1. Chapter 10 Sampling Design

2. How do we gather data? Surveys Opinion polls InterviewsStudies –Observational –Retrospective (past) –Prospective (future) Experiments

3. Population the entire group of individuals that we want information about

4. Census a complete count of the population

5. Why would we not use a census all the time? 1) Not accurate 2) Very expensive 3) Perhaps impossible 4) If using destructive sampling, you would destroy population Breaking strength of soda bottlesBreaking strength of soda bottles Lifetime of flashlight batteriesLifetime of flashlight batteries Safety ratings for carsSafety ratings for cars Look at the U.S. census – it has a huge amount of error in it; plus it takes a long to compile the data making the data obsolete by the time we get it! Suppose you wanted to know the average weight of the white-tail deer population in Texas – would it be feasible to do a census? Since taking a census of any population takes time, censuses are VERY costly to do!

6. Sample A part of the population that we actually examine in order to gather information Use sample to generalize to population

7. Sampling design refers to the method used to choose the sample from the population

8. Sampling frame a list of every individual in the population

9. M & M Activity Select 5 M&M PILES that you think are representative of the population of M&M’S in regards to length. Find the mean length of your sample

10. consist of n individuals from the population chosen in such a way that –every individual has an equal chance of being selected –every set of n individuals has an equal chance of being selected Simple Random Sample (SRS) Suppose we were to take an SRS of 50 GR students – put each students’ name in a hat. Then randomly select 50 names from the hat. Each student has the same chance to be selected! Not only does each student have the same chance to be selected – but every possible group of 50 students has the same chance to be selected! However, suppose I separated the males and females and drew 25 of each. I still have a random sample of 50 students, but it is NOT A SRS. WHY????

11. Stratified random sample population is divided into homogeneous groups called strata SRS’s are pulled from each strata Homogeneous groups are groups that are alike based upon some characteristic of the group members. Suppose we were to take a stratified random sample of 50 GR JUNIOR AND SENIOR students. Since students are already divided by grade level, grade level can be our strata. Then randomly select 25 seniors and randomly select 25 juniors

12. Systematic random sample select sample by following a systematic approach randomly select where to begin Suppose we want to do a systematic random sample of GR students - number a list of students (There are approximately 500 students – if we want a sample of 50, 500/50 = 10) Select a number between 1 and 10 at random. That student will be the first student chosen, then choose every 10 th student from there.

13. Cluster Sample based upon location randomly pick a location & sample all there Suppose we want to do a cluster sample of GR students. One way to do this would be to randomly select 10 classrooms during 2 nd period. Sample all students in those rooms!

14. Multistage sample select successively smaller groups within the population in stages SRS used at each stage To use a multistage approach to sampling GR students, we could first divide 2 nd period classes by level (AP, Honors, Regular, etc.) and randomly select 4 second period classes from each group. Then we could randomly select 5 students from each of those classes. The selection process is done in stages!

15. CONVENIENCE SAMPLING: using an easily available or convenient group to form a sample. CAN YOU GIVE AN EXAMPLE?? PROBABLY THE MOST POORLY DRAWN TYPE OF SAMPLE!!! STAY AWAY FROM CONVENIENCE SAMPLES IF AT ALL POSSIBLE!!

16. PROBABILITY SAMPLES ANY SAMPLE CHOSEN BY CHANCE ALL OF THE PREVIOUSLY MENTIONED SAMPLING METHODS CAN BE CLASSIFIED AS PROBABILITY SAMPLES

17. Sampling Methods Sampling with replacement means that after each successive item is selected for the sample, the item is “replaced” back into the population and may therefore be selected again. Example: Choose a sample of 5 digits by spinning a spinner and choosing the number where the pointer is directed.

18. Sampling Methods Sampling without replacement means that after an item is selected for the sample it is removed from the population and therefore cannot be selected again. Example: A hand of “five card stud” poker is dealt from an ordinary deck of playing cards. Typically, once a card is dealt it is not possible for that card to appear again until the deck is reshuffled and dealt again.

