FCS 681 Research Methods
Exercise #3: Sampling
1. A researcher plans a study of housing quality of low-income households in Y County, CA.
He needs a sample of 500 households to accomplish his purpose. He ascertains from the Y county Housing Authority that there are 5,000 households living in public housing (requiring low income for eligibility) in the county. He obtains a list of these households’ names and addresses, numbers them from 1 to 5,000, and chooses 500 of these households using a computer-generated list of random numbers. He tries to collect data from these 500 households via a mailed questionnaire. Comment by Yali Yang: Population, your answer is not specific -2
a. To what population does this researcher wish to generalize?
The researcher wants to use a population of 500 households to infer a population of 5, 000 in his research study.
b. What is the sampling frame in this study?
The sampling frame used in the study is 500 households living in public housing to accomplish the research study of the general population.
c. What type of sampling does this researcher do (be precise)?
The researcher uses Simple Random Sampling.
d. Describe the chance that each household in the sampling frame has of ending up in the sample.
Each household has an equal chance of being selected into the sample since the computer generated alistthat provides a random number between 1 and 5,000households. The researcher assigns each member of apopulation a unique number when numbering them from 1 to 5000 then selects500 via theuse of random numbers computer-generated list thus actual sample of memberschosenin a sufficient number.
e. How well does this sampling frame reflect his stated population? Why?
The sampling frame does not quantify the actual population since he starts by having the selected sample before knowing the general population. Therefore, he incorporates biases in the research by stating the sampling frame early in advance.
f. What could he do if he wanted to improve the external validity of the research?
To improve the validity, he could have used a consistentStratified sampling method so that errors of the actual analysis to decline. Therefore, through theutilization of the method it will decrease the failure of the research and promote high external validity.
2. A researcher wants to study L.A. public university seniors
’ career choices and plans to collect data from CSUN, UCLA, and CSULA. The researcher receives permission to use the registration records on the three campuses. CSUN has 8,000 seniors, UCLA has 10,000 seniors, and CSULA has 5,000 seniors. He needs 500 seniors in his study, so on each campus’s list, he randomly picks a name to start with and then selects each rthsenior on the list until he has 500 seniors drawn. Comment by Yali Yang: Population, not just 23000 in 3 campus -2
a. What is the theoretical population to which the researcher wishes to generalize?
The theoretical population is 23,000 seniors in the three campuses, but the researcher wants to use 500 seniors in generalizing the theoretical population. Comment by Yali Yang: This is the answer to question b. -4
b. What is the accessible population in this study?
Thepopulation that is accessible is 5,000 since its easy when selecting the seniors for the research study. The less the population, the lower the cost, less time used to perform the sample selection.c. What type of sampling plan does this study utilize (be precise)?
The study uses the Systematic Random Sampling method. It is because it computes the sampling interval of the population, and then randomly select a start in which it ends up in choosingrth senior until the 500 seniors are drawnfrom the list.
d. What is the value of r in that the researcher should use (show your work)?
The value of r is given as follows: r=N/n, where N= number in population
n = number needed in sample rounded up to an integer.
r = 23,000/500
r = 46
e. What is the number of seniors that will be obtained from each campus?
The total number needed from the three campuses is 500; therefore, 500 divided amongst the three will be approximately 167 seniors from each of them. Comment by Yali Yang: Calculate the number from each of the three campus. -2
f. Describe the chance that each senior has of ending up in this sample.
The chance of each senior ending up in the sample depends on the population of a campus.The lower the population a campus has, the higher the chance,and the larger the population a campus has, the lower the chance a senior will have in getting into the sample of the study.
g. What is the advantage of this sampling plan over a simple random sampling plan?
The sampling method is very simpler and quicker than simple random sampling. Also, it is easy to analyze data and figure out error from the study. Finally it provides maximum external validity, assuming no ordering in the list or files of names.
h. What must this researcher ascertain
before he can be reasonably confident that using this sampling plan will produce a representative sample? Comment by Yali Yang: Avoid periodic problem. -2
The researcher must learn how to use probability sampling technique so that each value fraction of the sampleselected without biases. It will reducefailure of sampling plan that advocate in the research study.
