1. Experimental Design

2. Definitions: Observational study 1) Observational study Observe outcomes without imposing any treatment Experiment 2) Experiment Actively impose some treatment in order to observe the response

3. I’ve developed a new rabbit food, Hippity Hop. Rabbit Food Makes fur soft & shiny! Increases energy! 100% of daily vitamins & essential oils!

4. Can I just make these claims? What must I do to make these claims? Who (what) should I test this on? What do I test? NO Do an experiment Rabbits The type of food

5. Experimental unit 3)Experimental unit The single individual (person, animal, plant, etc.) to which the different treatments are assigned Factor 4) Factor Is the explanatory variable Level 5) Level A specific value for the factor

6. Response variable 6) Response variable What you measure Treatment 7) Treatment A specific experimental condition applied to the units

7. I plan to test my new rabbit food. What are my experimental units? What is my factor? What is the response variable? Rabbits Type of food How well rabbits grow

8. Hippity Hop I’ll use my pet rabbit, Bunny! Since Bunny’s coat is shinier & he has more energy, then Hippity Hop is a better rabbit food!

9. Control group 8) Control group A group that is used to compare the factor against; can be a placebo or the “old” or current item Placebo 9) Placebo A “dummy” treatment that can have no physical effect

10. Old Food Hippity Hop Now I’ll use Bunny & my friend’s rabbit, Rabbit. Bunny gets Hippity Hop food & Rabbit gets the old rabbit food. WOW! Bunny is bigger & shinier so Hippity Hop is better!

11. Old Food Hippity Hop The first five rabbits that I catch will get Hippity Hop food and the remaining five will get the old food. The Hippity Hop rabbits have scored higher so it’s the better food!

12. Old Food Hippity Hop Number the rabbits from 1 – 10. Place the numbers in a hat. 12 3 4 5 6 78 9 10 The first five numbers pulled from the hat will be the rabbits that get Hippity Hop food. I evaluated the rabbits & found that the rabbits eating Hippity Hop are better than the rabbits eating the old food! The remaining rabbits get the old food. 3 9 85 7

13. Blinding 10) Blinding Method used so that units do not know which treatment they are getting Double blind 11) Double blind Neither the units nor the evaluator know which treatment a subject received

14. Rabbit Food Hippity Hop Rabbit Food makes fur soft and shiny, & increases energy for ALL types of rabbits! Can I make this claim?

15. Principles of Experimental Design Control of effects of extraneous variables on the response – by comparing treatment groups to a control group (placebo or “old”) Replication of the experiment on many subjects to quantify the natural variation in the experiment Randomization – the use of chance to assign subjects to treatments

16. AP Statistics Monday, 05 October 2015 OBJECTIVE TSW examine the components of Experimental Design. TODAY’S ASSIGNMENT –WS Experimental Design #1 Due on Wednesday, 07 October 2015.

17. WS Sampling Design 1)a)stratified b)simple random sample c)stratified d)systematic e)convenience 2)Joe, Mary, Kathy, Sam, Neil 3)Example: To perform a stratified sample, one could divide the group of 18 by gender, 8 females and 10 males. Randomly select 2 females and 3 males.

18. WS Sampling Design 4)a)response b)voluntary response, convenience sampling, undercoverage, non-response c)voluntary response, non-response d)voluntary response, non-response, (possible wording of the question) e)voluntary response, undercoverage, non- response (possibly wording of the question)

19. The ONLY way to show cause & effect is with a well-designed, well-controlled experiment! The ONLY way to show cause & effect is with a well-designed, well-controlled experiment!! The ONLY way to show cause & effect is with a well- designed, well-controlled experiment!!!

