Some Terms Associated with Sampling



SamplingSampling is an important step in the entire research process. Sampling involves procedures used to select research participants. It simply means taking part of some population to represent the whole population. Nearly every survey uses some form of sampling. Suppose the researcher has defined his research problem and has examined the relevant literature to determine what theories and data are available to guide him. On the basis of this knowledge the researcher has developed hypotheses to be tested, or has stated research questions to guide the research. He has also operationally defined his concepts and variables in the hypotheses to make this test possible. The next thing the researcher has to do is to collect data from the population he wishes to investigate.If the researcher could investigate every member in the population, he would surely have answers to his research questions. But populations could be very large and for practical reasons, it is usually impossible to study every element in the population. (Kerlinger, 1973). It would be too costly, and many individuals or groups would not be available for interview, or observation, or to complete questionnaires (Descombe1998). The researcher resolves this problem by studying a sample and generalising the findings from the sample to the population.According to authoritative sources (Kerlinger, 1973; Babbie1999; Descombe, 1999), this is the most efficient way to do research, because there are methods that allow researchers to estimate characteristics of populations by measuring only a small sample of population elements. The researcher has to ensure that the sample is representative of the population from which it was selected otherwise, what he finds in the sample may not be true for the population. Of course, there are times when a researcher may want to study every element of some population. This is when the population is small enough so that every element can be measured without much additional cost and effort. It will also be the case where the researcher is not interested in generalising to some larger group (Kerlinger, 1973; Descombe, 1999; Babbie, 1999). Some Terms Associated with SamplingPopulationIn discussions of sampling, the term population and universe are often used interchangeably. In this course I shall use the term population. In a layman’s language, population is mainly used to describe people but in research terms it has a wider meaning. Population refers to the entire group of people, events or organisations, or things that the researcher wishes to investigate. (Descombe, 1999). If the Librarian of the University of Ghana is interested in investigating use of the library by students of the University, then all students of the University of Ghana will be the population of the study. If a professor wishes to investigate the behaviour of freshmen at lectures, his population will consist of all freshmen of the University. However, if the professor is interested only in the behaviour of freshmen in his class, then the freshmen in his will be his population. Thus the term population refers to all members in the group that happen to be the focus of a study.One goal of scholarly research is to describe the nature of a population. In some cases this is achieved by studying an entire group. The process of examining every member of a population is called a census. In many situations, however, the chance of investigating an entire population is not feasible due to time and resource limitations. The usual procedure in these instances is to select a sample from the population. SampleA sample is a subset of the population that is taken to represent that population. This means that, some, but not all, members of the population would form the sample. If 1,000 students are selected from a population of 30,000, these 1,000 members would form the sample for the study. By studying these 1,000 students, the researcher would draw conclusions about the entire student population of 30,000 considered for the study. One important consideration in sampling is that the sample must be representative of the population from which it is drawn. Being representative means to be typical of a population, that is, to reflect the characteristics of the population (Kerlinger (1973). From a research point of view, therefore, a representative sample means that the sample has ‘approximately the characteristics of the population relevant to the research in question (Kerlinger (1973). If for instance gender is the variable (characteristic) relevant to the research, a representative sample will have approximately the same proportions of men and women as the population. A sample which is not representative of the population, regardless of its size, is inadequate for testing purposes: the results cannot be generalised. (Kerlinger, 1973).To generalise means to apply conclusions reached from studying the elements in a sample to the population from which the sample was drawn. The researcher concludes that the results of the study sample are the same as would have been if every member of the entire population had been studied. Element and subjectA single member of a population is called an