Chapter 9 sampling and statistical tool
- 1. Chapter 9 58 Sampling THE SAMPLING Define what a sampling is. Identify a good and defective sampling. Explain how to determine a sample size Discuss and identify the different types of sampling techniques 9.1 Sampling Defined The following are the terms that a researcher should comprehend. o Sampling is a process of choosing a representative portion of a population to represent the entire population. o Sample. It is a proportion, an element or a part of the population which is scientifically and randomly drawn that actually possesses the same characteristics as the population. This implies that every person has an equal opportunity to be selected for your sample o An element is considered as a member of a population. It is a unit in which data is collected and analyzed o Population pertains to total number of elements to be studied. It includes all members of a defined group that we are studying or collecting information on the data driven decisions. o Parameter is the summary description of a given variable in a population. The mean income, the mean age of all the families are parameters. The age distribution of all people is a parameter. o Sample size is the number of subjects in your study. o Margin of Error is the allowable error in percent due to the use of the sample, instead of the population o Sampling Error is the error attributed to chance difference between a random sample and the chosen population. It does not result from measurement or computation errors but contributory to inaccuracy of data. Sample vs Population As follows are some reasons why researchers use a sample rather than the entire population in the conduct of their study. 1. Sometimes population is difficult to identify who makes up the entire population.
- 2. Chapter 9 59 Sampling 2. Sample is cheaper, faster, more accurate and can yield to more comprehensive information. 3. Getting the population is too costly in terms of human resources and other expenses, and time consuming. 4. In population, there is a lot of error to control and monitor. 5. Sometimes lists are rarely up to date. 9.2 Good and Defective Sampling Keys to Good Sampling formulate the aims of the study decide what analysis is required to satisfy this aims decide what data are required to facilitate the analysis collect the data required by the study Defective Sampling 1. Sampling that is too small or not a representative will be biased, invalid and unreliable. 2. The sampling becomes very complicate if the population is too large or has many sections and subsection. 3. The sample (respondents) should have common characteristics in order to eradicate faulty conclusions. 4. The sampling becomes biased and unrepresentative if the researcher does not possess the necessary skills and technical know-how of the sampling procedure. 9.3. The Sample Size One of the most frequent problems in statistical analysis is the determination of the appropriate sample size. One may ask why sample size is so important. The answer to this is that an appropriate sample size is required for validity. If the sample sizes are too small, it will not yield valid results. An appropriate sample size can produce accuracy of results. Moreover, the results from the small sample size will be questionable. A sample size that is too large will result in wasting money and time. It is also unethical to choose too large a sample size. There is no certain rule of thumb to determine the sample size. Some researchers do, however, support a rule of thumb when using the sample size. For example, in regression analysis, many researchers say that there should be at least 10 observations per variable. If we are using three independent variables, then a clear rule would be to have a minimum sample size of 30. Some researchers follow a statistical formula to calculate the sample size. Size of sample depends on some factors: 1. Degree of accuracy required 2. Amount of variability inherent in the population from which the sample was taken 3. Nature and complexity of the characteristics of the population under consideration Determine sample size Slovin Formula: Where: n = sample size N = population size e = desired margin of error
- 3. Chapter 9 60 Sampling Example1: What should be the representative sample size if the population from which the sample will be taken is 10,000 and the desired margin of error is 2%? Solution: To determine the sample size, use the formula; The sample size is 2,000 This formula in finding the sample size cannot be used when the normal approximation of the population is poor or small. Example 2: The population of Barangay Dodong is 10,600. What would be your representative sample size of Brgy. Sebuas if the population is 10,600 and the desired margin of error is 5%? 9.4 Types of Sampling Techniques 1. Non-probability Sampling (Non-scientific). This type of sampling does not provide every member of the population an equal chance of being selected as part of the sample. Additionally, the data gatherers choose sample cases as they WISH. These have 3 kinds: a. Purposive sampling is used when the researcher selected samples which are according to the purposes of the researcher. b. Quota sampling is used if a stratum is small in the population but important to the research questions being presented. This is done by merely looking for individuals with requisite characteristics. c. Convenience sampling, exactly what the name suggests, are oftentimes what we have to use because of reality. We cannot draw a sample, but we have a group that is accessible, is representative of our target population and just available to us. Instead of becoming purists and throwing out the chance for collecting data for decisions, use what you have with the honest acknowledgement that there are limitations. 2. Probability Sampling (Scientific sampling). In this type of sampling, the researcher follows a procedure that assures that all elements in the population are given equal chance of being selected as a sample unit. There are 6 types: a. Simple random sampling may be done by drawing of lots or with the use of a table of random digits. This gives all elements as equal chance of being selected as a sample. Steps in Simple Random Sampling 1. Determine the population of the study 2. Determine the desired sample size ( You can use Pagoso formula, Gay’s formula or other formulae in determining sample size) 3. List down the respondents (population) of the study in a sheet of paper. 4. Write in a small sheets of paper, names of the respondents or codes, roll these pieces of papers and place them in a box big enough to accommodate them. Shake thoroughly the box
