1. Status for AP Congrats! We are done with Part I of the Topic Outline for AP Statistics! (20%-30%) of the AP Test can be expected to cover topics from chapter 1-3. Coming up… Part II (10%-15%) Sampling and Experimentation: How to plan and conduct a study. For Today: Put name on sticky note and fold into 4 ths …

2. Designing Studies Section 4.1 Reference Text: The Practice of Statistics, Fourth Edition. Starnes, Yates, Moore

3. Objectives Describe the difference between a population and a sample. Describe what is meant by bias in a sample. Describe what is meant by a: –Voluntary Response Sample –Convenience Sample Describe what is meant by a : –Simple Random Sample Describe other complex sampling methods: –Stratified Random Sample –Cluster Sample & Clusters What it means to make an inference Describe what can go wrong with gathering data: –Under coverage, non response, response bias, wording of the question

4. Population vs. Sample The entire group of individuals we want information about is called the population –Note: “individual” does not have to mean people, could be objects, animals… Since its impossible to study the entire population, what do we do instead? We take a sample! Definition: The population in a statistical study is the entire group of individuals about which we want information. A sample is the part of the population from which we actually collect information. We use information from a sample to draw conclusions about the entire population.

5. Sampling and Surveys Population Sample Collect data from a representative Sample... Make an Inference about the Population.

6. Methods of collecting data How do we choose a sample from a population? How do we chose while making sure we reduce Bias? Cluster Voluntary Response Simple Random Sample Stratified Convenience Sample

7. Commonly Used Sampling Methods: BIAS Definition: A voluntary response sample consists of people who choose themselves by responding to a general appeal. Voluntary response samples show bias because people with strong opinions (often in the same direction) are most likely to respond. Definition: Convenience Samples is choosing individuals who are easiest to reach results in. Commonly used at places where people congregate School lunch grounds, Grocery stores, shopping malls, theaters, etc. Questioners choose respondents by who happens to walk by.

8. Bias in Sampling The design of a study is biased if it systematically favors certain outcomes. There has to be randomness! –A voluntary response sample is biased in that it favors negative outcomes regardless of the question. –A convenience sample is usually biased in that it favors the opinions of people in a certain location at a certain time. There is no guarantee that such opinion is representative of the population as a whole. –In both cases a conscious choice is made to include/exclude a respondent We want a method in which the choice is random and does not depend on any individual This is what we strive for as scientists, phycologists, and statisticians.

9. Simple Random Samples: Non Bias In practice, people use random numbers generated by a computer or calculator to choose samples. If you don’t have technology handy, you can use a table of random digits. Definition: A simple random sample (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 the sample actually selected.

10. Activity! Simple Random Sample of 4 Put your name on the sticky note, fold into 4 ths Place in hat I’ll randomly select 4 people from the hat. –Do all possible SRS of 4 people have equal chance? Why? Next Scenario: Put all girls in one hat & boys in another hat I’ll randomly select 2 from each hat. –Do all possible SRS of 4 people have equal chance? Why?

11. Calculator: SRS Calculator: From a population of 25 individuals choose an SRS of size 4 TI83: Math > PRB> 5:rand int( 1,25)>Enter -Should be able to hit enter each time for a new number, no repeats TI89: Catalog > F3: rand int(1,25) > enter -Should be able to hit enter each time for a new number

12. Complex Sampling Methods Its difficult to actually get an SRS from a population of interest for multiple reasons –Difficult to obtain actual population list –Time consuming –Costly –Geographically difficult So we look to other methods to collect data while maintaining unbiased random selection…

13. Stratified Random Sample Stratified Random Sample- First classify the population into groups of similar individuals or “sub-samples”, called strata. Then chose a separate SRS in each stratum and combine these SRSs to form the full sample. Examples: Population of HS  divided into Freshmen, Sophomores, Juniors, Seniors

14. Cluster Sample Stratified can be more precise information than SRS but both methods are hard to use when population is large and spread out…so we turn to Cluster Sampling where groups are “near” one another. Definition: To take a cluster sample, first divide the population into smaller groups. Ideally, these clusters should mirror the characteristics of the population. Then choose an SRS of the clusters. ALL individuals in the chosen clusters are included in the sample.

15. Example: Sampling at a School Assembly Describe how you would use the following samplingmethods to select 80 students to complete a survey. (a) Simple Random Sample (b) Stratified Random Sample (c) Cluster Sample

16. Inference The purpose of a sample is to give us information about a larger population. The process of drawing conclusions about a population on the basis of sample data is called inference. Why should we rely on random sampling? 1)To eliminate bias in selecting samples from the list of available individuals. 2)The laws of probability allow trustworthy inference about the population Results from random samples come with a margin of error that sets bounds on the size of the likely error. Larger random samples give better information about the population than smaller samples.

17. Sampling and Surveys Sample Surveys: What Can Go Wrong? Most sample surveys are affected by errorsin addition to sampling variability. Good sampling technique includes the artof reducing all sources of error. Definition Undercoverage occurs when some groups in the population are left out of the process of choosing the sample. Nonresponse occurs when an individual chosen for the sample can’t be contacted or refuses to participate. The wording of questions is the most important influence on the answers given to a sample survey.

18. What Can Go Wrong?! Sampling Errors: The margin of error tells us how much sampling variability to expect, and we can control it by choosing the size of our random sample. Under coverage- occurs when some groups in the population are left out of the process of choosing the sample –Example: SRS of households  what about homeless, dormitory, prison Nonresponse- occurs when an individual chosen for the sample cant be contacted or refuses to participate. –Warning: don’t confuse this with voluntary response.

19. What Can Go Wrong?! Response Bias- A systematic pattern of incorrect responses in a sample survey leads to a response bias –Did you visit the dentist the past 6 months? Yes, when in fact it was 8 months Wording of the Question- most important influence on the answer given to a sample survey. Confusing or misleading questions can introduce strong bias, and changing the wording can greatly change the survey’s outcome, even the order in which asked.

20. Objectives Describe the difference between a population and a sample. Describe what is meant by bias in a sample. Describe what is meant by a: –Voluntary Response Sample –Convenience Sample Describe what is meant by a : –Simple Random Sample Describe other complex sampling methods: –Stratified Random Sample –Cluster Sample & Clusters What it means to make an inference Describe what can go wrong with gathering data: –Under coverage, non response, response bias, wording of the question

21. Homework Worksheet/ TBA