element, and a subject is a single member of a sample. In the example above, the 1,000 members from the population of 30,000 formed the sample for the study; each student in the sample is a subject and each member of the population is an element. Sampling frameA list of all cases, objects, or groups in a population is called a sampling frame. Thus the sampling frame contains the same number of units as the population of the study. For example if a researcher wants to study the learning habits of current Level 400 mathematics students, the sampling frame would be the list of the names of all Level 400 mathematics students of the current year. Other examples of ready-made lists which may potentially be used as sample frames are the payroll of an organisation, a list of all students of a University, the electoral register and telephone directories. Assuming that a sample is chosen according to proper guidelines and is representative of the population, the results of the study using the sample can be generalised to the population. Kerlinger (1973) has however, warned that generalising results must be done with some caution because of the error that is inherent in all sample selection methods. Population Parameter and Sample StatisticThe population parameter is population characteristic you want to investigate, for example, the average age of all Level 400 students or the average income of all Senior Members of this University. A sample statistic is the finding of a survey on the basis of information obtained from a sample, (for example the average age of Level 400 students calculated from information obtained from those who were selected to provide information on their age); or the average income of Senior Members, (calculated from the information obtained from those Senior Members who participated in the study). The sample statistic then becomes the basis of estimating the prevalence of a characteristic in the study population.SamplingThe process by which samples are selected from a population is known as sampling. The researcher selects a sufficient number of items from a population so that by studying the sample, and understanding the properties or characteristics of the sample subjects, he would be able to generalise the properties or the characteristics to the population elements. All conclusions drawn about the sample being studied are generalised to the population. In other words sample statistics are used as estimates of the population parameters. When to study the entire populationIdeally, it will be best to study every member of the population in any research project so that the findings of the study can command a lot of respect. Since ideal conditions are usually difficult to meet and still there is the desire to obtain results that are respectable, it will be in place to consider the conditions under which a researcher should obtain the ideal, which is, studying the entire members of the population. The following are some of the reasons why a researcher may study the entire population:When the entire size of the population is smallWhen there is more time for the project When the resources (human and material) available for the project are adequate.When the sole objective of the study is to make a complete count of the population. Why is it necessary to sample?In research investigations involving several hundreds and even thousands of elements, it would be practically impossible to collect data from, or to test or to examine every element. Even if it were possible, it would be prohibitive in terms of time cost and other human resources. A sample may provide you with the needed information quickly. For example, you are a Doctor and a disease has broken out in a village within your area of operation. The disease is contagious and it kills within hours. Nobody knows what it is. You are required to conduct quick tests to help save the situation. If you try a census of those affected, they may be long dead when you arrive with your results. In such a case just a few of those already infected could be used to provide the required information.Studying a sample rather than the entire population is also sometimes likely to lead to more reliable results, mostly because there will be less fatigue, and hence fewer errors in collecting data, especially when elements involved are many in number.In a few cases, it would also be impossible to use the entire population to know or test something. Good examples of this occur in quality control. For example to test the quality of a fuse to determine whether it is defective or not, it must be destroyed. To obtain a census of the quality of a lorry load of fuses, you have to destroy all of them. There will be no fuses to sell. This is contrary to the purpose served by quality-control testing. In this case, only a sample should be used to assess the quality of the fuses.Sample Selection Methods Literature on research methods identifies two primary methods of selecting samples from a population. These are probability sampling and non-probability sampling. Each of these has several different techniques. Probability sampling involves using selection techniques whereby the probability of selecting each participant or element is known. These