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# Sample surveys

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### Sample surveys

1. 1. Census A sample that consists of the entire population
2. 2. Why would we not do a census? 1) Not accurate for a large population 2) Very expensive 3) Perhaps impossible 4) If using destructive sampling, you would destroy population • Breaking strength of soda bottles • Lifetime of flashlight batteries
3. 3. Simple Random Sample 1. number the population 2. use a method to randomly select the desired sample size from entire population Advantages: every member of population always has equal chance of being selected Disadvantages: sample may not be representative of population; difficult with large populations
4. 4. Cluster Random Sample 1. divide population into clusters 2. use a method to randomly select one or more clusters 3. Perform a census within each of the clusters Advantages: can work well if population is easy to divide or there are established clusters Disadvantages: not everyone has equal chance of being chosen; selected clusters may not be representative of population
5. 5. Stratified Random Sample 1. divide population into strata 2. use a method to randomly select a sample from each strata Advantages: guarantees representation from each strata Disadvantages: not everyone has equal chance of being chosen; strata (of interest) may be difficult to determine; population may be difficult/laborious to sort
6. 6. Systematic Random Sample 1. use sample size and population size to determine (estimate) “magic number” 2. use a method to randomly select number using “magic number” as range; add to determine corresponding selections Advantages: allows rapid method to select from large population; helps provide representation throughout population Disadvantages: not everyone has equal chance of being chosen; sample may not be representative
7. 7. Multi-Stage Random Sample 1. use a method (SRS, cluster, stratified) to randomly select (large) groups 2. use a method (SRS, cluster, stratified to randomly select (smaller) groups 3. repeat until participants are chosen
8. 8. Role of Sampling Design Statistical inference provides ways to answer specific questions from data with some guarantee that the answers are good ones. Statistical inference will not be accurate if the method of collecting data is flawed.
9. 9. Other Sampling Designs Suppose the principal is interested in finding out if MacArthur students think more trees should be planted. She makes an announcement and instructs students to come by her office to let her know if tree planting is an issue they support. Will this sample of students give her an accurate picture of all students’ feelings at MacArthur?
10. 10. Voluntary Response A voluntary response sample consists of people who choose themselves by responding to a general appeal. Voluntary response samples over represent people with strong opinions.
11. 11. Other Sampling Designs The principal is surprised to find most of the students coming in her office are in favor of the tree planting. Feeling that maybe her design may not have worked, she ventures into the hallways and starts asking students. Will this sample of students give her an accurate picture of all students feelings at MacArthur?
12. 12. Convenience Sample In a convenience sample the interviewer makes the choice. It is a self selected sample Convenience samples produce bias results and show favoritism
13. 13. What type of sampling method is appropriate for the given situations? 1) Before implementing a plan designed to reduce flight time, and hence conserve fuel and energy, the US Air Force needs an estimate of the total number of miles flown by a particular type of aircraft during a given month. Air Force records show that there are 1500 aircraft of this type at 96 different airfields around the country.
14. 14. 2) Time Magazine wishes to know whether its readership is satisfied with the current format used for printing the magazine. 3) As part of an appraisal of the retail value of homes in Dallas a sample of homes will be taken to find the average value of a house.
15. 15. Random-random sample practice 1. simple random sample 2. convenience sample 3. cluster sample 4. voluntary response 5. systematic sample 6. stratefied sample 1. MacArthur seniors 2. UT graduates 3. Blender magazine subscribers 4. Texans 5. national pet stores 6. Travis middle school
16. 16. Cautions about sample surveys Suppose we use a random sample in a survey, what could confound our results? Bias is any systematic failure of a sampling method to represent its population undercoverage  the issue occurs when a sampling design misses a part of the population nonresponse bias  the issue occurs when a significant part of the population refuses to participate in the survey or cannot be contacted • voluntary response bias – individual chooses whether to participate in a sample
17. 17. response bias  the issue occurs when the person asking the question makes the respondent uncomfortable and possibly influence their answer • wording of question occurs when a question is leading and attempts to persuade a respondent toward a particular answer Remember: sample results sometimes simply do not necessarily match the population.
18. 18. Identify potential problems To obtain a sample of households, a television rating service dials numbers taken at random from telephone-directories. Teen magazine sent a mail-in questionnaire to 500 randomly selected subscribers. One of the questions was the following: “Knowing that the cover price would likely increase, would you prefer the number of advertisements in the magazine to be limited.?”
19. 19. Identify potential problems To evaluate the reliability of cars owned by its subscribers, Consumer Reports magazine publishes a yearly list of automobiles and their frequency-of-repair records. The magazine collects the information by mailing a questionnaire to subscribers and tabulating the results from those who return it.
20. 20. Identify potential problems For a survey of student opinions about high school athletic programs, a member of the school board obtains a random sample of students by listing all high school students and using a random number table to select 30 of them. After making phone calls last weekend, she notes six of the students said that they didn’t have time to participate in the survey.
21. 21. Defining Important Terms population: the entire group of interest sample: the selected group that information was collected from sample variability: sample to sample difference sample design: refers to the method used to choose the the sample from the population good: simple random sample, cluster, stratified, systematic  poor: voluntary response, convenience sampling randomization: random selection in which each individual is given a fair, random chance of selection; the use of chance or probability during the selection process
22. 22. Remember! Bias is introduced by the way a sample is selected or how the data is collected from the sample. Increasing sample size does not reduce bias; but the degree of accuracy can be improved Bad sample designs yield worthless data. Sample results are only estimates of the population. A poor design systematically favors certain outcomes or results. Since we deliberately use chance, the results obey the laws of probability allowing fairly consistent results (within a margin of error).
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