SAMPLING-PROCEDURE.pdf
- 1. SAMPLING PROCEDURE ABDULRAHMAN M. ISMAEL Senior High School Department Philippine Engineering and Agro-industrial Colllege, Inc. Marawi City Ismael.am67@s.msumain.edu.ph February 1, 2022
- 2. II. Sampling Procedures In sampling, only a relatively small number of respondents or experimental units will be involved, thus, it is commonly used in practice. We examine some of the advantages for doing so. 1. It entails lesser cost, lesser effort and it is less time consuming. a. Since the size of the sample is small compared to the population, the time, cost and effort involved on a sample study are much less than the study done on population. For population, huge fund is required because of the resources to be used which may include more manpower and materials. b. It will also take a much shorter period of time to gather data from a sample than from a population. Thus, sampling can lead to more well-timed results as well. Advantages of Sampling
- 3. 2. It is less cumbersome and more practical to administer. It is easier to handle and manage and not as much burden in your part if you take only data from a smaller number of respondents. 3. Some experiments are destructive so it is not possible to involve the whole population. For example, a car manufacturer might want to test the durability of cars being produced. Obviously, each car could not be crash-tested to determine its durability or else the company has nothing to sell anymore. To overcome this problem, samples are taken from populations, and estimates are made about the total population based on information derived from the sample.
- 4. Sampling also has disadvantages, the biggest of which is that the sample may not truly reflect the characteristic of the population and this would lead to wrong conclusions. Hence, care must be taken in choosing a sample. Also, a sample must be large enough to give a good representation of the population, but small enough to be manageable. A. Probability Sampling or Random Sampling In probability sampling, each element has a known probability of selection, and a chance method such as “draw lots” or using numbers from a random number table is used in selecting the specific units to be included in the sample. Types of Sampling Procedures
- 5. (1) Simple Random Sampling (SRS) This is the simplest form of random sampling where every subset of size n of the population has an equal chance of being selected. A simple random sample can be done using the “fishbowl” method, “draw lots” method or using random numbers. In drawing a simple random sample, the researcher is in effect mixing up the units in the population before a sample of n units is selected Steps in Simple Random Sampling (SRS): (1) Assign a number to each element of the population using the numbers from 1 to N. (2) Select n numbers from 1 to N using random process like fishbowl method or draw lots, or you can use random numbers which can be generated by a scientific calculator, or you can use table of random numbers.
- 6. (a) Each name in a telephone book could be numbered sequentially. If the sample size is to include 1,000 people, then 1,000 numbers could be randomly generated by computer or numbers could be picked out using a random process, for instance, draw lots. These numbers could then be matched to names in the telephone book, thereby providing a list of 1,000 people. (b) Choose a random sample of five (5) students from the following 30 students using the random number of your calculator. Examples:
- 7. A disadvantage of simple random sampling is that we can never be assured that all sectors or groups are represented in the sample. For instance, in Example (b) above, there is a possibility that all elements drawn will be girls or all will be boys. To avoid the above mentioned possibility, we need to contemplate and employ other sampling procedures that can lead to more representative sample in which the sample units are spread evenly over the entire population. This sampling procedure is called systematic random sampling. (2) Systematic Random Sampling This is also called interval sampling. It means that there is a gap or interval between each selection. Researchers obtain systematic samples by numbering each subject of the population and then selecting every k the element in the population where the first unit is chosen at random.
- 8. Steps in taking a Systematic Random Sample: (1) Assign a number to each element of the population using the numbers from 1 to N. (2) Determine the sampling interval k: NOTE: If k is not a whole number, then it is rounded to the nearest whole number. For example, suppose N = 400 and n =15 then k = 400/15 is equal to 26.67. That is, 26.67 is rounded-off to nearest whole number 27. (3) Select a random start r where 1≤ r ≤ k. The sample will include the r th element, (r+k)th , (r +2k)th, (r +3k)th and so on until you reach the desired sample size.