techniques rely on random processes in the selection of the sample. Examples of probability sampling techniques are simple random sampling, stratified sampling, systematic sampling, and cluster sampling.Unlike probability sampling, in non-probability sampling, random processes are not used in the selection of the sample, thus making it impossible to know the probability of selecting a given participant or element from the population. As a result, it is more difficult to claim that the sample is representative of the population, thus limiting the ability of the researcher to generalise the results of the study. Non-probability sampling techniques include purposive sampling, convenience sampling, quota sampling and snowball sampling.Probability / Random SamplingAs we have noted above, probability sampling is a sampling process that uses random processes or chance procedures to select a sample. This is why it is also known as random sampling. Probability sampling has one important characteristic, which is that, every element in the population, more precisely the sampling frame, has a known probability of being selected for the sample. For example if a sample of 10 students is to be selected from a population of 50, each student will have 1 in 50 chance of being selected. Furthermore, when random processes are used to select a sample it is possible to estimate sampling error, or the chance variations that may occur in the sampling process. The term random in a layman’s sense usually means haphazard, as when an interviewer picks out people as they come out from a shop. Those who look approachable to the interviewer or those who do not seem to be in a hurry may be chosen. This means the researcher has the tendency to be subjective. Besides, this method has no sampling frame, therefore the chances of all those visiting the shop on that particular day being selected are not known.In research terms, however, the random selection of units in the population is carried out according to a specified objective method such as giving each unit a number, putting all the numbers in a box and picking out blindly one number at a time until the required size of the sample is drawn. This method is popularly known as balloting or the lottery method. As we shall see later there are more scientific ways to ballot or pick samples. Types of Probability / SamplingThere are four types of probability sampling methods, namely, simple random sampling; systematic sampling; stratified sampling; and cluster sampling. Let’s take a look at these one after the other.Simple random sampling A simple random sample is obtained when every individual or element in the population has an equal chance of being selected, and the selection of one person does not interfere with the selection chances of any other person. This process is considered to be free from bias because no factor is present that can affect selection. The random process leaves subject selection entirely to chance. (Moser and, Kalton, 1979 Kerlinger 1973; Babbie 1982).If the Head of Information Studies Department (HOD) is to select 30 out of 120 Level 400 students for an award, he may use different ways to obtain a random sample of 30 students. The HOD may use what is popularly known as the fishbowl technique, (which is commonly referred to as balloting or the lottery method); or a table of random numbers; or a computer- generated random numbersUsing the fishbowl techniqueIf the HOD chooses to use the fishbowl technique, he will do the following: Write the names of all the 120 students, (elements of the population which is the sampling frame), on slips of paper. Place the slips of paper in a bow, box, hat, or similar container.He will then mix up the slips of paper thoroughly, close his eyes, and then dip his hand into the container and pick out a slip. The name of the candidate is recorded. He continues this process until he selects his sample of 30.The question we need to ask at this point is what claim has this method of selection to fairness? Notice that each time the HOD is about to pick a slip with his eyes closed, only one student will be lucky to be selected, and all the students are competing on equal footing for that chance. The same equal competition is repeated on further picking of candidates until the required number is achieved. Mixing the slips thoroughly ensures that no student’s slip is permanently on top or bottom, or side or anywhere in such a manner as to give him or her advantage or a handicap.This selection process will give the students not selected the feeling that the process was fair and that they were not discriminated against, since they were given the same chance to compete for the 30 awards. If the HOD were to use these students for a study, the 30 selected, would constitute a random sample of the population.The technique described above can be accomplished in two ways. If, after each name is selected, it is put back into the container, the method is called random selection with replacement. If the names are not replaced after they are picked, this is called random selection without replacement. Descombe (1999) has noted that there is not a lot of difference between the two procedures when the population size is