Sampling Procedures

GRADUATE SCHOOL
Notre Dame University
Cotabato City

SAMPLING PROCEDURE

A Written Requirement in Nursing Research

Submitted by:

Scheryzad G. Masukat, RN

Submitted to:

Lorenita T. Celeste, RN MAN

Sampling is the process of selecting a part called sample from a given population with ultimate goal of making generalization about unknown characteristics of the given population.

Steps in Sampling Process / Procedures * Define the population (element, units, extent and time) * Specify sampling frame(Telephone directory) * Specify sampling unit (retailers, our product, students, unemployed) * Specify sampling method/technique * Determine sampling size * Specify sampling size-(optimum sample) * Specify sampling plan * Select the sample

Good Sample * The sample should be true representative of universe. * No bias in selecting sample * Quality of the sample should be same * Regulating conditions should be same for all individual * Sampling needs to be adequate * Estimate the sampling error * Sample study should be applicable to all items

Advantages of SAMPLING 1. Sampling enables the investigation of a large population.
When the population is too big, then it is almost impossible to collect data from all the elements of the population. 2. Sampling reduces cost. 3. Sampling enables the completion of the study within a reasonable period of time. 4. Sapling avoids consuming all the source of data.

Principles of SAMPLING 1. There should be an adequate sample size 2. Sample elements should be selected in such way that they are truly representatives of the population elements.

GUIDELINES FOR DETERMINING ADEQUATE SAMPLING

What is a good size?

The answer to this question is influenced by a number of factors including the responses of the study, the population size, the risk of selecting a “bad” sample and the allowable sampling error.

The size of a sample is usually determined before the start of a study. But there are no fixed rules for determining the size of a sample. However, there are broad guidelines in determining the right size sample. Some of these are the following. 1. When the universe or population is more or less homogeneous and only the typical normal or average is desired to be known a smaller sample is enough. However, if differences are desired to be known, a larger sample is needed.

2. When the universe or population is more or less heterogeneous and the typical normal or average is desired to be known, a larger sample is needed. However, if only the differences are desired to be known, a smaller sample is sufficient.

3. The proportional size of a sample is inversely proportional to the size of the population. A larger proportion (percent) is required of a smaller population and a smaller proportion may do for a bigger population. For a population of 5,000, a sample of 10 percent may do but for a population of 500, a proportion of 30 percent may be more desirable.

4. For a greater accuracy and reliability of results, a greater sample proportion is desirable. This is especially true in descriptive research.

5. In biological and chemical research rxpeeriments such as testing the effects of drugs and other substances, the use of a few persons is sufficient to determine the reactions of humans to such drugs and other substances. This is feasible since the biological and physiological systems of humans are almost if not exactly the same.

6. When the subjects (sample) are likely to be destroyed during the research experiment, it is more feasible to use non-humans such as animals especially rats.

7. In addition, in most theses and dissertations surveyed from 20 to 25 percent had been used as sample proportions. This is in theses and dissertations dealing with descriptive research. Some even used high proportions. It seems that the sample proportions of 20 to 25 percent used in descriptive research are acceptable as ideal enough by most people concerned in research. But as mentioned before when the population is too big, say running into thousands, the proportion may be lessened.

8. For a more definite way of determining the sample size, the following formula (Slovin) maybe utilized:

In which: n = is the size of the size of the sample N = is the size of the population E = is the margin of error

The margin of error (e) is the non-precision level the researcher is willing to accept. This is inherent to the research, which makes use of sampling design. This does not mean a wrong answer or a wrong step in a solution.

The margin of error (e ) may be any percent value less than or equal to 10%, so that its complementing confidence level (100% - e) is 90% or higher.

Example:

If the population consists of the College of Health Sciences students enrolled in this semester with a size of 1600, what could be a good sample size for a survey involving these students?

Solution
Given: N = 1600 E = 5% (a number within the range of 1% to 10%
Required: n
Equation: Steps:

Substitution

n=16001+1600(.05) Changing 5% to .05

n=16001+1600(.05) Simplifying (.05)2 = .0025

n=16001+4 Multiplying 1600and .0025

n=16005 Adding terms in the denominator

n=320 - answer Dividing expressions

A group of 320 students from the CHS constitute the sample. However, the size of the sample may be a little higher than 320 when e is lower than 5% or may be a little lower than 320 when e is higher than 5%.

