STAT 110 - Section 5 Lecture 11

1. STAT 110 - Section 5 Lecture 11 Professor Hao Wang University of South Carolina Spring 2012 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAA

2. Last time: Experiment (I) Completely randomized (II) Matched Pairs Design (III) Block Design

3. Group task: An Experiment • A taste test is being conducted to compare Dr. K to Dr. Pepper. You have 21 individual participants • Discuss with your group: • Design a completely randomized experiment • Identify lurking variables • Design a matched pairs experiment • How to blind and how to randomize?

4. 14 people preferred Dr. K over Dr. Pepper and 7 preferred Dr. Pepper over Dr.K. The percentage of people who preferred Dr. K was: A – 14/7 = 2% B – 14/21 = 66.7% C – 7/14 = 50% D – 7/21 = 33.33%

5. The experiment found that 14 people preferred Dr. K over Dr. Pepper and 7 preferred Dr. Pepper over Dr.K, for a total sample size of 21. Approximately what is the margin of error for 95% confidence? A – 1/14 = 7.1% B – 14/21 = 66.7% C – 1/sqrt(21) = 21.8% D – 3%

6. Flipping a coin to see which soda the subject drank first A – Would hopefully remove confounding with the lurking variable of which you tasted first B – Would hopefully remove confounding with the lurking variable of preferring things just because they are biased towards name brands C – Would hopefully remove confounding with the explanatory variable of which you tasted first D – Would hopefully remove confounding with the explanatory variable of preferring things just because they are biased towards name brands

7. The drinker not seeing which drink they were given made the experiment A – A Block Design B – Double Blind C – Single Blind D – Randomized

8. The drinker not seeing which drink they were given A – Would hopefully remove confounding with the lurking variable of which you tasted first B – Would hopefully remove confounding with the lurking variable of preferring things just because they are biased towards name brands C – Would hopefully remove confounding with the explanatory variable of which you tasted first D – Would hopefully remove confounding with the explanatory variable of preferring things just because they are biased towards name brands

9. Chapter 8 Measurement

10. Example • To measure the length of my bed, I use a tape measure as the instrument. • I can choose either inches or centimeters as the unit of measurement. • If I choose centimeters, my variable is the length of the bed in centimeters.

11. measure – assign a number to represent a property of a person or thing instrument – device used to make a measurement units – used to record the measurements (feet, pounds, inches, gallons, etc.) variable – the result of a measurement that takes different values for people or things that differ in whatever we’re measuring

12. Example • To measure a student’s readiness for college, I might ask the student to take the SAT. • What’s the instrument? • What are the units? • What’s the variable?

13. Valid and Invalid Measurements valid – a variable is a valid measure of a property if it is relevant or appropriate as a representation of that property • Is it valid to measure length with a tape measure? • Is it valid to measure a student’s readiness for college by his/her height?

14. Valid and Invalid Measurements • If we use a count for highway deaths, and notice an increase from year to year, we would report that deaths have increased, so it would appear highways are more unsafe. The Fatal Accident Reporting System reported 40,716 deaths in 1994 and 42,642 deaths in 2006 • But number of licensed drivers increased from approximately 160 million to 203 million • More people drive more miles • Count is not a valid measure of highway safety. Rather than a count, we could use a rate, like number of deaths per mile driven

15. Errors in Measurement:Is your bathroom scale accurate? If your scale always weighs 3 pounds too high, then Measure weight = True weight + 3 pounds

16. Suppose your scale reads 3 pounds too high because its aim is off, but this morning it sticks and weighs you ½ pound lighter, then Measure weight = True weight + 3 pounds-1/2 pound Yipee, you jump off and back on the scale to see the ½ lb weight loss again, but this time it sticks to add ¼ lb Measure weight = True weight + 3 pounds+1/4 pound

17. Your scale has two kinds of errors • If it didn’t stick, the scale would always read 3 pounds too high. This systematic error that occurs every time we make a measurement is called BIAS. • Your scale sticks, but how much it sticks changes each time you step on it. We can’t predict the error due to stickiness, so we call it RANDOM ERROR.

18. Errors in Measurement bias – systematic deviation from the true value of the property random error – repeated measurements on the same individual give different results reliable – when random error is small measured value = true value + bias + random error

19. A scale that always reads the same when it weighs the same item is perfectly reliable even if it is biased. Reliability says only that the result is repeatable. Bias and lack of reliability are different kinds of error. No measuring process is perfectly reliable. The average of several repeated measurements of the same individual is more reliable (less variable) than a single measurement. Use averages to improve reliability.