large, but sampling without replacement does not strictly meet the definition of the random selection process. In the example above, each student has 1 chance in 120 of being selected. If the names are not replaced, the probability of each subsequent name being drawn increases. This means, for example, that the second name to be picked will have a probability of 1 in 119, and the third, 1 in 118, respectively to be included in the sample. So, if a name is selected, it should be replaced. If it comes up again, it should be put back into the container. Each person in the population then continues to have the same opportunity, or percentage of chance, to be selected. It is important to point out that there is some controversy regarding which of the two sampling methods is more appropriate. Do not worry about this at this level, since authorities in the field acknowledge that where the population is large and only a small proportion of it is to constitute the sample, (for example 10 per cent sample from a population of 20,000) it will not matter which method is used because they will both result in samples that are quite similar (Baumgartner, 2002). Baumgartner (2002) notes, however, that most researchers sample without replacement since an individual cannot be used as a subject again after once being selected.The method of sampling just described may be appropriate for small sampling frames. With large sampling frames a table of random numbers or a computer package can be used to draw samples. (Descombe,1999). These offer a more convenient and sophisticated way to select a random sample. Using a table of random numbers Let us consider how a table of random numbers can be used to draw a simple random sample. If you have understood the method just described above very well, you can use a table of random numbers to select a random sample without much difficulty. Let me first begin by explaining what random numbers are. Suppose slips of paper, each bearing a number from 1 to 120 are crumpled, thoroughly shuffled in a bag, and then picked one after the other and listed. You will recognise that the numbers will not be in any particular order whether the numbers are even, odd, small, or large. Such a list of numbers which is not in any particular order is referred to as a Table of Random Numbers. The numbers, being in random order, can be used for selecting members of a sample. To do so, however, a more efficient method of generating random numbers must be used than the over simplified method I have just described. A computer can be programmed to generate a list of one-digit, two digits, or three or four digits etc numbers in a random order. A list of random numbers can be found at the back of any textbook on statistics. The table below is part of a table of three-digit numbers in random order. Table of Random NumbersA B CDEFGHI157020526429223637088670428545007090009153265230344011010160018627117008671148647973107570863112386666104035112443025173623249917448475742322418079491611473546738361080033795187051055756274806043019721569109082521338059350220116067251090826742768108719112107179624034017092718004001775009098066584310381110071041751744144065082478537055692095322489298119210300109320350280390114352181404232137005194862532048633051871329558015567996243392755049115555118687687012081339362264105044230536732360016027003579932002034097050268108020529066543438070150190099200210069410230201062290063340360003043490315118403480102320316001209 120150170084210300041030 Let’s go back to our previous example and see how the HOD would use a table of random numbers to select the sample of 30 out of a population of 120 students. The HOD will first of all assign a serial number to every Level 400 student from 1 to 120. Candidate 1 becomes 001; candidate 2 is numbered 002; candidate 8 is numbered 008; candidate 48 is numbered 048 and so on. He will then close his eyes, open a page of a table of random numbers, place his finger at any point. The number on which the finger has been placed is recorded as the first member of the sample. To select the other members of the sample, the HOD will the go down the list of numbers, recording the numbers which fall within 001 and 120 until the 30 members of the sample have been selected. Since the numbers are randomly listed, it would not matter if the HOD moved down the table, or up the table, or from left to right or from right to left. If the HOD decides to go down in the table from a random starting point of 010 until a sample of 30 has been drawn, the sample will include students numbered 010; 112; 059; 092; and so on.It is possible for the HOD to meet the same number a second time. If this happens he must ignore that number as he needs different cases. You may have noticed that this is like the case of sampling without replacement that is, not putting the unit back into the sampling frame. Alternatively the HOD might select a number which is outside the range of those in his sampling frame. If he selects say 150 which is beyond 120 he will simply have to ignore it and continue reading off numbers until he reaches his sample size.Going by this procedure, a researcher can select a set of random numbers for different samples which are unlikely to be