Sampling a single population

1. Sampling a single population

2. Why sample? • A population is an arbitrarily designated collection of units. • Populations can be described by parameters that we may want to know the values of. • Measuring all units of a population is often impractical or impossible. • Therefore, we have to estimate the parameter of interest by taking a subset of units (= a sample). • Note: estimating the parameter from a sample is an example of induction

3. Factors to consider in designing a sampling scheme • I. Selecting sample units: avoid ‘inductive fallacies’ • Unrepresentative sample • Taking a random sample is the best way to avoid this (sometimes have to approximate randomness) • In some cases, sample units are inevitably self-selected • Sample size too small: how many units are enough??? -Depends on variability…

4. Factors to consider in designing a sampling scheme • …variability

5. Factors to consider in designing a sampling scheme • I. Selecting sample units: avoid ‘inductive fallacies’ • II. Measurements • Precision and bias…

6. 1 2 • Speed gun • Speed gun • Calibration problem 3 4 • Count out loud • Too much coffee • Count out loud

7. Factors to consider in designing a sampling scheme • I. Selecting sample units: avoid ‘inductive fallacies’ • II. Making measurements • Precision and bias: • a precise and unbiased measurement is most desirable, but if we are only interested in a comparison between samples, bias may not affect the results if it is the same for both samples

8. Summary • Sampling is an inductive inference and a way to estimate population parameters • Types of samples: random and self-selected • Sample size required depends on variability • Strict standardization of measurements helps to ensure precise estimates

9. References • Ramsey & Schafer. 1997. The Statistical Sleuth. Duxbury Press. • Or see ~ any statistics textbook…

10. Received (MW):

11. Received (TR):

12. Project I • Is there a difference in the average height of buildings on either side of SW Broadway?

13. Project I • Decide on a sampling scheme and measurement methodology as a group, then you can divide up for measurements • Using MS Excel to get random numbers • No talking between groups!!! • Use any tools or resources available, but cannot look up heights of the buildings you are sampling (looking up others is ok) • Report due Monday, Jan 24th (2 weeks)

14. Project I Groups (MW): 1 Larkin Musich Wise Davis Scholz 2 Wentworth Gray Wilson Adams Sandes 3 Gentry Johnson Putterman Proden Bailey 4 Havelka Buller Driver Odermatt Mayer 5 B. Davis Shabazz Lewis Whitaker Rademaker Cross 6 Harger Raglione C. Davis Saul Baker Hieb 7 Blair Button Mack Hovee Cunningham Elliott

15. Project I Groups (TR): 1 Glowacki Chan Hatfield Warren Vanzant Soldati Hanley 2 Tappan Casper Wells Semprevivo Scott Ramos Tyler 3 Stevens Bosch Evans Shaffer- Ross Robinson 4 Sharma Meazell Raman Perera Meeker Fitzgibbon 5 Soares Nemirow de Luna Clevenger Caldwell Brodie 6 Lee Abdullahi Katzberg Bui Barnicoat Nguyen 7 Hern Bolliger Zielony Hott Reid Blunt