# sampling

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### Sampling :

Sampling by Lucell Larawan

### Selecting the study population :

Selecting the study population Suppose one of you is interested in a study “Income Levels of CPU Students in the Year 2013-2014.” The source of information or sampling unit (who is to be sampled) are the students of CPU from all departments and colleges. They are called the subjects or respondents. After knowing the sampling unit, the researcher decides on how to select the sample.

### Concepts in sampling :

Concepts in sampling Population: basically the universe of units from which the sample is to be selected. Sample: the segment of the population that is selected for investigation. It is a subset of a population. Sampling frame: the listing of all units in the population from which the sample will be selected. Representative sample: a sample that reflects the population accurately

### …cont :

…cont Sampling bias: a distortion in the representativeness of the sample that arises when some members of the population stand little or no chance of being selected for inclusion in a sample. Probability sample: a sample that has been selected using random selection so that each unit in the population has a known chance of being selected. Non-probability sample: a sample that has not been selected using a random selection method.

### …cont :

…cont Sampling error: the difference between a sample and the population from which it is selected, even though a probability sample has been selected. Non-sampling error: the difference between the population and the sample that arise either from deficiencies in the sampling approach, such as inadequate sampling frame or non-response, or from such problems as poor question wording, poor interviewing, or flawed processing of data.

### …cont :

…cont Non-response: occurs when some members of the sample refuse to cooperate, cannot be contacted, or for some reason cannot supply the required data Census: the enumeration of an entire population

### Types of sampling :

Types of sampling Probability Simple random Systematic sampling with a random start Stratified sampling Cluster sampling Double sampling Multistage sampling

### Slide 8:

B. Non-probability sampling Convenience Purposive Snowball

### Types of probability sample: simple random sample :

Types of probability sample: simple random sample A. Simple random sample—each unit of the population has an equal probability of inclusion in the sample Example: We have a budget to interview 450 employees of a company which has 9,000 employees. We follow the steps in devising our sample: Define the population. We have decided that this will be all full-time employees of the company. This is our N which is 9,000.

### …cont :

…cont 2) Select or devise a comprehensive sampling frame. The company has a Human Resource Office that keeps the records of all employees who meet our criteria—the full-time employees. 3) Decide you sample size (n). We have decided that this will be 450. 4) List all the employees in the population and assign them consecutive numbers from 1 to N. In our case, this will be 1 to 9,000. 5) Using a table of random numbers, select n (450) different random numbers that lie between 1 and N (9,000).

### …cont :

…cont 6) The employees to which the n (450) random numbers refer constitute the sample.

### B. Systematic random sample :

B. Systematic random sample With this kind of sample, you select units directly from the sampling frame—that is without resorting to the table of random numbers. Example: For a study, you wish to draw a sample of 15 insulin-dependent patients from 30 eligible patients.. These 30 were identified from the hospital records. Population: 30 insulin-dependent diabetic patients Sampling frame: a list of names of eligible patients Sampling unit: an insulin-dependent diabetic

### …cont :

…cont Steps in drawing the sample patients: List the 30 eligible patients in alphabetical order and number them from 1 to 30. Determine the sampling interval (k) by dividing the size of the population by the number of units desired: K = 30/15 = 2. Select a random start by picking at random any number from 1 to 30. For example, you picked 10. From number 10, the random start, take every second name in the list. When you reach number 30, go back to number 1 and continue drawing your sample units until you come up with 15 numbers.

### C. Stratified random sample :

C. Stratified random sample In the language of sampling, this means stratifying the population by a criterion and selecting either a simple random sample or a systematic sample from each of the resulting strata. Example: In a study “Attitudes of Employees in Company X Towards Implementing Project A.” The study population consists of 75 employees: 30 employees from operations, 20 from marketing, 10 from finance, and 15 from the client service. If the attitudes towards implementing project A are expected to differ, a sample of each group must be drawn.

### Slide 15:

From the previous example: Population: all the 75 employees Sampling frame: list of employees by department Sampling unit: employees of Company X Steps in drawing the sample: 1) Classify the 75 employees: operations, marketing, finance, client service. 2) Determine the sample size using the appropriate formula. For instance 30 is the desired sample size. 3) Allocate the needed sample size (n) among the four strata either equally or proportionately if the numbers in the various strata vary. To do this divide the stratum size by the population size (N) and multiply the quotient by the needed sample size. 4) With the sub-sample size, select the sample from each stratum using either simple random sampling or systematic sampling.

…cont

### D. Multi-stage cluster sampling :

D. Multi-stage cluster sampling In this sampling technique, the selection of the sample is accomplished in two or more stages. The population is first divided into a number of first-stage units from which the sample is drawn. Then the population in the sampled first stage units are divided into second stage units. More stages may be added, if desired, by dividing the population into a hierarchy of sampling units corresponding to the different sampling stages. This process is usually used when the population can be divided into hierarchies. The sampling process in each hierarchy is considered one stage.

### Slide 18:

Example: In a study on “Entrepreneurial Profile of Small and Medium Scale Business Owners in Province X,” one may wish to select a sample of 200 men and women who are entrepreneurs. Suppose you wish to include three of the seven towns of the province and three barangays in each sample town, and select from each barangay. Population: all entrepreneurs in province X Sampling frame: list of entrepreneurs in province x Sampling unit: a man or woman who is an entreprenuer

### Slide 19:

Steps in drawing the sample: Draw sample towns in the province. List the names of towns in the province and using simple random sampling draw the three sample towns. Draw a sample of barangays in the sample towns. Secure a list of all barangays in each of the three sample towns and using simple random sampling, draw three sample barangays in each of the three sample towns. Draw a sample of entrepreneurs in the sample barangays. List the names of the businessmen of the three sample barangays taken from three sample towns. Using simple random sampling or systematic sampling with a random start, select the sample in each of the sample barangay.

