are collected from each and every unit inthe selected cluster. The clusters used are generally,already existing natural or administrative groupings ofthe universe, for example, schools, colleges, universities,

factories, political divisions, sub-divisions, etc.


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Cluster Sampling

Advantagesi. This method provides significant cost gain as the collection of

data from neighboring units is easier and cheaper.

ii.This method is useful in the absence of ready availability of thedata about the universe.

iii.Because the sample units are located at one place, data can becollected quickly.

Disadvantages

i. If the number of clusters is large then the representativecharacter of the sample is affected.

ii.The result obtained under this method are less accurate becausethe error may be in the cluster sampling as compared to the

simple random sampling.


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Area Sampling

It is a special type of cluster sampling in which thesample items are clustered on the basis of geographicalarea. For this, the universe is first of all divided intocertain parts on geographical basis of sampling. In this

method the boundaries of the area should be welldefined. Generally govt. agencies use area sampling tocollect data about the effectiveness of their programmeslike public distribution system, jawahar rozgaryojna,eradication of polio etc. this type of sampling is

extensively used in the collection of agriculturalstatistics.


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Area Sampling Advantages

i. Since most of the data available in the govt. departments is onarea basis, therefore area sampling is the best technique forconducting studies involving geographical area.

ii.Since the investigator can interview many respondents at oneplace, the process of interviewing becomes more efficient.

iii.It ensures proportional representation of each of the segments ofthe universe.

Disadvantages

i. It requires the arrangement of units in a geographical systemwhich is a stupendous task.

ii.The sampling error may be high as the areas are not similar.

iii.Each geographical area is not equally represented.

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Presentation on Probability Samples