Producing Data

1. Producing Data Chapter 5

2. Designing Samples Section 5.1

3. Convenience Sampling • Sampling that chooses the individuals that is easiest to reach Probability Sample • A sample chosen by chance and that chance, or probability must be known

4. Simple Random Sample (SRS) • Random Sample – avoid biasness • All individuals were chosen in an equal way and have an equal chance of being chosen Table of Random Digits • Used to help assign a simple random sample • Label each piece of population with a numerical label • Use table to select labels

5. Stratified Random Sample • Strata- groups of similar individuals • Divide data into strata then chooses SRS for each Strata and then combine • ie music genres Multi Stage Sampling Design • Selects smaller groups within populations stages and then chooses SRS

6. Designing Experiments Chapter 5.2

7. Designing Experiments • Experimental Units • Unit having experiment done to them • Subjects • When unit is human being • Treatment • Experimental condition

8. Designing Experiments • What is the purpose of an experiment? • To look at the response of one variable to the change in another or interaction of several factors • Give good evidence for causation • Study only those factors we are interested in while controlling the others • Explanatory vs Response Variables • Explanatory  Independent  Factors • Response Dependent • Placebo  “Dummy Variable” • Many experiments have multiple factors  Levels

9. Designing Experiments • Experiments • Design • Units  Treatment  Observed Response • Control Group • Control affects of outside effects • Bias • Favoritism for one group/outcome • Control • First basic principle of statistical design of experiments

10. Designing Experiments • Outline of a Random Experiment • Split into two groups of students • Give half students blue test and other half green test • Check scores on test • How does change affect this study? • Effects of chance will average out with large enough sample of population • You must use enough experimental units to reduce chance variation

11. Designing Experiments • Principles of Experimental Design • Control • Randomize • Replicate • Statistical Significance • An observed effect so large that it would rarely occur by chance • “Good Evidence”

12. Designing Experiments • Principles of Experimental Design • Control • Randomize • Replicate • Statistical Significance • An observed effect so large that it would rarely occur by chance • “Good Evidence”

13. Designing Experiments • Cautions in Experiments • Need to be sure to treat all units identically in every way except tested variable • Use of “Double Blind” Technique • Neither the units nor the personnel know treatments

14. Designing Experiments • Designs of Experiments • Randomized • Matched Pairs • Block

15. Simulating Experiments Section 5.3

16. Designing Experiments • Chance • What is the chance of a flight actually being overbooked? • What is the chance of a cop catching you speeding? • What is the chance of you marrying your high school sweetheart? • How can we answer these questions?

17. Designing Experiments • Do an actual experiment many times and calculate the relative frequency • Can be costly, slow, and logistically difficult • Develop a probability model and use it to calculate a theoretical answer • Must know probability which may be unknown because of too many variables • Develop a model that reflects the truth about the experiment and then simulate repetitions for the experiment. • Quicker than actually repeating the experiment • Allows us to analyze mathematically

18. Designing Experiments • Simulation • The imitation of chance behavior, based on a model that accurately reflects the experiment under consideration • Simulation Steps • State the problem  Define the experiment • State the Assumptions • Assign digits to repeat outcomes • Simulate many repetitions • State your conclusion • Independence (In terms of probability) • One result does not affect the next

19. Designing Experiments • Simulation Steps • State the problem  Define the experiment • Will I pass three or more of my classes this semester? • State the Assumptions • Each class is independent of another • Passing each class has the same probability (Yea right ) • Assign digits to repeat outcomes (TORD) • Even Digits Pass, Odd Digits  Fail • One Digit represents one class • Start at Line 128 • Simulate many repetitions • Find 10 repetitions and their outcomes • State your conclusion • Estimate Probability  2/10= 20%

20. Designing Experiments • Assigning Digits in simulations • Sex of a Child • Picking a pair of shoes • Picking a male student from the class • Find Probability then assign numbers • Sales of ice cream when a store has 35% chocolate, 25% vanilla, 10% peanut butter, and 30% coffee

21. Simulations with Calculator • RandInt • Math Prob  Rand( start, end ,# of numbers)