19. SRS Advantages –Unbiased –Easy Disadvantages –Large variance –May not be representative –Must have sampling frame (list of population)

20. Stratified Advantages –More precise unbiased estimator than SRS –Less variability –Cost reduced if strata already exists Disadvantages –Difficult to do if you must divide stratum –Need sampling frame

21. Systematic Random Sample Advantages –Unbiased –Ensure that the sample is distributed across population –More efficient, cheaper, etc. Disadvantages –Large variance –Can be confounded by trend or cycle –Formulas are complicated

22. Cluster Samples Advantages –Unbiased –Cost is reduced –Sampling frame may not be available (not needed) Disadvantages –Clusters may not be representative of population –Formulas are complicated

23. Identify the sampling design 1)The Educational Testing Service (ETS) needed a sample of colleges. ETS first divided all colleges into groups of similar types (small public, small private, etc.) Then they randomly selected 3 colleges from each group. Stratified random sample

24. 2) A county commissioner wants to survey people in her district to determine their opinions on a particular law up for adoption. She decides to randomly select blocks in her district and then survey all who live on those blocks. Identify the sampling design Cluster sampling

25. 3) A local restaurant manager wants to survey customers about the service they receive. Each night the manager randomly chooses a number between 1 & 10. He then gives a survey to that customer, and to every 10 th customer after them, to fill it out before they leave. Identify the sampling design Systematic random sampling

26. Bias ERROR favors certain outcomes Anything that causes the data to be wrong! It might be attributed to the researchers, the respondent, or to the sampling method!

27. Voluntary response People chose to respond Usually only people with very strong opinions respond An example would be the surveys in magazines that ask readers to mail in the survey. Other examples are call- in shows, American Idol, etc. Remember, the respondent selects themselves to participate in the survey! Remember – the way to determine voluntary response is: Self-selection!!

28. Convenience sampling Ask people who are easy to ask Produces bias results An example would be stopping friendly-looking people in the mall to survey. Another example is the surveys left on tables at restaurants - a convenient method! The data obtained by a convenience sample will be biased – however this method is often used for surveys & results reported in newspapers and magazines!

29. Undercoverage some groups of population are left out of the sampling process Suppose you take a sample by randomly selecting names from the phone book – some groups will not have the opportunity of being selected! People with unlisted phone numbers – usually high-income families People without phone numbers – usually low- income families People with ONLY cell phones – usually young adults

30. Nonresponse occurs when an individual chosen for the sample can’t be contacted or refuses to cooperate telephone surveys 70% nonresponse People are chosen by the researchers, BUT refuse to participate. NOT NOT self-selected! This is often confused with voluntary response! Because of huge telemarketing efforts in the past few years, telephone surveys have a MAJOR problem with nonresponse! One way to help with the problem of nonresponse is to make follow contact with the people who are not home when you first contact them.

31. Response bias occurs when the behavior of respondent or interviewer causes bias in the sample wrong answers Suppose we wanted to survey high school students on drug abuse and we used a uniformed police officer to interview each student in our sample – would we get honest answers? Response bias occurs when for some reason (interviewer’s or respondent’s fault) you get incorrect answers.

32. Wording of the Questions wording can influence the answers that are given connotation of words use of “big” words or technical words Questions must be worded as neutral as possible to avoid influencing the response. The level of vocabulary should be appropriate for the population you are surveying –. – if surveying doctors, then use more complex, technical wording.

33. Source of Bias? 1) Before the presidential election of 1936, FDR against Republican ALF Landon, the magazine Literary Digest predicting Landon winning the election in a 3-to-2 victory. A survey of 10 million people. George Gallup surveyed only 50,000 people and predicted that Roosevelt would win. The Digest’s survey came from magazine subscribers, car owners, telephone directories, etc. Undercoverage – since the Digest’s survey comes from car owners, etc., the people selected were mostly from high-income families and thus mostly Republican! (other answers are possible)

34. 2) Suppose that you want to estimate the total amount of money spent by students on textbooks each semester at a local college. You collect register receipts for students as they leave the bookstore during lunch one day. Convenience sampling – easy way to collect data or Undercoverage – students who buy books from on-line bookstores are included.

35. 3) To find the average value of a home in Friendswood, one averages the price of homes that are listed for sale with a realtor. Undercoverage – leaves out homes that are not for sale or homes that are listed with different realtors. (other answers are possible)

36. Bias is introduced by the way in which a sample is selected so that increasing the size of the sample does nothing to reduce the bias However, larger samples generally give more accurate results than smaller samples even though they do not mitigate the effects of a Bias selection. Important Note on Bias

37. A LAST WORD OF CAUTION Don’t be confused by the term Sampling Error This term refers to the fact that every sample drawn from the same population can be expected to differ in its results. IT DOES NOT IMPLY THAT THERE IS A MISTAKE IN THE SAMPLING PROCESS

38. Summary In summary, a probability sample allows us to find out information about a large population by collecting data from a small number of observational units within that population. We have to be careful, however, because doing a probability sample improperly can result in biased, inaccurate results.