Sampling Methods Topic 4

Best Sampling Methods Simple Random Sample (SRS) Involves selecting individuals at random from the population without replacement Every member of the population has an equal chance of being included in the sample. A sample of size n is to be chosen from the population where every conceivable group of people of the required size has the same chance of being the selected sample. You need a list of the units in the population (sampling frame) and a source of random number (calculator, die, table of random digits, coin).

Best Sampling Methods Multi-Stage Sample Example: Take a random sample of the counties in the US. From the selected counties, take a random sample of the towns. From the selected towns, take a random sample of the neighborhoods in those towns. From the selected neighborhoods, take a random sample of the households.

Good (But Not As Good) Sampling Methods Random Digit Dialing Start by making a list of all possible phone exchanges (area code and next 3 digits). Find proportion of all households that have each exchange. Generate a sample that has approximately those same proportions by randomly generating the last 4 digits of the phone number. Example: National polls by phone

Good (But Not As Good) Sampling Methods Stratified Random Sampling Divide the population into groups Groups do NOT have to be of equal size Groups MUST share some common characteristic Take an SRS from WITHIN EACH group to achieve the desired overall sample size. Example: Survey students from SHS but first divide them into freshmen, sophomores, juniors, and seniors. Then, take an SRS from each class.

Stratified Random Sample 500 Freshmen------------------------------------- Take SRS of 500 freshmen to get desired amount 400 Sophomores--------------------------- Take SRS of 400 sophs to get desired amount 450 Juniors------------------------------------- Take SRS of 450 jrs to get desired amount 550 Seniors---------------------------------------------- Take SRS of 550 srs to get desired amount

Good (But Not As Good) Sampling Methods Cluster Sample Divide the population into groups Groups do NOT have to be of equal size Groups MUST share some common characteristic Take SRS of GROUPS and use ALL from those selected groups to achieve desired sample size. Example: A college has 15 dorms with 6 floors in each dorm (total of 90 clusters). Randomly select the desired number of groups/clusters and use EVERYONE on those floors for the sample.

Cluster Sample Floor 1-------------------------- … Floor 90----------------------------------- After numbering the clusters, randomly select full clusters to be part of the sample.

Good(But Not As Good) Sampling Methods Systematic Sample Divide the population into groups Groups MUST be equal size (if possible) Groups do NOT have to be based on any common characteristic Number of groups = final intended sample size Randomly select one member from the first grouping and use that same number position from EACH of the groups.

Systematic Sample Group A: 1 2 3 4 5 6 7 8 9 10 Group B: 1 2 3 4 5 6 7 8 9 10 Group C: 1 2 3 4 5 6 7 8 9 10 Group D: 1 2 3 4 5 6 7 8 9 10 Group E: 1 2 3 4 5 6 7 8 9 10 Final intended sample size is 5 Randomly select a number from 1-10. Then use the number position from each group. EX: 4

Poor Sampling Methods Volunteer Sample Convenience Sample Quota Sample People volunteer to be part of the sample Convenience Sample Use the most convenient group available Quota Sample Interviewers interview a fixed quota of members of the population. Quotas are organized around categories proportional to population.

Review of “response bias” Suppose that SRSs of adult Americans are asked to complete a survey describing their attitudes toward the death penalty. Suppose that one group is asked, “Do you believe that the U.S. judicial system should have the right to call for executions?” whereas another group is asked, “Do you believe that the death penalty should be an option in cases of horrific murder?” Would you anticipate that the proportions of “yes” responses might differ between these two groups?

This is called “wording of the question” bias

Review of “response bias” Suppose that SRSs of students on this campus (college) are questioned about a proposed policy to ban smoking in all campus buildings. If one group is interviewed by a person wearing a t-shirt and jeans and smoking a cigarette, whereas another group is interviewed by a nonsmoker wearing a business suit: Would you expect that the proportions declaring agreement with the policy might differ between these two groups?

This is called “surveyor influence bias” or “interviewer bias”

Review of “response bias” Suppose that an interviewer knocks on doors in a suburban community and asks the person who answers whether he or she is married. If the person is married, the interviewer proceeds to ask, “Have you ever engaged in an extramarital affair?” Would you expect the proportion of “yes” responses to be close to the actual proportion of married people in the community who have engaged in an extramarital affair?

This bias is due to lack of confidentiality

Review of “response bias” Suppose that SRSs of adult Americans are asked whether or not they approve of the president’s handling of foreign policy. If one group is questioned prior to a nationally televised speech by the president on his or her foreign policy and another is questioned immediately after the speech: Would you be surprised if the proportions of people expressing approval differed between these two groups?

This is called “knowledge of the topic bias” or “timing of the question bias”

Other types of bias Household bias Nonresponse bias Only one member of a household is interviewed. This person may not be representative of all members of that household. This often leads to UNDERCOVERAGE Nonresponse bias Voluntary Response bias Many others