Week 4
Running head: SAMPLE DESIGN 1
SAMPLE DESIGN 10
Thanks for the submission of the assignment.
While there are a number of margin comments in each part of the assignment, here are some general comments.
First, you need to meet the basic requirements of the assignment such as using a minimum of 5 scholarly sources and adhering to APA formatting. Remember that a scholarly source is only a journal article that has undergone the rigors of peer review. I am also concerned that there is little evidence that you are completing the required reading in the text. Please understand that this was selected by the faculty due to both its content and level. The assignments are directly tied to this reading. You also need to eliminate the extra spaces in the document. APA requires that the entire document be double-spaced with no additional spaces between sections or paragraphs. This also has an impact on the length the paper. I reformatted the first part of the assignment to illustrate.
In part one you are required to describe the steps you would go through to draw a particular sample. It is not necessary to describe steps for information that is given to you such as the sample size. Remember that your scholarly writing needs to be concise and to the point. You don’t want to include information that is not essential or that is repetitious.
You also were required to provide a critical analysis of the procedure used in the given situation. For instance, stratified sampling results in a more precise estimate if the stratification variable is related to the variable that is being measured. In this case, if occupation were related to the variable you are measuring, you would be creating strata that are homogenous within. If that is the case, you would obtain a more precise estimate since only within strata variability is taken into account in the calculation of the standard error of the estimate. The between strata variability is not taken into account. If, on the other hand, occupation was not related to what is being measured, dividing the population would not be creating more homogenous groups so there would be no impact on the precision of the estimate. While that is not necessarily a problem, you have incurred additional cost of dividing the population into strata for no reason.
The next assignment involves measurement and, like this one, has multiple parts. Measurement is a critical topic in any quantitative study. It is the assigning of numbers to represents attributes of objects. You don’t measure a person but a person’s height, weight, attitude, perceptions, etc. Many attributes that are measured in research, including business and related functional areas, are abstract. In order to measure an attribute, you first have to define it. As you will read, there are two types of definitions, a conceptual definition and operational definition. The conceptual definition is what you would find in a dictionary that often defines a concept in terms of other concepts. For instance, intelligence may be defined as the ability to think abstractly. What is abstract thinking? Another abstract concept.
In addition to defining a construct conceptually, it needs to be defined operationally. The operational definition specifies the operations needed to measure the concept. In the case of intelligence, it may be defined as a person score on a particular IQ test. The measurement of a person’s intelligence would be their score on an IQ test.
As you read about measurement and the requirements of the assignment, please let me know if you have any questions. I’d be happy to clarify.
Dr. P
Dr. Susan M. Petroshius 80 6/2/2020
Evaluating Sampling Method and Sample Size
Evaluating Sampling Method and Sample Size
Part 1: Drawing a Sample
According to Tillé and Wilhelm (2017), designing a sample is a crucial exercise that plays a huge part in a study because it determines the accuracy of the insights drawn at the tail end. While a good sample is representative, accurate, and is adequate in size, it should also allow the researcher to carry out the study to the fullest without running into cost constraints. As such, one should follow certain steps when drawing the sample. This section illustrates the sample design process using the following three scenarios. Comment by Susan Petroshius: It is not clear where these steps are coming from. For instance, you need to define the target population and then the sampling frame. These are noted in the stages outlined in Exhibit 16.1 in the text. This is required reading for a reason.
a. A stratified sample of 75 doctors, 75 lawyers and 75 engineers who belong to a professional organization in that you belong to.
Probability sampling techniques leverage random approach to increase the chances of obtaining the most accurate representation of the population. Stratified random sampling is one such technique, which is an approach that focuses on a particular group within the target population (Boschetti, Stehman & Roy, 2016). The scenario in this case is focusing on three strata, a group of doctors, a group of lawyers, and a group of engineers. Comment by Susan Petroshius: Source? Comment by Susan Petroshius: This is not true as shown in this example where there are three groups.
Ideally, stratified sampling should mitigate human bias during the process of designing a sample. To this end, the following steps are recommended for selecting the sample. Comment by Susan Petroshius: Source? The preliminary information on the procedure is not necessary. You are being asked to explain the steps you would go through to draw the sample and then provide a critical analysis. Remember that you want your scholarly writing to be both precise and concise.
Step 1: define the population
The target population is a professional organization, which means it includes people from all professions. However, our interest is in just three groups that is lawyers, doctors, and engineers. Nevertheless, the professional group is our N . Comment by Susan Petroshius: The population is not the organization but member of the organization. In this case, the population is not all of those in the organization but only those who are in one of the three professions. Comment by Susan Petroshius: This population is only those in the three professions. Comment by Susan Petroshius: This is the size of the population, not a description of.
Step 2: Choose the relevant stratification
The second step entails stratification of the population into relevant strata. Since we are interested in lawyers, doctors, and engineers, this step will involve stratification of the professional organization into lawyers, doctors, and engineers. Comment by Susan Petroshius: There is no “we.” See: https://apastyle.apa.org/style-grammar-guidelines/grammar/first-person-pronounsIt is only appropriate to use “we” if you are actually writing with another person. Comment by Susan Petroshius: What is the stratification variable?