c. SAMPLING Techniques Once the sample size is determined and the list of population elements is available. The next question to answer is “How could the sample elements be selected from the population element?” The basic principle to remember in the process of selecting is “the sample elements should truly represent the population elements”. This means that characteristics of the sample may or may not be taking all the characteristics of the population and that sample elements should not contain any characteristics not found in the population elements.

c.1 Probability Sampling Techniques There are techniques that allow every element of the population an equal chance of being selected as a sample element. The selection may be done using: 1. Random Sampling is the method of selecting a sample size (n) from a universe (N) such that each member of the population has an equal chance of being included in the sample and all possible combinations of size (n) have an equal chance of being selected as the sample. There are several ways of drawing sample unit at random, it can be done by: a) Lottery Sampling or b) Table of Random Numbers c) Use of Calculators

Lottery Sampling. The lottery sampling method is usually carried out by assigning numbers to each number of the population. For example, we may write down names of each number of the population on pieces of paper. These papers are then placed in a box or container drum. The box or lottery drum must be shaken thoroughly to prevent some pieces of paper from sinking at the bottom, where they will have less chances of being drawn. From the box or lottery drum, the required number of sample units is picked.

Table of Random Numbers. The use of the Table of Random Numbers is another example of random sampling. Under this technique, the selection of each member of the population is left adequately to chance, and every member of the population has an equal chance of being chosen. (A sample Table of Random Numbers is found in the Appendix of this material)

Use of Calculators. Some calculators have a key labeled RAN that gives random numbers. The numbers that appear when this key is pressed have three decimals places. If the population is less than a hundred, select the first two digits and disregard the decimal point. The numbers are either one or two digits. Consider the following example:

RAN | Interpretation | 0.1850.2840.6780.7260.4100.014 | 18286772411 |

2. Systematic Sampling This method uses prior knowledge of the individuals comprising a universe with the end in view to increasing precision and representation of samples. When sample units are obtained by drawing every, say 4th or 7th or 10th item on a list, the process of selecting the sample is called systematic sampling. To get the Kth interval, we use Nn . We usually get a number from 1 to K for a random start. All other sample numbers are readily obtained by adding K to the previous number. Example: Suppose a sample of 75 students is to be chosen from the population of 325 students. Identify the sample numbers by systematic sampling with a random start. Solution: Step 1. Nn=K 32575=4.33 K = 4 Step 2. Choose a number from 1 to K by lottery. In this case, using 4 small pieces of paper, write on each piece one number from 1 to 4. Draw out one piece of paper by lottery. Record the number on the chosen piece show 3, then the first sample number is 3. Step 3. List down all sample numbers starting from number 3 called the random start. Add K or 4 to the previous number to get the number. 1.) 3 2.) 7 3.) 11 4.) 15 5.) 19 +4 6.) 23 75.) __ 3. The Stratified Sampling In this method the population is first divided into groups – based on homogeneity – in order to avoid the possibility of drawing samples whose members comes only from stratum. In stratified sampling, the distribution of sampling units is proportionate to the total number of units n each stratum. The bigger the population, the more sample units are drawn, the less population, the less the sample units. That is why this method is often called stratified proportional sampling. In contrast, simple random takes this proportion to chance. Stratified sampling is often used in polls of public opinion in order to secure representative proportions of opinions of various classes of people. Classifications may be based on districts, socio-economic status, sex, work, etc.. depending on the problem being studied. In surveys or market research, we often have to stratify or assign into groups the items in the universe to be sampled. When the universe can be divided into two more groups based on homogeneity. It is often possible to increase the precision of the estimate by taking a sample from each stratum instead of using a simple random sample of the same total size. The sample will still be a probability sample so long as a random method of selection is used in drawing the sample units from each of the strata or groups.

The sample size per stratum is obtained using the formula; subpopulation size population size x desire sample size

Example A stratified sample of size n=500 is to be taken from a population size of N=4000, which consist of three strata of size N1=2000, N2=1,200 and N3=800. If the allocation is to be proportional, how large a sample must be taken from each stratum? Solution: n1=N1N x desired sample size n2=N2N x desired sample size n1=20004000 x 500 n2=1,20004000 x 500 n1=250 n2=150 n3=N3N x desired sample size n3=8004000 x 500 n3=100