the same. This is because the number selected first at random will dictate the selection of the others to follow. What this means in the case of our example is that different samples of 30 students selected by the HOD are likely to be different.For many research projects, the two techniques of random sampling described will enable the researcher to obtain a representative sample for study. But there are occasions in which representativeness is not necessarily guaranteed by simple random sampling. Moser and Kalton (1979). I will discuss this later under stratified sampling.Systematic Sampling Simple random sampling is similar in some way to a procedure called systematic sampling, in which every nth subject or unit is selected from a population. Systematic sampling involves selecting units of the sample at regular intervals from the sampling frame. To do this the researcher must follow this procedure:Number the units - the population from 1 – NDecide on the n, (sample size), that is requiredSelect an interval size k = N/nrandomly select any number between 1 and kfinally take every kth unitGoing back to our example, the HOD has a population that has N=120 people in it and that he wants to take a sample of n=30.To use systematic sampling, the HOD will list the units in the population in a random order. The sampling interval will be120/30 = 4 In this case the interval size, k = 4Now the HOD would select randomly any number between 1 and 4. Imagine that the HOD selected 3. Now, to select the sample, he would start with the 3rd unit in the list and take every k-th unit (every 4th unit because k = 4). With this start the HOD would be sampling units 3 (David);7 (Dorcas); 11(Anna);15 (Agnes);19 (Frempong); and so on to 120 and he would come up with 30 students in his sample. (See Table 3.2).Systematic Sampling A B C D E F G 1 Jerome 16 Linda 31 Lawrence 46 Worlase 61 Selasi 76 Alex 91 Bernard 106 Courage2 Felix 17 Irene 32 Vera 47 Maame 62 Rhodaline 77 Alhassan 92 Bernice 107 Cynthia3 David 18 Frank 33 Golda 48 Felicia 63 Gloria 78 Amofah 93 Bessie 108 Daniel4 Caroline 19 Frempong 34 Augustine 49 Naadu 64 Aaron 79 Anastasia 94 Bismark 109 Daniella5 William 20 Micheal 35 Peal 50 Obesebea 65 Abdallah 80 Andrew 95 Brandon 110 Samuel6 Simon 21 Anthony 36 Belinda 51 Rabiatu 66 Abdul 81 Andy 96 Brenda 111 David7 Dorcas 22 Joana 37 Stephen 52 Florence 67 Abigail 82 Claudia 97 Bright 112 Dawuni8 Thomas 23 Eugenia 38 Serwaa 53 Henri 68 Addai 83 Ansah 98 Bryan 113 Delphina9 Boateng 24 Martha 39 Spurgeon 54 Eugenia 69 Adonis 84 Atta 99 Caios 114 Dennis10 Dorcas 25 Sandra 40 Joy 55 Francis 70 Adubea 85 Augustine 100 Catherine 115 Diana11 Anna 26 Milicent 41 Charles 56 Freedom 71 Adwoa 86 Ayatulah 101 Cephas 116 Divine12 Ebenezer 27 Jeannette 42 Judith 57 Micheal 72 Agyapong 87 Baba 102 Charles 117 Dominic13 Daniel 28 Emelia 43 Rita 58 Pascal 73 Agyekum 88 Babara 103 Christabel 118 Dorothy14 Mike 29 Racheal 44 Daniel 59 Eric 74 Akuorkor 89 Beatrice 104 Christiana 119 Drumond15 Agnes 30 Humphrey 45 Belinda 60 Eugene 75 Albert 90 Benjamin 105 Colins 120 DouglasIt is important to note that members of the sample are always determined by where the random start begins from. In the example above if the systematic selection had started with 2 (Felix), the sample would have been different. In order for systematic sampling to work, it is essential to arrange the units in the population in random order. Systematic sampling is fairly simple to do and is widely used for its convenience and time efficiency. In almost all sampling situations, systematic random sampling yields what is essentially a simple random sample (Descombe,1998). Stratified Random Sampling Stratified sampling involves dividing the population into homogeneous groups, and then conducting a simple random sampling in each group. First of all, elements in the population (that is in the sampling frame) are distinguished according to their value on some relevant characteristic such as army rank:(generals, captains, privates etc) or gender: (male , female) or socio-economic status: (upper, middle and lower class). These characteristics form the sampling strata. Each stratum is homogenous in the sense that they portray similar characteristics or they are identified by similar properties. In a heterogeneous population characteristics of elements differ widely in those populations.Next, elements are sampled randomly from within these strata: so many generals, so many captains, etc. In order to use this method more information is required before sampling than is the case with simple random sampling. Each element must belong to one and only one stratum.Stratified samples can be proportional or non-proportional. In proportional stratified sampling, the number of elements sampled in each group is proportional to its representation in the population. The HOD is aware that the population comprises males and females. Assuming there are 40 females and 80 males. The HOD needs a stratified sample of 30 students. If the HOD draws a simple random sample, he may end up with somewhat disproportionate numbers from each group. In this situation the sample may comprise say 25 males and 5 females. This may occur purely by chance. But considering the proportion