- 4. Chapter 9 61 Sampling 5. Draw the sample one at a time after shaking the box until the desired sample size is drawn. The names are drawn include in the sample. b. Systematic sampling is an often-used sampling strategy and cost effective. Again, you must have a population sampling frame list that is in random order and non-overlapping. Determine both the size of the population and the size of the sample you want to work with. Then, divide the sample size (n) into the population (N) size to get your key number, symbolized as “k”(sampling interval) a method of selecting a sample by taking the kth (sampling interval) units from an ordered (alphabetical /chronological) population. The formula applied is : K=N/n (where: K is desired interval, N population and n is the sample size) Steps in Simple Random Sampling 1. Identify the population of the study 2. Determine the desired sample size, then, apply the formula above. For example. Is you have a population of 800 and your desired sample size is 10%, then you will have a sample of 80. Applying the formula above 800/80=10), the sampling interval is 10 3. Hence, every 10th in the list (or arrangement of households as the case may be) is taken as a member of the sample 4. Close your eyes and run your finger down the list and then stop. The number, which the finger points to at, is the random start number. 5. From the random start number, pick every 10 th in the list (or arrangement of the households) until the desired sample size of 80 is obtained. c. Stratified random sampling is used when the population is heterogeneous and it is important to represent the different strata or sub-populations. There is a proportional representation of strata in the sample - proportional to the population strata. We divide the entire population into strata (groups) to obtain groups of people that are more or less equal in some respect. Steps in Simple Random Sampling 1. Determine the stratum or class to which all elements in the population belong. 2. Group the elements of the population according to the characteristics inherent in the whole class or stratum 3. Apply either the pure random sampling method or systematic sampling in the actual selection of the sample. Do this for every class or stratum. Note: The same sample size should be proportional or the same percent is applied for each class or stratum. For example: Types of Farmers Population Fraction Sample size Rice farmers 30 30/75 x 30 12 Sugar farmers 20 20/75 x 30 8 Vegetable farmers 10 10/75 x 30 4 Cutflower producers 15 15/75 x 30 6 TOTAL 75 30 d. Cluster Sampling – selecting a clusters of elements or blocks where each consists of heterogeneous elements (Calderon et al, 1993). Steps in Cluster Sampling 1. Make a listing of sampling unit, the primary sampling units ( the first clusters to be sampled), the secondary sampling unit within the primary sampling, etc.
- 5. Chapter 9 62 Sampling Suppose the provinces are the primary sampling units, the towns are the secondary sampling units and the barangay are the final sampling units. These are called natural clusters 2. Since the sample is 20%, 20% of 9 provinces equals to 1.8 or 2 provinces. Select these two ( 20 provinces either by pure or systematic random sampling) 3. Within each of these two provinces, select 20% of the towns either by pure random or systematic random sampling method. 4. Within each town selected, choose 20% of the barangays. Since there are only one elementary school in one barrio or barangay, this is the final sampling unit. The respondents may be stratified into teachers, parents and pupils. The respondents have to be taken from these stratified groups either pure random or systematic random sampling. Example: Desired sample : 50 Population : 100 with 10 clusters Step1 . Number 10 clusters 1-10 Step2. Use simple random sampling . Step3. Identify the groups represented by the numbers drawn e. Multi-stage Sampling – selection of sample is accomplished in two or more stages. Example: Desired sample : 50 Population : all men with 0-6 yrs old children in province Stage1 . Draw sample towns in the province. List all the names in the province and use random sampling to draw the three sample towns. Stage2. Draw sample barangays in the sample towns. Secure a list of all barangays in each of the sample towns and using simple random sampling, draw 3 sample barangays in each of the three sample towns. Stage3. Draw a sample of married men in the sample barangays.List their names per sample barangays from the 3sample towns then use random sampling to select the men with 0-6 yrs old children. Guidelines with regards to the minimum number of items needed for a representative sample (Gay,1976): Descriptive studies – a minimum number of 100, 10 percent of the population. for smaller population, a minimum of 20% may be required Co-relational studies – a sample of at least 50 is deemed necessary to establish the existence of a relationship Ex post facto research of causal comparative studies-15 subjects or groups can be defended if they are very tightly controlled Experimental studies – minimum of 30 per group or 15 subjects per group Sometimes experimental studies with only 15 items in each group can be defended if they are very tightly controlled If the sample is randomly selected and is sufficiently large, an accurate view of the population can be had, provided that no bias enters the selection process
- 6. Chapter 9 63 Sampling THE RESEARCH SAMPLING NAME: __________________________________________ SCORE: ___________________ YEAR & SECTION: _________________________________ DATE: _____________________ Instructions: Restate your research problem, research objectives and identify your population. Determine the most appropriate sampling technique that you will use then solve for your sample size. Research Title: _____________________________________________________ _____________________________________________________ The Sampling Technique that I will use is: ____________________________ because__________________________________________________________ _________________________________________________________________ _________________________________________________________________ _______________ To compute for the sample size, I will use _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________