4. Cluster Sampling The cluster sampling is sometime referred to as an area sample because it is frequently applied on a geographical basis. On this basis, district or blocks of a municipality or a city are selected. These districts or blocks constitute the clusters. Cluster sampling is useful in selecting sample when blocks in community or city are occupied by heterogeneous groups. For example, if a community in Manila has lower, middle, and upper income residents living side by side, we may use this community as a source of sample to study the different socio-economic groups in Manila. By concentrating on this particular area, we can save more time, effort and money than if we covered different communities throughout Manila. In general, we can get more precise results under cluster sampling when each cluster contains as varied a mixture as possible and at the same time one cluster is as nearly alike as the other. This sampling is a reverse case of stratified sampling where the strata are internally as homogeneous as possible and at the same time each stratum is different from one another as much as possible. Thus, in our previous stratified sampling example, each stratum comprised internally homogeneous items and the three groups were quite different from one another with regard to income. A cluster is an intact group possessing a common characteristic. An example is a population consisting of all the 800 nurses in 20 hospitals in a large city. To illustrate how the desires sample size of 200 nurses could be selected given this population, we follow the steps bellow: a) Prepare a list of the cluster comprising the population and determine the sample size. Our logical cluster would be by hospitals in the city. Assume that our sample size is 200 nurses. b) Estimate the average number of members per cluster in the population. Assume that the average number of nurses per hospital is 40. c) Divide the required sample size by the average number of member per cluster to get the number of clusters to be selected. Since our sample size is 200 nurses and the average number of nurses per hospitals is 40, the number of clusters needed is 200÷40 or 5. d) Select the needed number of clusters. By using the Table of Random Numbers, select the 5 hospitals from the population list of 20 hospitals. Include all the members in the selected clusters. Since there is an average of 40 nurses per hospital and we shall only use 5 hospitals, our sample size of 200 nurses is completed. To illustrate the steps mentioned, we summarize the data as follows: Number of hospitals, N=20 Average number of nurses per hospital, X=40 Desired sample size, n=200 Required clusters,Y=nX=20040=5 clusters c.2 Non-Probability Sampling Techniques Some units/elements of the population are deliberately ignored as the choice of elements for the sample. Thus, there is no equal probability in the selection of sample elements (Pagoso and Montaña, page 56-57). 1. Purposive Sampling This is based on certain criteria laid down by the researcher. People who satisfy the criteria are interviewed. A researcher might want to find out, for example, the reaction of the banking community to particular Central Bank circulation. Instead of interviewing the executives of all banks, he purposely can choose to interview the key executives of only five biggest banks in the country if he believes that it is the reaction of the big ones that counts anyway. Of course, the answers obtained through this procedure are not representative of the entire banking system. Or a researcher may want to find out whether the production of “burong talangka” conforms to the minimum standards of health and safety. There are several small and medium-scale procedures would be rather difficult. What the researcher can do is to study and analyze only the two major procedures of this product.

2. Quota Sampling This is a relatively quick and inexpensive method to operate. Each interviewer is given definite instruction about the section of the public he is to question, but the final choice of the actual persons is left to his own convenience or preference, and is not predetermined by some carefully operated randomizing plan. Each interviewer then proceeds to fill the prescribed quota. As the following example will show, this method has its pitfalls. Suppose there is a survey to estimate what percent of the population of Quezon City consider basketball as one of their favorite sports. One interviewer might report that 100 percent of his quotas of 70 people are basketball fans. However, it may later be found out that this interviewer reached his quota by going to the Araneta Coliseum to enjoy watching his favorite team compete and at the same time interview some thrilled viewers during the game. 3. Convenience Sampling A researcher might want to find out the popularity of a radio program. Since the researcher has a telephone he might simply use it and “randomly” pick is samples from the telephone directory. This method, of course, biased against non-telephone users. Or a researcher might want to find out whether the production of “bola-bola” of fish balls confirms to the minimum standards of health and safety. There are hundreds of ambulant peddlers of this product. Thus it is impossible for the researcher to make a complete list, much less to interview all the producers and test all their products. So what the researcher can just do is to get samples of the product, say, from the fish ball peddler near his school or near his resident.

BIBLIOGRAPHY:

Navarra, Sonia A. (2007). Stat 111 Elementary Statistics. Notre Dame University – College of
Arts and Sciences: Natural Science/ Math Department.

Somoray, Ana M (2012, September 10). Sampling Procedure. Retrieved July 7, 2013, from http://www.slideshare.net/anasomoray/chapter-4-sampling-procedure

Bibliography: Navarra, Sonia A. (2007). Stat 111 Elementary Statistics. Notre Dame University – College of Arts and Sciences: Natural Science/ Math Department. Somoray, Ana M (2012, September 10). Sampling Procedure. Retrieved July 7, 2013, from http://www.slideshare.net/anasomoray/chapter-4-sampling-procedure