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DefinitionSampling: is the process of selecting a few (a sample) from a bigger group, the sampling population, to become the basis for estimating or predicting the prevalence of an unknown piece of information, situation or outcome regarding the bigger group.Sample: is a subgroup of population you are interested in.
Adv. & Disad. Of Sampling ProcessAdvantages Saves time Saves financial and human resourcesDisadvantages Unable to find out the information about the population’s characteristics of interest to you but you only estimate or predict them The possibility of an error in your estimation exists
Sampling Terminology Term DefinitionPopulation/stud The large general group of many cases from which a researcher draw ay population sample and are usually denoted by the letter (N)Sample A smaller set of cases a researcher selects from a larger group and generalizes to the populationSample size The number of selected cases from larger population from who you obtain the required information and is usually denoted by the letter (n)Sampling The method you use to select your sampledesign/strategySampling unit/ The name for a case or single unit to be selectedsamplingelementSampling frame The list of units composing a population from which a sample is selectedSample statistics Information obtained from your respondentsPopulation A characteristic of the entire population that is estimated from a sampleparameters/population mean
Principles of Sampling Average age of four people: A, B, CPrinciple One: & D. In a majority of cases of A is 18 yrs, B is 20, C is 23 & D is 25 sampling there will be a Average age is : 21.5 (18+20+23+25 difference between the sample statistics and the true = 86 divided by 4) population mean, which is By selecting a sample of two we attributable to the selection can estimate their average age. of the units in the sample And we can have six possible combinations of two: 1. A & B 2. A & C 3. A & D 4. B & C 5. B & D 6. C & D
Difference between Sample average & population Average (2 cases) Sample Sample Population Difference bet 1 average mean &21. A & B2. A & C 1 19.0 21.5 -2.53. A & D4. B & C 2 20.5 21.5 -1.55. B & D6. C & D 3 21.5 21.5 0.0 4 21.5 21.5 0.0 5 22.5 21.5 +1.0 6 24.0 21.5 +2.5
Average age of four people: A, B, CPrinciple Two: & D. The greater the A is 18 yrs, B is 20, C is 23 & D is 25 Average age is : 21.5 (18+20+23+25 = sample size, the more 86 divided by 4) accurate will be the By selecting a sample of three we estimate of the true can estimate their average age. And we can have four possible population mean combinations of three: 1. A + B+C 2. A + B+D 3. A + C+D 4. B + C+D
Difference between Sample & Population Average (3 cases) Sample Sample average Population Difference bet 1 & mean 21. A + 1 20.33 21.5 --1.17B+C2. A +B+D3. A + 2 21.00 21.5 -0.5C+D4. B +C+D 3 22.00 21.5 +0.5 4 22.67 21.5 +1.17
Principle Three: The greater the difference A is 18 yrs, B is 26, C is 32 in the variable under study & D is 40 in a population for a given Average age is: 29 sample size, the greater (18+26+32+40 = 116 will be the difference divided by 4) between the sample statistics and the true population mean
Difference between Sample Statistics & Population Mean (2 cases) Sample Sample Population Difference bet1. A & B average mean 1&22. A & C3. A & D 1 22 29.00 -7.004. B & C5. B & D 2 25 29.00 -4.006. C & D 3 29 29.00 0.00 4 29 29.00 0.00 5 33 29.00 +4.00 6 36 29.00 +7.00
Difference between Sample and Population Average (3 cases)Sample Sample Population Difference bet 1 & average mean 2 1 25.33 29.00 --3.67 2 28.00 29.00 -1.00 3 30.00 29.00 +1.00 4 32.66 29.00 +3.66 1. A + B+C 2. A + B+D 3. A + C+D 4. B + C+D
Factors affecting the inferences of sampleThe size of the sampleThe extent of variation in the sampling population
Aims in selecting a sampleTo achieve maximum precision in your estimates within a given sample sizeTo avoid bias in the selection of your sampleBias in the selection of a sample can occur if:Sampling is done by a non-random methodThe sampling frame does not cover the sampling population accurately and completelyA section of a sampling population is impossible to find or refuses to cooperate
Random/probability sampling Designs Each element in the population has an equal and independent chance of selection in the sample.Equal : means the probability of selection of each element in the population is the same. That is, the choice of an element in the sample is not influenced by other considerations such as personal preference.Independent : means that the choice of one element is not dependent upon the choice of another element in the sampling That is, the selection or rejection of one element does not affect the inclusion or exclusion of another.A sample can only be considered a random/probability sample and representative of the population under study if these conditions are met. If not, bias can be introduced into the study.
Advantages of Random/Probability SamplesAs they represent the total sampling population, the inferences drawn from such samples can be generalized to the total sampling population.Some statistical tests based upon the theory of probability can be applied only to data collected from random samples. Some of these tests are important for establishing conclusive correlations.
