1. Producing Date: Sampling Chapter 8

2. Group Task Your group is going to run a study on the effects of cell phones and students’ grades here at Spring- Ford. Task: Your group needs to survey 100 students. It needs to be representative of the all grades. You must create a survey that introduces no bias. With you group figure how you will do this.

3. Group Cont… Answer the following 1. How are you going to get 100 participants in your study?

4. 2. Does everyone in the population (school) have an equal chance of being selected? 3. Can you think of anyone or any groups that might be left out?

5. Study: Texting and Driving http://news.cnet.com/8301-1035_3-10296992-94.html

6. Observation versus Experiment Observational Study = observes individuals and measures variables of interest but does not attempt to influence the responses. purpose is to describe some group or situation Experiment = deliberately imposes some treatment on individuals in order to observe their responses purpose is to study whether a treatment causes a change in the response used to understand cause and effect

7. Example p192 #8.1: A study of cell phones and the risk of brain cancer looked at a group of 469 people who have brain cancer. The investigators matched each cancer patient with a person of the same sex, age, and race who did not have brain cancer, then asked about use of cell phones. Result: “ Our data suggest that use of handheld cellular telephones is not associated with risk of brain cancer.” Is this an observational study or an experiment? Why? What are the explanatory and response variables?

8. In both types of studies, you have to be aware of confounding = when the effects of two variables (explanatory or lurking) on a response variable cannot be distinguished from each other. Observational studies of the effect of one variable on another often fail because the explanatory variable is confounded with lurking variables Well-designed experiments take steps in their design to defeat confounding

9. Example Example: Observational studies suggest that drinking wine rather than beer or hard liquor lead to added health benefits. What lurking variables related to wine drinkers are confounding the results of these studies? Wine versus Beer Health Diet and Lifestyle

10. Sampling In most cases we want to gather information about a large group of individuals. Time, cost, and inconvenience forbid contacting every individual. Instead, we must gather information about only part of the group in order to draw conclusions about the whole.

11. Population = the entire group of individuals about which we want information Sample = a part of the population from which we actually collect information. We use a sample to draw conclusions about the entire population. Population Sample

12. A sampling design describes exactly how to choose a sample from the population. It is not so easy to choose a representative sample from a large and varied population. First step in a proper sample survey is to say exactly what population we want to describe. Second step is to say exactly what we want to measure (to give exact definitions of our variables).

13. Example: p. 194 #8.4: A political scientist wants to know how college students feel about the Social Security system. She obtains a list of the 3456 undergraduates at her college and mails a questionnaire to 250 students selected at random. Only 104 questionnaires are returned. What is the population of the study (=what group does she want information about)? What is the sample (=from what group does she actually obtain information)?

14. Lesson 2: Sampling

15. Study http://www.cbsnews.com/8301-500165_162- 57317464/study-links-sitting-around-to-cancer/

16. Add these definitions… Statistic: A numerical calculation that describes a sample Parameter: A numerical calculation that describes a population

17. Sampling Badly Convenience Sample = a sample selected by taking the members of the population that are the easiest to reach. Surveyor just chooses individuals close at hand Often produces unrepresentative data Ex: a sample of mall shoppers almost always overrepresents middle-class and retired people Almost always leads to bias = a systematic error caused by a bad sampling design that causes results to favor certain outcomes = the outcomes will miss the truth about the population

18. Sampling Badly cont… Voluntary Response Sample = consists of people who choose themselves by responding to a broad appeal Usually biased because people with strong opinions are most likely to respond Ex: write-in, call-in, and online polls

19. Sampling Properly Convenience and voluntary response sampling both rely on personal choice (of the surveyor or the respondents) which ultimately produces bias. A sample chosen by chance allows neither favoritism by the sampler nor self-selection by respondents. Bias is eliminated by giving all individuals an equal chance to be chosen.