20. Example 1 A farm-product manufacturer wants to determine if the yield of a crop is different when the soil is treated with three different types of fertilizers. Fifteen similar plots of land are planted with the same type of seed but are fertilized differently. At the end of the growing season, the mean yield from the sample plots is compared. Experimental units? Factors? Levels? Response variable? How many treatments? Plots of land Type of fertilizer Fertilizer types A, B, & C Yield of crop 3

21. Example 2 A consumer group wants to test cake pans to see which works the best (bakes evenly). It will test aluminum, glass, and plastic pans in both gas and electric ovens. Experiment units? Factors? Levels? Response variable? Number of treatments? Two factors - type of pan & type of oven Type of pan has 3 levels (aluminum, glass, & plastic) & type of oven has 2 levels (electric & gas) How evenly the cake bakes 6 Cake batter

22. Example 3 A farm-product manufacturer wants to determine if the yield of a crop is different when the soil is treated with three different types of fertilizers. Fifteen similar plots of land are planted with the same type of seed but are fertilized differently. At the end of the growing season, the mean yield from the sample plots is compared. Why is the same type of seed used on all 15 plots? What are other potential extraneous variables? Does this experiment have a placebo? Explain It is part of the controls in the experiment. Type of soil, amount of water, etc. NO – a placebo is not needed in this experiment

23. Experiment Designs Completely randomized – all experimental units are allocated at random among all treatments Random assignment

24. Treatment C Treatment B Completely randomized design Randomly assign experimental units to treatments Treatment A Treatment D

25. Randomized block – units are blocked into groups and then randomly assigned to treatments Random assignment

26. Treatment B Randomized block design Randomly assign experimental units to treatments Treatment A Put into homogeneous groups Treatment ATreatment B

27. –match up experimental units according to similar characteristics & randomly assign one to one treatment & the other automatically gets the 2nd treatment –have each unit do both treatments in random order –the assignment of treatments is dependent Matched pairs - a special type of block designMatched pairs - a special type of block design

28. Pair experimental units according to specific characteristics. Next, randomly assign one unit from a pair to Treatment A. The other unit gets Treatment B. Treatment A Treatment B This is one way to do a matched pairs design – another way is to have the individual unit do both treatments (as in a taste test).

29. 12) Confounding variable – the effect of the confounding variable on the response cannot be separated from the effects of the explanatory variable (factor)

30. Suppose we wish to test a new deodorant against one currently on the market.

31. Treatment B Treatment & group are confounded Treatment A Treatment B One group is assigned to treatment A & the other group to treatment B. Confounding Confounding does NOT occur in a completely randomized design!

32. Example 4 An article from USA Today reports the number of victims of violent crimes per 1000 people. 51 victims have never been married, 42 are divorced or separated, 13 are married, and 8 are widowed. Is this an experiment? Why or why not? What is a potential confounding variable? Age – younger people are more at risk to be victims of violent crimes No, no treatment was imposed on people.

33. Example 5 Four new word-processing programs are to be compared by measuring the speed with which standard tasks can be completed. One hundred volunteers are randomly assigned to one of the four programs and their speeds are measured. Is this an experiment? Why or why not? What type of design is this? Factors? Levels? Response variable? Yes, a treatment is imposed. Completely randomized one factor: word-processing program with 4 levels speed

34. Example 5 Four new word-processing programs are to be compared by measuring the speed with which standard tasks can be completed. One hundred volunteers are randomly assigned to one of the four programs and their speeds are measured. Is there a potential confounding variable? Can this design be improved? Explain. NO, completely randomized designs have no confounding variables You could do a block design where each person uses each program in random order.

35. Example 6 Suppose that the manufacturer wants to test a new fertilizer against the current one on the market. Ten 2-acre plots of land scattered throughout the county are used. Each plot is subdivided into two subplots, one of which is treated with the current fertilizer, and the other with the new fertilizer. Wheat is planted and the crop yields are measured. What type of design is this? Why use this method? When does randomization occur? Matched pairs design Randomization occurs when one of the treatments is assigned to the first acre of each two-acre plot

36. Randomization reduces bias by spreading any uncontrolled confounding variables evenly throughout the treatment groups. Variability is controlled by sample size. Larger samples produce statistics with less variability. Blocking also helps reduce variability. Is there another way to reduce variability?

37. High bias & low variability Low bias & low variability Low bias & high variability High bias & high variability Identify the bias and variability level