Procedure for using a table of random numbers Identify the total number of elements in the study population. The total number of elements in a study population may run up to four or more digits. Number each element starting from 1. If the table for random numbers is on more than one page, choose the starting page by a random procedure. Again select a column or row that will be your starting point with a random procedure and proceed from there in a predetermined direction Corresponding to the number of digits to which the total population runs, select the same number, randomly, of columns or rows of digits from the table Decided on your sample size Select the required number of elements for your sample from the table If you happen to select the same number twice, discard it and go to
Difference Systems of Drawing a RandomSampleSampling without replacementSampling with replacement
Type of Specific Random/ProbabilitySampling DesignsSimple random sampling (SRS)Stratified random samplingCluster sampling
Procedure for Selecting Simple Random Sampling1. Identify by a number all elements or sampling units in the population2. Decide on the sample size (n)3. Select (n) using either the fishbowl draw, the table of random numbers or a computer program
Stratified Random SamplingIn this sampling the researcher attempts to stratify the population in such a way that population within a stratum is homogeneous with respect to the characteristic on the basis of which it is being stratified.It is important that the characteristics chosen as the basis of stratification are clearly identifiable in the study populationFor example, it is much easier to stratify a population on the basis of gender than on the basis of age, income or attitude.Once the sampling population has been separated into non-overlapping groups you select the required number of elements from each stratum, using the simple random sampling technique.
Types of stratified Random SamplingProportionate stratified sampling : the number of elements from each stratum in relation to its proportion in the total population is selected.Disproportionate stratified sampling: consideration is not given to the size of the stratum.
Cluster SamplingBased on the ability of the researcher to divide the sampling population into groups, called cluster, and then to select elements within each cluster, using the SRS technique.Depending on the level of clustering, sometimes sampling may be done at different levels. These levels constitute the different stages (single, double or multi-stage cluster sampling).
Non-random/non-probability SamplingDesignsThese are used when the number of elements in a population is either unknown or cannot be individually identified.In such situations the selection of elements is dependent upon other considerations.
Types of Non-random/non-probabilitySampling Designs1. Quota sampling2. Accidental sampling3. Judgmental or purpose sampling4. Snowball sampling
Quota SamplingThe researcher is guided by some visible characteristic, such as gender or race, of the study populationThe sample is selected from a location convenient to the researcher, and whenever a person with this visible relevant characteristic is seen that person is asked to participate in the study.The process continues until the researcher has been able to contact the required number of respondents (quota).
Quota Sampling Advantages: It is the least expensive way of selecting a sample You do not need any information, such as a sampling frame, the total number of elements, their location, or other information about the sampling population It guarantees the inclusion of the type of people you need Disadvantages: The resulting sample is not a probability one, the findings cannot be generalized to the total sampling population The most accessible individuals might have characteristics that are unique to them and hence might not be truly representative of the total sampling population
Accidental samplingWhereas quota sampling attempts to include people possessing an obvious/visible characteristic, accidental sampling makes no such attempt.The method of sampling is common among market research and newspaper reporters.It has same advantages and disadvantages as quota sampling.As you are guided by any obvious characteristics, some people contact may not have the required information
Judgmental or purpose samplingIs the judgment of the researcher as to who can provide the best information to achieve the objectives of the study.The researcher only goes to those people who in his/her opinion are likely to have the required information and be willing to share it.This type of sampling is extremely useful when you want to construct a historical reality, describe phenomenon or develop something about which only a little is known.
Snowball samplingIs the process of selecting a sample using networks.To start with, a few individuals in a group or organization are selected and the required information is collected from them.They are then asked to identify other people in the group or organization, and the people selected by them become a part of the sample.This process continued until the required number or a saturation point bas been researched.This method is useful for studying communication patterns, decision making or diffusion of knowledge within a group.
Mixed Sampling Design :Systematic Sampling DesignSystematic Sampling has the characteristics of both random and non-random sampling designsIn systematic sampling the sampling frame is first divided into a number of segments called intervals.If the first interval is the fifth element, the fifth element of each subsequent interval will be chosen
Procedure for Selecting a Systematic SamplePrepare a list of all the elements in the study population (N)Decide on the sample size (n)Determine the width of the interval (k) = total population sample sizeUsing the SRS, select an element from the first interval (nth order)Select the same order element from each subsequent interval
Calculation of sample SizeDepends on what you want to do with the findings and what type of relationships you want to establish.In qualitative research the question of sample size is less important as the main focus is to explore or describe a situation, issue, process or phenomenon.
Calculation of sample Size In qantative research and particularly for cuase- and-effect studies, you need to consider the following: 1. At what level of confidence do you want to test your results, findings or hypotheses? 2. With what degree of accuracy do you wich to estimate the population parameters? 3. What is the estimated level of variation (standard deviation, with respect to the main variable you are studying, in the study population?
Calculation of Sample Size The size of the sample is important for testing a hypothesis or establishing an association, but for other studies the general rule is the larger the sample size, the more accurate will be your estimates. In practice, your budget determines the size of your sample. Your skills in selecting a sample, within the constraints of your budget, lie in the way you select your elements so that they effectively and adequately represent your sampling population.