20. S ampling Properly cont… Simple Random Sample (SRS) = An SRS of size n consists of n individuals from the population chosen in such a way that every set of n individuals has an equal chance to be in the sample actually selected. Ex: Drawing names from hat (obviously not always practical) Usually technology is used to create a SRS. Using a Random Number Table or Random Number Generator is very common

21. Example: Using a SRS (calculator) Lets say we were conducting a study about how math teachers at Spring-Ford (10-12) feel about Standardized Tests. The current Math teachers are in the following table. Use a simple random sample of 5 teachers to collect data. ArtzerounianLenkoGillespieMichewiczBurghardt BadwayDoranHerbstMooreThomas CappellettiBommentreQuinbyO'TooleBommentre CorropoleseFlynnHornePalladino

22. Stratified Random Sample = First classify the population into groups of similar individuals (called strata), then choose a separate SRS in each stratum and combine these SRSs to form the full sample. Used when you want to sample important groups within the population separately and then combine these samples. The strata are chosen based on facts known before the sample is taken. Ex: Election poll population can be divided into urban, suburban, rural (Try # 12 on page 201 using the calculator.)

23. Cluster Sample = Population naturally separated into subgroups (called clusters), each having similar characteristics; all members in one or more (but not all) clusters are selected (whole groups) make sure all clusters have similar make-up Ex: counties, homerooms, grade-levels, zip codes, course sections

24. Cluster Stratified Group 1 Group 2 Group 1 Group 3 Group 2 Group 3 S1 S3 S2 Sample

25. Systematic Sample = each member of population is assigned a number, then sample members are selected in regular intervals starting from a randomly selected starting number Ex: every 3 rd, 5 th, 10 th, 100 th, … easy to use, but should be avoided in case of a pre-existing pattern in the population

26. Examples : You are doing a study to determine the opinion of students at your school regarding gun control. Identify the sampling techniques you are using if you select the samples listed. Explain your choice. 1. You select a class at random and question each student in the class. 2. You divide the student population with respect to majors and randomly select and question some students in each major.

27. 3. You assign each student a number and generate random numbers. You then question each student whose number is randomly selected. 4. You select students who are in your statistics class. 5. You assign each student a number, and after choosing a starting number, question every 25 th student.

28. Create a Sample Example Lets say you are conducting a study on ________________________________________ about the seniors here at Spring-Ford. How would you create/collect your sample?? Answer the following 1. Does everyone in the population have an equal chance of being selected? 2. Can you think of anyone or any groups that might be left out?

29. Producing Data: Sampling cont… Lesson 3

30. Cautions about Sample Surveys Undercoverage = when some groups in the population are left out of the process of choosing the sample. Since an accurate and complete list of the population is rarely available, most samples suffer from some degree of undercoverage Ex: A sample survey of households excludes… homeless, prison inmates, college dorms Ex: An opinion poll conducted by phone will miss… People without phones, people who only use cell phones (no house phone), people who are unlisted, people who screen their calls, etc. The results of national sample surveys usually have bias if the people not covered differ from the rest of the population (which is often the poor)

31. Cautions about Sample Surveys cont… Nonresponse = when an individual chosen from a sample can’t be contacted or refuses to participate. More serious source of bias than undercoverage Often reaches 50% or more, even with careful planning and several callbacks Usual solution is to substitute other people from the same area or with the same characteristics to avoid favoring other groups where nonresponse was not an issue.

32. Cautions about Sample Surveys cont… Response Bias: Caused by the behavior of the respondent or of the interviewer Respondents will give false responses if they know they “should have” done what is being asked about (ex: wear seatbelts, vote in elections) Interviewer race or gender can influence responses depending on topics Questions requiring the respondent to recall past events give inaccurate results because of faulty memory Wording of questions is the most important influence on answers given in surveys. Confusing or leading questions can introduce strong bias. Even minor changes in wording can change the survey’s outcome. Ex: “How do you feel about government assistance for the poor?”—13% of Americans think we are spending too much. Same question: “How do you feel about welfare?” – 44% of Americans think we are spending too much ***One last idea: The larger the sample the more accurate the results will be!

33. Class Work Work Sheet