3. A researcher wishes to investigate health conditions of the elderly (aged 65+) householders in Z County, CA
. Previous research suggests that elders’ place of residence (metro (a.k.a. urban) versus non-metro (rural)) is an important variable affecting their health conditions. So, in 2008 from a county map, she randomly selects census tracts[footnoteRef:2], of which the county has 155 (100 metro and 55 non-metro as defined in the U.S. Census Bureau 2000 census). She selects 10% of the “metro” tracts and 10% of the “non-metro” tracts. Data collectors are sent to each selected tract and instructed to interview each eligible householder within each tract until they all have been interviewed. Comment by Yali Yang: Population, -4 [2: ]
a. What is the theoretical population to which this researcher wishes to generalize?
The researcher wants to generalize the research through the use of randomly selected Census tracts of the county having 155, 100 members from urban and 55 from rural areas. Comment by Yali Yang: This is the answer to question b. -4
b. What is the sampling frame in this study?
The sampling frame used is the 10% of the urbancensus tracts1 and the 10% of the rural tracts areas.It will cater the list of people forming the theoretical population of the research
c. What type of sampling plan does this researcher utilize (be precise)?
The researcher employs the Systematic Random Sampling where the sampling frameused does not vary but follows the actual step by random step selection. Therefore, it uses 10% that is the constant rate of selecting the population sample into actual sample Comment by Yali Yang: Cluster random sampling -4
d. Describe the chance each elderly householder in this county has of ending up in the sample.
The chance of each elder has been equal since eachdefined population has an equal chance of selection from the sampling frame into the actual sample.The county provided the elders from the urban and the rural possible number, that is, 100 and 55 respectively thus by use of 10% each of the areas shows that each elder has a high and equal chance of being selected to the sample.
e. In your opinion, are there any problem(s) of the sampling plan?
I think there are no issues in the sampling plan since utilization of each sampling frame is made into consideration for the research to be successful. Each sample is examined on 10% out of the total sampling frame.
4. Researchers wanted a sample of a state’s population of two-parent families with exactly two children under 18 years old. An important variable in their study was age of the younger child in the family. The state has 100 counties; they randomly selected 5 of these from the list of the state’s counties. They conducted a school census in these 5 counties, in which they measured the number of parents in each child’s home, the number of children, and the ages of the children in the family. They retained only those children who had exactly two parents and one sibling. They divided families into groups that had younger children of five different ages: under 1, one year old, 2-5 years old, 5-11 years old, and 12-17 years old. Each of these lists had a different number of families. They randomly selected 42 of the families on each list (for a total sample of 210 families).
a. What was the theoretical population to which the researchers wanted to generalize?
The theoretical population that the researcher intends to generalize to is the state’s population with the two-parent families with exactly two children under 18 years old.
b. What were the sampling frames
in this study? Comment by Yali Yang: There are 2 stages, so 2 sampling frames. 1st stage, 2nd stage
The sampling frames of study are the randomly selected fivecounties from the list of 100 counties in the state. Comment by Yali Yang: This is the sampling frame for the 1st stage, what about 2nd stage? -2
c. What type of sampling did they use (describe it as completely as possible)?
They used multistage random sampling. First they chose the state in which they would conduct the research then they list the counties found in the state which are 100 in total. Secondly, they decide to perform random selection in which they chose the five counties as the sampling frames of study.Third, they conduct the census tomeasure the number of parents in each child’s home. Finally, they divide the families by the random selected 42 households in a total of 210 families. Comment by Yali Yang: Multi-stage stratified random sampling, -2
d. What is the age of the younger child
variable called? Comment by Yali Yang: Used to divide sampling frame into groups/stratum, it is called stratification variable -2
It’s called the actual sample because they are the subject that completesthe study and their data is used in data analysis by the researchers.
e. Why do you think these researchers did not plan a simple random sampling plan?
It is because the research study was difficult-to-enumerate populations when using the simple random sampling plan. Therefore, they advocated for Multi-stage random sampling plan thathad fewer errors as compared to the simple random sampling.
5. A team of researcher wants to analyze the incidence of unresolvable car repair complaints among California consumers in the past 12 months. They contact the California Department of Consumer Affairs and obtain a list of the problems that CA consumers complained to their office about in the past 12 months. They divide the complaints into those that relate to automobile repairs and all others. Then they use the automobile repair complaints as their sample.
a. What type of sampling do these researchers use?
Researchers used Purposive Sampling because they want to analyze the incidence of the unresolvable car repair complaintsfrom California consumers.They selected the subject for their research to make ajudgment after their analysis.
b. Evaluate the external validity of this sampling plan, given the researchers’ purpose.
The Purposive sampling subject itself to only California consumers and not any other town or city thus its external validity is not catering for thewhole population size of the state and also does not represents the others cities in the actual reality. Therefore, has Low external validity.
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