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.
a. To what population does this researcher wish to generalize?
The 5,000 households of the low-income households in Y County, CA.
b. What is the sampling frame in this study?
5000 households living in public housing.
c. What type of sampling does this researcher do (be precise)?
Simple random sampling,
d. Describe the chance that each household in the sampling frame has of ending up in the sample.
They are independent and have an equal chance to be selected for the sample.
e. How well does this sampling frame reflect his stated population? Why?
The sampling frame does not represent the general population very well because not every person in the population lives in public housing. The sampling frame does not include other low income families, or other income levels, who do not live in public housing.
f. What could he do if he wanted to improve the external validity of the research?
He could include families with different income levels, and sample from different groups of populations- not only those living in public housing. An increase in sample size will not help since it’s still only representing the families living in public housing. He could change the sampling frame from public housing to low income, or obtain a list of low income households and do simple random sampling. He may also gather a general list from public housing, and use stratified sampling to apply to different income levels.
The researcher could ensure the dropout rate of his questionnaire is as low as possible and responders answer back at a high degree. Additionally, the researcher could do questionnaires at different times to lower variability to the answers.
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’ list, he randomly picks a name to start with and then selects each rth senior on the list until he has 500 seniors drawn.
a. What is the theoretical population to which the researcher wishes to generalize?
L.A. public university seniors.
b. What is the accessible population in this study?
500 seniors from 3 different colleges in L.A.
c. What type of sampling plan does this study utilize (be precise)?
Systematic Random Sampling. The researcher selects from a total of 23,000 LA public university’s senior population. He starts at some predetermined point in the list and chooses every Tth senior to be a participant in his study.
d. What is the value of r in that the researcher should use (show your work)?
r= N/n
500 seniors to be chosen, 23,000 seniors altogether from the schools.
23,000/500 = 46 is the rth
e. What is the number of seniors that will be obtained from each campus?
(CSUN: 8,000/46=173 seniors)
CSUN-173; UCLA-217; CSULA- 109
f. Describe the chance that each senior has of ending up in this sample.
Number of seniors that will be obtained from each campus/ divided by the number of seniors of that campus
Each senior has an equal chance. However, they are dependent on each other, since the researcher selects every 46th seniors.
g. What is the advantage of this sampling plan over a simple random sampling plan? Systematic random sampling is very simple and less time consuming than simple random sampling and there is no need for a numbered list with systematic random sampling.
h. What must this researcher ascertain before he can be reasonably confident that using this sampling plan will produce a representative sample?
· He should utilize a mixture of majors in order to avoid an order which is related to the specific major. If the order of sampling is related to specific majors, students who study other majors will be left out.
· Ensure that the seniors selected come from a mixed variety of majors/departments
· Ensure an equal percentage of students is chosen from each school.
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[1], 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.
a. What is the theoretical population to which this researcher wishes to generalize?
Theoretical population refers to the entire group of individuals to which researchers are interested in generalizing the conclusions. In this case, the study wishes to generalize health conditions of the elderly (aged 65+) householders in metro and non-metro areas of the Z County, CA.
b. What is the sampling frame in this study?
The sampling frame is census tracts from U.S. Census Bureau 2000.
c. What type of sampling plan does this researcher utilize (be precise)?
The researcher is using simple random cluster sampling (randomly selecting from census tract.) The researcher selects 10% of the “metro” tracts and 10% of the non-metro tracts.
d. Describe the chance each elderly householder in this county has of ending up in the sample.
· Each elderly householder is Independent, and they have an equal chance of being selected.
· The researcher is selecting 10% of metro and non-metro elders.
· 100 metro elders x 0.10 = 10 metro elders will be selected as a sample.
· Thus, this group of elders have a 1 in 10 chance of ending up in the sample.
· 55 non-metro elders x 0.10 = 5.5 non-metro elders will be selected as a sample.
· Thus, this group of elders have approximately 1 in 5 chance of ending up in the sample.
e. In your opinion, are there any problem(s) of the sampling plan?
When the researcher is utilizing the data, he or she should use the most recent set of data as participants may have been reclassified or changed their geographical location during that 8 year time gap. Furthermore, some participants may have moved without notice and are unable to respond.
This sampling plan is not immune from the problem of non-response 1. This is a phenomenon that the required information is not obtained from the persons selected in the sample. One effect of non-response is that it reduces the sample size. This does not lead to inaccurate conclusions, but due to the smaller sample size, the precision of estimators could be affected.
A more serious effect of non-response is that it can be selective. This occurs, if due to non-response, specific groups are under or overrepresented in the survey. If these groups were to behave differently, with respect to the survey variables, it may cause the result to be biased.
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 researcher would like to generalize two-parent families with emphasis of 2 children under age of 18.
b. What were the sampling frames in this study?
· 2 stages with 2 different sampling frames:
· 1st stage:
· The list of 100 counties, then randomly select 5 of the counties.
· 2nd stage:
· Obtained the list of all the 2 parent families with 2 children under 18 years, then subjects are randomly selected from that list of families.
c. What type of sampling did they use (describe it as completely as possible)?
Multistage stratified random sampling, they may also have used different stratum by age.
The researcher randomly selected 5 counties out of 100 (defining the cluster). Next they grouped the clusters into strata of clusters, putting similar clusters together in a stratum. Then they randomly pick one or more cluster(s) from each of the strata of clusters. Lastly, they sample the subjects within the sampled clusters (either all the subjects, or a simple random sample of them.)
d. What is the age of the younger child variable called?
Stratum/stratification variables.
e. Why do you think these researchers did not plan a simple random sampling plan?
A random sampling plan cannot guarantee that all necessary subjects will be selected. This plan requires the list for the whole county, which might guarantee that you are selecting samples from all the age groups, not just one of them.
Also, a simple random sampling plan will produce a larger sampling error. The researcher will have to complete the population list. Sampling might not representative of the whole population.
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?
Judgement/ Purposive sampling.
b. Evaluate the external validity of this sampling plan, given the researcher's’ purpose.
There are some problems with the external validity in this sampling plan:
1. This method can easily include researcher bias and the variability and bias of the estimates cannot be measured.
2. This plan only includes the consumers that are motivated to participate in the study. This group may be quite different from all the overall group California consumers with unresolvable car repair complaints.
3. This method requires assumptions about the population, which may or may not be true.
4. This method violates assumptions about statistical techniques.
All of the above problems might cause the samples not being a good representation for generalization.
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