- 9. (a) If a systematic sample of 6 students were to be selected in a class with an enrolled population of 48, the sampling interval would be: k = N/n =48 / 6 = 8 All students would be assigned sequential numbers. The starting point would be chosen by selecting a random number between 1 and 8. If this number is 5, then the sample will consist of ( rth=5th) element which is the 5 th student, (r+k = 5 +8)th element which is the 13th student, (r +2k = 5 +2(8))th element which is the 21st student, (r +3k = 5 +3(8))th which is the 29th student,(r +4k = 5 +4(8))th which is the 37th student until (r +5k = 5 +5(8))th which is the 45th student. (b) In a population of 1200 individuals, choose a systematic random sample of size 9. Solution: k = N/n = 1200/ 9 = 133.33 and since it is not a whole number, we need to round it off to nearest whole number, that is 133. Since k =133, we have r = 1, 2, 3,…, or 133. If we choose r =3, the sample points will be the 3 rd person, the 136th person, the 139th person, the 142nd person, the 145th person, the 148th person, the 151st person, the 154th person until the 157th person. Examples:
- 10. NOTE: The list from which the systematic sample is drawn should be examined that it must not have a periodic pattern because it could possibly result to a biased sample. (3) Stratified Random Sampling In this sampling procedure, the population of N units is first divided into homogeneous subpopulations called strata (homogeneous with respect to the characteristics of interest) and then a sample is drawn from each stratum. This type of sampling assures that all groups or strata are represented in the sample. Some stratification variables commonly used by the Social Weather Station (SWS) survey are location, age and sex. Other stratification may be religion, academic ability or marital status.
- 11. Steps in taking a Stratified Random Sample: (1) Classify the population into at least two homogeneous strata. The basis for classification must be closely related to the variable of interest. Suppose we are interested to determine the students’ opinion on the tuition fee increase, it may be logical to subdivide the population of students by income of parents, college, or by year level, or by tribe or a combination of these. (2) (2) Draw a sample from each stratum by simple or systematic random sampling. How many shall we take from each stratum? The most commonly used formula is proportional allocation. In proportional allocation, the number of units to be taken from each stratum is proportional to the size of the subpopulation; that is, between two strata of different sizes, a bigger sample will be taken from the bigger stratum. Proportional Allocation. If the size N of the population is divided into k homogeneous subpopulations or strata of sizes N1, N2, …, Nk, then the sample size to be taken from each stratum i is obtained using the formula
- 12. NOTE: If n_i is not a whole number, then it is rounded-off to the nearest whole number. (a) The manager of a girls’ dormitory wants to learn how the students feel about the dorm’s services. The students were classified according to the following scheme: If we use proportional allocation to select stratified random sample of size n = 40, how large a sample must be taken from each stratum? Examples:
- 13. (b) In an election survey in Makati City, registered voters are classified according to the following scheme: If one uses proportional allocation to select a stratified random sample of size n=345, how large a sample must be taken from each stratum? Solution;
- 14. Solution; (4) Cluster Sampling Cluster sampling assumes that the population is naturally separated by groups or clusters. A number of clusters are selected randomly and then all or parts of the units within the selected clusters are included in the sample. No units from the non-selected clusters are included in the sample. It differs from stratified sampling, because in the latter, sample units are selected from every group. You may be able to save much resource in cluster sampling compared to SRS or Stratified Random Sampling, but cluster sampling leads to less precise estimates. This is because when we sample each unit in a cluster, we would expect to get similar information which may be different from other clusters not selected.
- 15. Steps in taking Cluster Sampling: (1) Divide the population area into clusters. (2) Select randomly a few of these clusters. (3) Choose all the elements from the clusters selected or select only a portion of it. (a) Suppose the population of a study is residents of a condominium in a large city. If there are 10 condominium buildings in this city, the researcher can select two buildings randomly from the 10 and interview all (or a subsample) of the residents from these buildings. (b) Suppose an organization wishes to find out which sports senior students are participating in the Philippines. It would be too costly and would take too long to survey every student, or even some students from every school. Instead, 100 schools are randomly selected from all over the Philippines. These schools are considered to be clusters. Then every senior student in these 100 schools is surveyed. In effect, students in the sample of 100 schools represent all Senior students in the Philippines.
- 16. The advantages of Cluster sampling are: reduced costs; simplification of the fieldwork and more convenient administration. Instead of having a sample scattered over the entire coverage area, the sample is more localized in relatively few centers. However, it often gives less accurate results due to higher sampling error than for simple random sampling with the same sample size. In the above example, you might expect to get more accurate estimates from randomly selecting students across all schools than from randomly selecting 100 schools and taking every student in those chosen schools.
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