Subject: Statistical Inference by Dr. Fahd Amjad
Assignment:
Sampling
Techniques Subject: Inferential Statistics Submitte Submitted d to:
Dr. Dr. Fahd
Amjad Submitted by:
Danish
Alam Roll o.
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Subject: Statistical Inference by Dr. Fahd Amjad
Department: $anagement Sciences
Sampling Techniques Sample: De*nition:
“It is the subset of population.” Or
“It is the collection of data or elements from population by a dened procedure.”
Each element of sample is known as sample points.
For +,ample: A sample of heights of ! students collected from a population of "! students in a class.
Sampling: De*nition: “the act of taking a portion or sample from population is called sampling.” Or “It is concerned with the selection of a subset of indi#iduals from within a statistical population to estimate characteristics of whole population.”
Sampling Techniques:
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Subject: Statistical Inference by Dr. Fahd Amjad $here are two types of sampling% • •
Probability &ling 'on(Probability &ling
") 'robability Sampling (De*nition): Probability or random sampling gives all the members of population a known chance of being selected for inclusion in the sample and this does not depend upon previous events in the selection process. In other words, the selection of individuals does not aect the chance of anyone else in the population being selected. Or Probability sampling is a sampling technique wherein the samples are gathered in a process that gives all the individuals in the population equal chances of being selected.
There are four types of 'robability Samplingi) &imple *andom &ling ii) &ystematic &ling iii) &tratied &ling i#) +luster or ,ulti(&tage &ling
Diagram:
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Subject: Statistical Inference by Dr. Fahd Amjad
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ity l m u r s a s t p t t mre d o a r t aa u mn l t d i mla i nm g atl i a nm g g l i n g a m l i n
i
-iagram &howing types of Probability &ling.
i)
Simple Random Sampling:
This is the ideal choice as it is a perfect random method. Using this method, individuals are randomly selected from a list of the population and every single individual has an equal chance of selection. Or In statistics , a simple random sample is a subset of individuals (a sample ) chosen from a larger set (a population ). Each individual is chosen randomly and entirely by chance, such that each individual has the same probability of being chosen at any stage during the sampling process ii)
Systematic Random Sampling:
It is de*ned as “the statistical method in#ol#e in the selection of elements from an ordered sampling frame.” Or Systematic sampling is a frequently used variant of simple random sampling. hen performing systematic sampling, every !th element from the list is selected (this is referred to as the sample interval) from a randomly selected starting point. Or Page / of "%
Subject: Statistical Inference by Dr. Fahd Amjad " random sampling #ith a system is called Systematic $andom Sampling. %rom the sampling frame, a starting point is chosen at random, and choices thereafter are at regular intervals. Ad0antage: $he sample usually will be easier to identify than it would be if simple random sampling were used.
iii)
For +,ample: &electing e#ery !! th listing in a telephone book after the rst randomly selected listing. For +,ample if we ha#e a listed population of /!!! members and wish to draw a sample of 0!!! we would select e#ery "!th 1/!!! di#ided by 0!!) person from the list. In practice we would randomly select a number between and "! to act as our starting point. $he one potential problem with this method of sampling concerns the arrangement of elements in the list2 If the list is arranged in any kind of order e.g. if e#ery "!th house is smaller than the others from which the sample is being recruited there is a possibility that the sample produced could be seriously biased. Strati*ed Sampling:
Strati&ed sampling is a variant on simple random and systematic methods and is used #hen there are a number of distinct subgroups, #ithin each of #hich it is required that there is full representation. " strati&ed sample is constructed by classifying the population in sub'populations (or strata), base on some #ell'no#n characteristics of the population, such as age, gender or socio' economic status. The selection of elements is then made separately from #ithin each stratum, usually by random or systematic sampling methods. Or Strati&ed sampling refers to a type of sampling method. ith strati&ed sampling, the researcher divides the population into separate groups, called strata. Then, a probability sample (often a simple random sample) is dra#n from each group. Ad0antage: If strata are homogeneous this method is as “precise” as simple random sampling but with a smaller total sample si3e. For +,ample: $he basis for forming the strata might be department location age industry type etc.
&tratied sampling methods is further di#ided into two types% Page # of "%
Subject: Statistical Inference by Dr. Fahd Amjad
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In 'roportionate Sampling the strata sample si3es are made proportional to the strata population si3es. For +,ample if the rst strata are made up of males then as there are around 4!5 of males in the 67 population the male strata will need to represent around 4!5 of the total sample. In Disproportionate $ethods the strata are not sampled according to the population si3es but higher proportions are selected from some groups and not others. $his techni8ue is typically used in a number of distinct situations9 $he costs of collecting data may di:er from subgroup to subgroup. ;e might re8uire more cases in some groups if estimations of populations< #alues are likely to be harder to make i.e. the ,arket *esearch ;orld. =arger the sample si3e 1up to certain limits) the more accurate any estimations are likely to be. 1luster or $ulti!Stage Sampling:
2ene*ts and 3sage: +luster sampling is a fre8uently(used and usually more practical random sampling method. It is particularly useful in situations for which no list of the elements within a population is a#ailable and therefore cannot be selected directly. As this form of sampling is conducted by randomly selecting subgroups of the population possibly in se#eral stages it should produce results e8ui#alent to a simple random sample. It is often used in marketing research.