Step 3: list the population
This is the population of the entire professional organization, that is lawyers, doctors, engineers, accountants, financial analysts and so on. Comment by Susan Petroshius: This is not the case as previously noted.
Step 4: list the population as per the relevant stratification
This step involves listing the population from which the sample will be drawn. For example, if the professional group consists 100,000 members, we will need to alienate the number of doctors, lawyers, and engineers. The sample of 75 for each strata will then be drawn from the alienated population. Here, one should list the population of doctors, the population of engineers, and the population of lawyers. Comment by Susan Petroshius: What is this called? This is the sampling frame. Comment by Susan Petroshius: This is not the appropriate term. You need the sampling frame of the population which is all of the doctors, lawyers and engineers in the organization.
Step 5: choose the sample size Comment by Susan Petroshius: It is not necessary to include steps that are part of the problem that is given. You don’t have to decide on the sample size or the stratification variable, for instance. These are given to you.
The sample size, n, is the 75 doctors, 75 lawyers, and 75 engineers. In total, therefore, the sample size is 225 professionals from the professional organization. Comment by Susan Petroshius: You never describe how the sample is drawn. What is the procedure?
b. A simple random sample of 150 subscribers to your local newspaper.
Unlike stratified random sampling, simple random ensures that each unit from a population has an equal chance of appearing in the sample. Here, the researcher considers the whole of the target population (Etikan & Bala, 2017). In the case at hand, the target population is all the subscribers to the local newspaper. A simple random sample is the easiest approach to designing a sample for a study. The following steps should guide the selection of the sample. Comment by Susan Petroshius: According to who? Is this is the case, why is it not used more often?
Step 1: Define the population
Population entails all the units in a population under study. In the case at hand, the population under study is the subscribers to the local newspaper. If the number is 1,000, then this is the size of our target population, N.
Step 2: choose the sample size Comment by Susan Petroshius: This is not necessary. You have been given the sample size.
Choosing the sample size is easy, especially with a sample size calculator. In the case at hand, the chosen sample size is 150 subscribers, which is our n. Best practices hold that one should choose a sample size that is manageable subject to the proviso that it is within the time and budget limit, according to Etikan and Bala (2017).
Step 3: list the population Comment by Susan Petroshius: What is this list called?
The 150 sample has to come from the entire population of the local newspaper’s subscribers. If the number of the subscribers is 1,000, then this is the population, N, from which the sample, n, should be drawn.
Step 4: assign numbers to each subscriber.
According to Alvi (2016), simple random sampling is effective in the manner in which it equalizes the probability of a unit in a population being picked to appear in the sample. Here, one can assign each unit in the population a unique number such as 1, 2, 3 … One should assign consecutive numbers from 1 to the Nth unit of the population. In the case at hand, the assignment of numbers to the subscribers will range from 1 to 1,000, where the Nth subscriber’s number is 1,000. Comment by Susan Petroshius: Why?
Step 5: find random numbers
Randomly select 150 numbers from the population. If the population is so large that a manualized random selection is difficult, then one can use a computer program that automates the exercise. Comment by Susan Petroshius: How? This needs to be explained.
Step 6: Select the sample
The subscribers that will make it to the 150-size sample will be the ones whose assigned numbers were picked in the preceding step. If the numbers 007, 028, 198, and 763 were selected, then it means that the subscriber number seven, subscriber number twenty-eight, subscriber number 198, and subscriber number 763 will be part of the sample. Comment by Susan Petroshius: Good.
c. A systematic sample of 250 from a subscriber list of a trade publication.
Systematic random sampling is more like a variant of the simple random sampling method. Rather than selecting samples randomly from the population, this approach first arranges the units in a population in order and then picking participants in the established order (Sharma, 2017). The following are the recommended steps for drawing the sample in the case at hand. Comment by Susan Petroshius: Source? Comment by Susan Petroshius: How is this ordered? By what? What if there is periodicity in the sampling frame?
Step 1: define the population
This is the entire population in which we have interest. In the case at hand, we have interest in the entire subscriber list of the trade publication. If the trade publication states its subscriber list is 10,000, then we will work with this population i.e. N.
Step 2: choose the sample size
In the case at hand, the chosen sample size is 250 subscribers i.e. n.
Step 3: List the population
Here, one should identify the number of units in the target population. In our case, let us assume that the number of subscribers is 10,000.
Step 4: Assign each subscriber a number
We assign every single subscriber a unique number such as integers 1, 2, 3. These numbers will run from 1 to the Nth subscriber i.e. 10,000. Comment by Susan Petroshius:
Step 5: Compute the sampling fraction
The sampling fraction is the dividend of the sample, n, and the population, N. Assuming that the population size is 10,000 and the sample is as given, 250, then the sampling fraction will be:
From the foregoing, we will select one subscriber in every 40 subscribers drawn from the population of 10,000 subscribers. Therefore, we have to repeat the selection process for 250 times to create our sample.