of males and females in the population we can conclude that the sample is dominated by males; females are underrepresented. The sampling has resulted in what is called disproportionate random sampling. This scenario brings to mind what I said early on that simple random sampling does not always yield representative samples.To correct this situation the HOD might, stratify the population along gender lines and pick a proportional sample. That is, members represented in the sample from each stratum of the population will be proportionate to the total number of elements in the respective strata. This would mean that the HOD would sample 10 females and 20 males. This type of sampling is called proportionate stratified random sampling. Let’s see the steps involved in selecting a proportionate stratified sample.Identify all elements or sampling units in the sampling populationDecide on the different strata (k) into which you want to stratify the populationPlace each element into the appropriate stratumNumber every element in each stratum separatelyDecide on the total sample size (n)Determine the proportion (p) of each stratum in the study population = (Elements in the stratum divided by the total population size)Determine the number of elements to be selected from each stratum (sample size(n) x (p)Select the required number of elements from each stratum by simple random sample technique or systematic sampling technique.Going by our example, this is how the HOD arrived at the sample of 10 females and 20 males:Population120 studentsNumber of strata =2 (male and female)Sample size (n)= 30 Proportion of males in population = 80 / 120 = 2/3 Proportion of females in population = 40 /120 = 1/3 No. of males to be selected = 2/3 x 30 = 19.99 (20 Males) No. of females to be selected = 1/3 x 30 = 9.99 10Females)Proportional stratified sampling is used when the researcher wants to generalise the findings to the population as a whole In this case, the goal is to produce a sample that is a representative of the population as possible. To the extent that we have included important subgroups in the same proportions as in the population, we have guaranteed that our sample is similar to the population, at least on the stratified variables. (Baumgratner, 2002).In non-proportional stratified sampling an equal number of elements are selected for each group. This means that elements are selected in numbers that do not reflect their proportions in the population. In our example, the HOD may select a non-proportional sample by picking 15 males and 15 females. In this case males are underrepresented in the sample given that there are 80 males as against 40 females in the population.There are times when the researcher will want to use non-proportional sampling. One such situation is when the researcher’s purpose is not to generalise to the population as a whole but, rather, to make comparisons between subgroups. Another situation calling for the use of non-proportional sampling is when the researcher wants to ensure that representatives of an important but very small subgroup within a population are included in the sample (Baumgartner, 2002). Cluster Sampling Resources need to be taken seriously when it comes to the selection of samples. Identifying units to be included, contacting relevant respondents and travelling to locations can all entail considerable time and expense. The researcher, therefore, has to weigh the advantages of a purely random selection against the savings to be made by using alternative approaches. Some techniques can be cost effective without compromising the principles of random selection and the laws of probability. (Descombe, 1998). The most common alternative, and one used frequently for large-scale surveys, is cluster sampling. The logic behind it is that, it is possible to get a good enough sample by focusing on naturally occurring clusters of the particular thing that the researcher wishes to study. By focusing on such clusters the researcher can save a great deal of time and money that would have otherwise been spent on travelling to and fro visiting research sites scattered throughout the length and breadth of a very wide geographical area. The selection of clusters for research follows the principles of probability sampling as we have already discussed. The aim is to get a representative cluster, and the means of getting it rely on random choices of stratified sampling. This method, involves multiple stages in the selection of a sample. The population is divided into clusters or units and then into sub-units. At each level, the units and sub-units are randomly selected. Let’s consider a countrywide study of Junior High School students’ attitudes toward computer selection of successful candidates into Senior High Schools. The researcher may use cluster sampling to obtain results which will represent the views of JHS students countrywide.Knowing that the country is already divided into ten regions, the researcher would select this sample in stages as follows: Stage 1 Randomly select say three regions: ( Eastern, Ashanti and Northern) to represent the whole county.Stage 2 Randomly select some Districts in each regionStage 3 Randomly select towns in each DistrictStage 