1. 1.6 (extra) Design of Experiments: Principles Sampling design

2. Principles of Experimental Design Principles of Experimental Design: 1.Control of lurking variables on the response, most simply by comparing several treatments (including placebo) 2.Randomization, using random assignment of subjects to the treatments, this creates groups that are similar. 3.Replication of the experiment on many units to reduce chance variation in the results. 4.Double-blind: neither the subjects themselves nor the personnel who work with them know which treatment any subject has received. Random assignment Group 1 Group 2 Group 3 Treatment 1 Treatment 2 Treatment 3 Placebo Collect Responses

3. Types of Experimental Designs: 1.Matched Pair Design: Some matching between subjects is sometimes better than totally random. Example: Cereal beetle control in agriculture. Use of sticky boards to trap beetles: yellow or green boards are to be used. Which type of board works better? Discussion.

4. Poles are set-up in the field on which boards are mounted. How to distribute the boards on the poles for accurate results? If just one color per pole… Results can be biased. Alfalfa is natural beetle habitat. Possible other effects in the field. Oats Alfalfa

5. Better set-up: Each pole carries both color boards. One yellow board and one green board = A block of two units matched. Two colors per pole Results are more reliable. Oats Alfalfa Matched Pair Design

6. More general… 2.Block Design: For any size matching, not just 'pair'. Making blocks allows control of outside variables by grouping them. Men Women Treatment 1 Treatment 2 Treatment 3 Compare success Subjects Random assignment Treatment 1 Treatment 2 Treatment 3 Compare success Blocks should be formed based on the unavoidable sources of variability. Example:

7. The octane of fuel is a measure of its resistance to detonation with a higher number indicating higher resistance. An engineer wants to know whether the level of octane in gasoline affects the gas mileage of an automobile. Assist the engineer in designing an experiment. EXAMPLE Designing an Experiment

8. Step 1: Identify the response variable: miles per gallon. Step 2: Identify factors that affect miles per gallon: Engine size, outside temperature, driving style, driving conditions, characteristics of car. The octane of fuel is a measure of its resistance to detonation with a higher number indicating higher resistance. An engineer wants to know whether the level of octane in gasoline affects the gas mileage of an automobile. Assist the engineer in designing an experiment, starting with 12 cars. EXAMPLE Designing an Experiment

9. Step 3: We will use the 12 cars all of the same model and year. Step 4: We list the variables: Octane level: 1.Treatment A: 87 octane, 2.Treatment B: 89 octane, 3.Treatment C: 92 octane Engine size – fixed (since all 12 cars are the same) Temperature - uncontrolled, but will be the same for all 12 cars. Driving style/conditions - all 12 cars will be driven under the same conditions on a closed track - fixed. Other characteristics of car - all 12 cars will be the same model year, however, there is probably variation from car to car. To account for this, we randomly assign the cars to each octane level.

10. Step 5: Randomly assign 4 cars to the 87 octane, 4 cars to the 89 octane, and 4 cars to the 92 octane. Give each car 3 gallons of gasoline. Drive the cars until they run out of gas. Compute the miles per gallon. Step 6: Determine whether any differences exist in miles per gallon.

11. Diagram of the experiment: Treatment 1: Treatment 2: Treatment 3: Group 1: Group 2: Group 3:

12. Xylitol has proven effective in preventing dental caries (cavities) when included in food or gum. A total of 75 Peruvian children were given milk with and without Xylitol and were asked to evaluate the taste of each. The researchers measured the children’s’ ratings of the two types of milk. (Source: Castillo JL, et al (2005) Children's acceptance of milk with Xylitol or Sorbitol for dental caries prevention. BMC Oral Health (5)6.) EXAMPLE A Matched-Pairs Design (a)What is the response variable in this experiment? (b)Think of some of the factors in the study. Which are controlled? Which factor is manipulated? (c) What are the treatments? How many treatments are there? Rating Age and gender of the children; Milk with and without Xylitol is the factor that was manipulated Milk with Xylitol and milk without xylitol; 2 treatments

13. (d) What type of experimental design is this? (e) Identify the experimental units. (f) Why would it be a good idea to randomly assign whether the child drinks the milk with Xylitol first or second? (g) Do you think it would be a good idea to double-blind this experiment? Matched-pairs design, since there are 2 treatments to be compared 75 Peruvian children Remove any effect due to order in which milk is drunk. Yes!

14. The English Department is considering adopting an online version of the freshman English course. After some deliberation, the English Department thinks that there may be a difference in the performance of the men and women in the traditional and online courses. To accommodate any potential differences, they randomly assign half the 60 men to each of the two courses and they do the same for the 70 women. EXAMPLE A Randomized Block Design This is a randomized block design where gender forms the block. This way, gender will not play a role in the value of the response variable, test score. We do not compare test results across gender.

16. Method to use for “Randomization”: You will need to use random numbers. Use Table 1 in the textbook to get them. Another Example: Solve this problem A study of the effectiveness of antidepressant on patients was conducted on a sample of subjects (names below). The goal was to assess how antidepressant alone or antidepressant with stress management techniques affected the patients. Identify treatment(s) and placebo – How many? Design the experiment (drawing). Explain how the subjects are chosen for the treatment(s) or the placebo.

17. Hints: Identify the treatments: 1.antidepressant 2.antidepressant + stress management 3.placebo + stress management 4.placebo Therefore we have 4 blocks - Each block contains: 40/4 = 10 people Design the experiment (diagram) (on the board) The treatments/placebo must be assigned randomly to the subjects, thus the use of random numbers.

18. Number all the participants from 1 to 40. Use random pair digits (values less than 40) to assign treatments: Using table 1 and starting at line 05 (for example) (Note: For the HW, you must start at whichever line is requested in the problem): Group1: 36 09 28 32 40 38 29 34 16 12 Group2: 06 15 33 26 23 18 37 25 03 07 Group3: 31 10 13 14 27 26 35 22 30 11 (I got all the way to row #11 for this!) Group4: The remaining numbers between 1 and 40 that are not already above.