Step 6: Select the first unit
We need to select just one subscriber from the first group of 40. In this case, we will employ the system used in simple random sampling. One can use a random number table or if the group is large, then one can use a computer program. Assuming the computer program picks number 27, the first subscriber will be the 27th subscriber in the first group of 40.
Step 7: Select the sample
Having selected the first subscriber, we will use the same number to select the rest of the 250 subscribers. One will pick the 27th subscriber in each group of 40 subscribers until the 10,000 number is exhausted.
Part 2
a. When given the factors, the sample size outputted is 614. Other outputs are:
Critical t = 1.6473472
Non-centrality parameter δ = 2.4903856
Degrees of freedom = 612
Actual power = 0.8003237
Finally, the distributions plot appears as shown below:
Assuming that the result is a sample size beyond what we can obtain, we can use the compromise function to compute alpha and beta for a sample half the size of the result (614), which is 307. The resulting alpha is 0.0865281 and the resulting beta is 0.3461124. Comment by Susan Petroshius: This is not correct, but I cannot see what you have done wrong since you do not present the results. The sample size is 620 as shown on the table at the end of the paper.
The study should be conducted with a larger sample size. This is because the smaller sample size produces larger error probabilities of alpha and beta. With the sample size as 614, the alpha is 0.05 and the beta is 0.2. Reducing the sample size by half, as we have seen already, increases the probability of errors. Besides, the actual power when the sample size is 614 is 0.8003237. Comparatively, the actual power when the sample size is 307 is lower at 0.6538876, which is far lower. The possible tradeoff that may make the smaller sample size feasible is to increase the effect size from small (0.10) to medium (0.30). This will greatly reduce the alpha to 0.001521626 and the beta to 0.006086506. Comment by Susan Petroshius: As stated in the problem, this is not an option. The sample size is beyond what can be obtained. Comment by Susan Petroshius: This would be an appropriate tradeoff. If you conducted this analysis, you would see that there are drastic improvements making the study worth doing.
b. The sample size needed when given the factors is 969. Other outputs are: Comment by Susan Petroshius: This is correct.
Non-centrality parameter λ = 9.6900000
Critical F = 3.0050418
Numerator df = 2
Denominator df = 966
Actual power = 0.8011010
Finally, the distributions plot appears as shown below:
Using the compromise function, the new alpha is 0.0975735 and the new beta is 0.3902942. Further, the selected beta/alpha ratio is 4. This is because such a value reduces the probability of committing Type II error. The study is worth doing with a smaller sample because the probability of Type I and Type II errors are still low. In addition, the power is 0.6097058, which is closer to the ideal value of 0.8011010. Comment by Susan Petroshius: This is not acceptable. The minimum acceptable level is .80, not .60. Therefore, the study cannot be done with the smaller sample size unless a tradeoff is made with respect to effect size.
Part 3
The most appropriate sampling method for the intended research is simple random sampling. This is because it is the simplest yet the most likely to yield an accurate and more representative sample. The intended population is the customers that eat at a major fast food restaurant in a period of one month, approximately 10,000 customers. Comment by Susan Petroshius: This is not necessarily true. For instance, you can generate a more precise estimate with stratified sampling.
Procedure for drawing the actual sample
The first step is to define the population, which is the customers who eat at a fast food restaurant in a period of one month. This population is estimated to be about 10,000 people. Secondly, the Survey Monkey sample size calculator will be used to determine the size of the sample of the intended research. With a 95% confidence level and a 5% margin of error, the result outputted by the sample size calculator is 370. Comment by Susan Petroshius: The major problem that you have is that you cannot generate a sampling frame. You would need to have a list of all the population elements in order to draw the sample. That is not possible in this situation.
Thirdly, each customer will be assigned a number such that there are 10,000 numbers. Fourth, using random number tables and/or a computer program, random numbers will be selected. The selected random numbers will determine the customers that will be part of the 370 sample.
References
Alvi, M. (2016). A manual for selecting sampling techniques in research.
Boschetti, L., Stehman, S. V., & Roy, D. P. (2016). A stratified random sampling design in space and time for regional to global scale burned area product validation. Remote Sensing of Environment, 186, 465-478. doi:10.1016/j.rse.2016.09.016
Etikan, I., & Bala, K. (2017). Sampling and sampling methods. Biometrics & Biostatistics International Journal, 5(6), 00149.
Sharma, G. (2017). Pros and cons of different sampling techniques. International journal of applied research, 3(7), 749-752.
Tillé, Y., & Wilhelm, M. (2017). Probability Sampling Designs: Principles for Choice of Design and Balancing. Statistical Science, 32(2), 176-189. doi:10.1214/16-sts606
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critical t = 1.64735
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critical F = 3.00504
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