4 Randomly select a number of schools from each townStage 5 Randomly select individuals from the appropriate class and ask them to complete a questionnaire.Non-probability SamplingTypes of Non-Probability SamplingNon-probability sampling designs include convenience sampling, purposeful sampling, quota sampling and snowball sampling. Convenience sampling This is considered the weakest form of sampling because it does nothing to control bias. In this procedure, participants are recruited as they become available or because they happen to be convenient for the researcher. Such samples are often limited to personal contacts of the researchers or to people who happen to be available at meetings or in organisations or in a particular place and time. The Purposive sample Instead of obtaining information from those who are most conveniently available, it might sometimes become necessary to obtain information from specific targets, that is, specific types of people who will be able to provide the desired information, either because they are the only ones who can provide that information, or because they conform to some criteria set by the researcher.A particular survey may target individuals who are particularly knowledgeable about the issue under investigation. It may involve studying the entire population of some limited group or a sub-set of a population. In this procedure, the researcher uses his judgement and knowledge of the field to identify persons whom he considers to be leaders and experts in this area. One of the first things the researcher is likely to do is to verify that the respondent does in fact meet the criteria for being in the sample.Consider a researcher who wants to investigate the management styles of women managers. The only people who can give firsthand information are women managers and important top level executives in work organisations. Having themselves gone through the experiences and processes, they might be expected to have expert knowledge, and perhaps be able to provide good data or information to the researcher.Purposive sampling can be useful for situations where the researcher needs to reach a target sample quickly and where proportional sampling is not the primary concern. With a purposive sample the researcher is likely to get the opinions of his target population. Quota SamplingIn quota sampling, you select people non-randomly according to some fixed quota. It is a form of proportionate stratified sampling in which a predetermined proportion of people are sampled from different groups but on a convenience basis. In quota sampling you want to represent the major characteristics of the population by sampling a proportional amount of each. For instance, if you have a population of 405 women and 605 men, and that you want a total sample size of 100. You will continue sampling until you get these percentages and then stop. So if you get the 40 women for your sample, but not the 60 men you will continue to sample men but even if legitimate women come along you have already met your quota for women. The problem here is that even when the researcher knows that a quota sample is representative of the particular characteristics for which quotas have been set, he has no way of knowing if the sample is representative in terms of any other characteristics.Snowball samplingWith this approach the researcher initially contacts a few potential subjects and then asks them whether they know anybody with the same characteristics that he is looking for. For example, if the researcher wants to interview a sample of vegetarians or people who support particular political party etc., his initial contact may well have knowledge of the others. So in snowball sampling the researcher identifies one member of the population and then asks that member to identify others of the same characteristics in the population and so on.Snowball sampling is useful for hard-to-reach or hard-to-identity populations for which there is no sampling frame but the members of which are somewhat interconnected (at least some members of the population know one another). It can be used to sample members of such groups as drug dealers, prostitutes, practicing criminals, participants in alcoholics, anonymous groups, gang leaders, informal organisational leaders etc. (Descombe,1998) Although this method would hardly lead to representative samples, there are times when it may be the best method available.A team of researchers want to determine the attitudes of students about recreational services available in the student union on campus. The team stops the first 100 students it meets on a street in the middle of the campus and asks questions about the union of each of these students. What are the possible ways that this sample might be biased?Sample SizeIt is generally accepted that the quality of a sample depends on its size and the way it is selected. (Kerlinger, 1973;Babbie,1999; Descombe.1999). Samples will be representative of the population if they are relatively large and selected through probability sampling. But how large a sample must be to be representative of the population, or to provide the desired level of confidence in the results is a question which remains unanswered. According