### E. Cluster sampling :

E. Cluster sampling Cluster sampling is a method of selecting a sample of groups or clusters of elements. Clusters are usually exclusive sub-populations which together comprise a population. Each cluster consists of heterogeneous elements and each is typical of the population. For instance in a school where students in each grade level are assigned to heterogeneous rather than homogeneous sections, each section is considered a cluster. The procedure in this method is similar to the stratified sampling.

### F. Double sampling :

F. Double sampling The process includes collecting data from a sample using a previously defined technique. Based on the information found, a subsample is selected for further study. The reason for using double sampling or multiphase sampling is that it may be more convenient or economical to collect some information by sample and then use this information as the basis for selecting a subsample for further study. Example: In a dining club, you might use a telephone or another inexpensive survey method to discover who would be interested in joining such a club and the degree of their interest. (continued)

### Slide 22:

You might then stratify the interested respondents by degree of interest and subsample among them for intensive interviewing on expected consumption pattern, reactions to various services, etc.

### Non-probability sampling :

Non-probability sampling Convenience: Researchers have the freedom to choose whomever they find; thus the name “convenience.” Example: include informal pool of friends and neighbors, use of employees to evaluate the taste of a new snack food, a TV reporter’s “person-on-the-street” intercept interviews, etc. 2) Purposive: two types include judgmental and quota sampling Judgmental sampling occurs when a researcher selects members to conform to some criterion. Example: those who experiences on-the-job discrimination

### ..cont :

..cont Quota sampling: The logic behind this is that certain relevant characteristics describe the dimensions of the population. If a sample has the same distribution on these characteristics, then it is likely to be representative of the population regarding other variables on which we have no control. Two tests to meet: a) have a distribution in the population that we can estimate; b) be pertinent to the topic being studied. Example: Suppose the student body of Metro U is 55 percent female and 45 percent male. The sampling would call for sampling students at a 55 to 45 percent ratio.

### …cont :

…cont 3) Snowball: This has found a niche in applications where respondents are difficult to identify and are best located through referral networks. Example: The high end of the US audio market is composed of several firms that produce ultra-expensive components used in recording and playback of live performances. A risky new technology for improving digital signal processing is being contemplated by one firm. Through its contacts with a select group of recording engineers and electronics designers, the first stage sample may be identified for interviewing.

### Determining the sample size :

Determining the sample size Two important considerations: Availability of resources The requirements of a proposed plan of analysis Answer the following questions to solve the sample size: 1) What is the estimate for key proportions (p) to be measured in the study? If your study is about who would accept the new technology in a company, you can make a rough estimate of 0.50 (50%) if you have no idea about how many would accept the new technology.

### Slide 27:

2) What degree of accuracy (d) do you want? This is usually from 0.01 to .05. 3) What confidence level (Z) do you want to use? Usually, the 95% level is specified. This is represented by the Z value of 1.96. 4) What is the size of the population (N) that the sample is supposed to represent? The following formula (Parel, et al, 1985) is used for N which less that 10,000. n= NZ² [p(1-p)] Nd² + Z²[p(1-p)]

### Slide 28:

…cont Where: N= population n= desired sample size Z= the standard normal deviate, set at 1.96, corresponding to 95% level of confidence p= the proportion in the target population estimated to have a particular characteristic, 50 % (.50) d= degree of accuracy desired, usually set at either .05, .025 or .01

### Choosing Research Participants for Qualitative Studies :

Choosing Research Participants for Qualitative Studies Main concerns and debates: Gaining access Enabling the collection of appropriate data Your sample size depends on your purpose, your topic, the issues of credibility, your time and resources. Lincoln and Guba (1985) would add that sampling is conducted “to the point of redundancy…If the purpose is to maximize information, the sampling is terminated when no new information is forthcoming from new sampled units; thus redundancy is the primary criterion.”

### Differences between probability ad non-probability sampling :

Differences between probability ad non-probability sampling

### Slide 31:

As you already know, quantitative sampling depends on the power to generalize findings, but in qualitative research, it is not generalization we are concerned with, rather it is deeper understanding within a context that is the concern. Most qualitative researchers select purposive, or purposeful sampling for their technique. In this technique, participants, archived data, or documents are selected because they are representative of specific criterion the researcher is interested in studying. For example, if you are seeking to learn more a specific teaching method, you would purposively select teachers who have used this technique.

### Patton’s purposeful sampling techniques :

Patton’s purposeful sampling techniques

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### Minimum non-probability sample size by Guest et al (2006) :

Minimum non-probability sample size by Guest et al (2006)

### More about number of participants needed :

More about number of participants needed Despite the importance of estimating the required sample size when designing qualitative research, compared to probability samples there is little advice regarding the likely number of participants needed. Morse (1994) commented: “saturation is the key to excellent qualitative work.” Yet many texts still simply recommended establishing the size of a non-probability sample inductively—namely continuing to collect data until there is data saturation, the point at which no new information or themes are observed in the data.

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