The sample is generally done by &rst sampling at the higher level(s) e.g. randomly sampled countries, then sampling from subsequent levels in turn e.g. #ithin the selected countries sample counties, then #ithin these postcodes, then #ithin these households, until the &nal stage is reached, at #hich point the sampling is done in a simple random manner e.g. sampling people #ithin the selected households. Or It is often used in mareting research. In this technique, the total population is divided into these groups (or clusters) and a simple random sample of the groups is selected.* Ad0antage: $he close pro>imity of elements can be cost e:ecti#e 1I.e. many sample obser#ations can be obtained in a short time). Page 4 of "%
Subject: Statistical Inference by Dr. Fahd Amjad Disad0antage: $his method generally re8uires a larger total sample si3e than simple or stratied random sampling. For +,ample: A primary application is area sampling where clusters are city blocks or other well(dened areas. +luster &ling is generally used if%
+luster sampling is a sampling techni8ue used when ?natural? but relati#ely homogeneous groupings are e#ident in a statistical population. 'o list of the population e>ists. ;ell(dened clusters which will often be geographic areas e>ist. A reasonable estimate of the number of elements in each le#el of clustering can be made. Often the total sample si3e must be fairly large to enable cluster sampling to be used e:ecti#ely.
&) on!'robability Sampling (De*nition): +on'robability sampling is any sampling method #here some elements of population have no chance of selection (these are sometimes referred to as -out of coverage or under covered), or #here the probability of selection cant be accurately determined.* Or
" core characteristic of non'probability sampling techniques is that samples are selected based on the sub/ective /udgment of the researcher,
rather
than
random
selection
(i.e., probabilistic methods), #hich is the cornerstone of probability sampling techniques.* There are *0e main types of on!'robability Samplingi. +on#enience &ling ii. @udgment &ling iii. &nowball &ling i#. Ad hoc 8uotas sampling #. +ase &tudy &ling
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Subject: Statistical Inference by Dr. Fahd Amjad
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am showing types of 'on(Probability &ling
i)
1on0enience Sampling: " statistical method of dra#ing representative data by selecting people because of the ease of their volunteering or selecting units because of their availability or easy access. 0r It is a non'probability sampling technique. Items are included in the sample #ithout no#n probabilities of being selected. The sample is identied primarily by convenience. Ad0antage: &le selection and data collection are relati#ely easy. $he data in this type of sampling is easily a#ailable and can gather data 8uickly. Disad0antage: It is impossible to determine how representati#e of the population the sample is. The another disadvantages are the risk that the sample might not represent the population as a whole, and it might be biased by volunteers. For +,ample: A professor conducting research might use student #olunteers to constitute a sample.
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Subject: Statistical Inference by Dr. Fahd Amjad
ii)
7udgment Sampling: 1udgment sample is a type of non'random sample that is selected based on the opinion of an e2pert. $esults obtained from a /udgment sample are sub/ect to some degree of bias, due to the frame and population not being identical. 8r The person most no#ledgeable on the sub/ect of the study selects elements of the population that he or she feels are most representative of the population. It is a non-probability sampling techniue. Ad0antage: It is a relati#ely easy way of selecting a sample. Disad0antage: $he 8uality of the sample results depends on the Cudgment of the person selecting the sample. For +,ample: A reporter might sample three or four senators Cudging them as reDecting the general opinion of the senate.
iii)
Sno9ball Sampling: A snowball sample is a non(probability sampling techni8ue that is appropriate to use in research when the members of a population are dicult to locate. " sno#ball sample is one in #hich the researcher collects data on the fe# members of the target population he or she can locate, then ass those individuals to provide information needed to locate other members of that population #hom they no#. &nowball sampling is hardly likely to lead a representati#e sample but there are times when it may be the best or only method a#ailable. For instance if you are studying the homeless you are not likely to nd a list of all the homeless people in your city. owe#er if you identify one or two homeless indi#iduals that are willing to participate in your study it is likely that they know other homeless indi#iduals in their area and can help you locate them. $he same goes for underground subcultures or any population that might want to keep their identity hidden such as undocumented immigrants or e>( con#icts. Gecause snowball sampling is hardly representati#e of the larger study population it is primarily used for e>ploratory purposes.
i0)
Ad oc ;uota Sampling:
Buota sampling is a type of non(probability sampling that in#ol#es a two(step process9 Page < of "%
Subject: Statistical Inference by Dr. Fahd Amjad
. &pecify a list of rele#ant control categories or 8uotas such as age gender income or education. A 8uota is some specic re8uirement or predened category. $he target population is rst segmented into mutually e>clusi#e sub(groups which means that one indi#idual can be a member of only one category or sub(group. $he researcher takes special care to obtain a sample that is similar to the target population on some specied control category. 0. +ollect a sample that has the same properties as the target population. $o do this the researcher must know the distribution of these properties across that population.
For e,ample letHs look at a target population of college students at a local college. Gecause the researcher can access this data he knows that in this gi#en population "5 of the students are male and 4J5 are female. For a sample si3e of !!! the researcher knows that "! males and 4J! females will need to be inter#iewed from that population.
References: www.google.com www.wikipedia.org.com.
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