some authoritative sources (Kerlinger,1973; Babbie, 1999, Descombe, 1998) there is no simple answer to this question. Again while literature on sampling provides information concerning mathematical and statistical techniques which are used to calculate sampling size, no single sample size formula or method is available for every research (Descombe, 1999). Besides the use of mathematical and statistical techniques, there are factors which researchers need to consider when determining sample size. (Descombe, 1998). Though these principles are not based on mathematical or statistical theory, they provide a useful starting point for researchers.Factors to Consider When Determining Sample SizeCost and timeSample size is almost invariably controlled by cost and time. Although researchers may wish to use a large sample for a survey, the economics of such a sample are usually restrictive. Research at any level is very expensive, and these costs have great influence on a project. The general rule is to use as large a sample as possible within the economic constraints of the study. If a small sample is forced on a researcher, the results must be interpreted accordingly, that is, with caution regarding generalisation. (Descombe, 1999).Likely response rateDescombe (1998) has noted that a survey rarely achieves a response from every contact. Especially when using postal questionnaires and the like, the rate of response from those contacted, is likely to be very low. As far as sample size is concerned, the important thing for the researcher to consider is that the number in the original sample may not equal the number of responses that are finally obtained. The researcher needs to predict the kind of response rate he or she is likely to achieve, based on the kind of survey being done, and build into the sample size an allowance for non-responses. For instance if the researcher wants to use a sample of say 100 people for research and is using a postal questionnaire survey for which a response rate of 30 per cent is anticipated, the original sample size needs to be 334.Agreeing with Descombe, Fraenkel and Wallen(2000 ) advise that researchers should always select a larger sample than is actually required for a study, since non-response must be compensated for. They note that subjects drop out of research studies for one reason or another, and allowances must be made for this in planning the sample selection. Heterogeneous populationIf a variable of interest to the researcher varies widely in a population it is advisable to pick a higher than lower percentage sample of the population. The accuracy of the resultsAny sample, by its very nature, might produce results which are different from the ‘true’ results based on a survey of the total population. Inevitably, there is an element of luck in terms of who gets included in the sample and who gets excluded, and this can affect the accuracy of the findings which emerge from the sample. Two different samples of 100 people, chosen from the same population and using the same basic method, will produce results that are likely to be slightly different. (Freankel and Wallen, 2000).It is generally acknowledged that, the larger the sample used the better. The larger a sample becomes, the more representative of the population it becomes and so the more reliable and valid the results based on it will become. (Babbie, 1999). This means for instance that that a 50% sample is better than a 30% sample, which in turn is better than a 10%. By this principle, the researcher should go for the higher sample percentages for, in doing so, he is approaching the 100% sample size. It has been pointed out, however, that a large unrepresentative sample is as meaningless as a small unrepresentative sample, so researchers should not consider numbers alone. Quality is always more important in sample selection than mere size. (Babbie, 1999).Careful planningA well selected random sample, does yield results whose amount of error can be reliably estimated through statistical techniques, and so can be as useful, as those of larger samples whose members were not properly randomly selected . By this principle, the researcher should exercise a great deal of patience and effort in planning and choosing the members of his sample, as well as in the choice of data collecting instruments. Where this has been done, what seems to have been lost through studying a low percentage of the population can be regained through very good and systematic data collection procedures (Descombe, 1999) There are also certain practices among social researchers that the beginner can adopt. One such practice suggests that if the population is a few hundreds, a 40% or more sample will do; if many hundreds a 20% sample will do; if a few thousands a 10% sample will do; and if several thousands a 5% or less sample will do. (Alreck and Seatle, 1985). Learning form othersConsulting the work of other researchers provides a base from which to start. If a survey is planned and similar research indicates that a representative sample of 400 has been used regularly with reliable results, a sample larger than 400 may be unnecessary. ................
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