Chapter 1 Section 5

1. Chapter 1Section 5 The Design of Experiments

2. 1 2 3 4 Chapter 1 – Section 5 • Learning objectives • Define designed experiment • Understand the steps in designing an experiment • Understand the completely randomized design • Understand the matched-pairs design

3. 2 3 4 1 Chapter 1 – Section 5 • Learning objectives • Define designed experiment • Understand the steps in designing an experiment • Understand the completely randomized design • Understand the matched-pairs design

4. Chapter 1 – Section 5 • Data can be collected in two main ways • Through sample surveys • Through designed experiments • Sample surveys lead to observational studies • Designed experiments enable researchers to control variables, leading to additional conclusions

5. Chapter 1 – Section 5 • A designedexperiment is a controlled study • The purpose of designed experiments is to control as many factors as possible to isolate the effects of a particular factor • Designed experiments must be carefully set up to achieve their purposes

6. Chapter 1 – Section 5 • Some variables in a designed experiment are controlled, those are the explanatoryvariables • These variables are also sometimes called the factors • Factors • Are part of a controlled environment • Has values that can be changed by the researcher • Are considered as possible causes

7. Chapter 1 – Section 5 • Examples of factors are • The dosage of a drug in a medical experiment • The type of teaching method in an education experiment • One drug by itself compared to that drug used in conjunction with another

8. Chapter 1 – Section 5 • The designed experiment analyzes the affects of the factors on the responsevariable • Response variables • Are not part of a controlled environment • Has values that are measured by the researcher • Measure the effects

9. Chapter 1 – Section 5 • Examples of response variables are • The blood pressures of the patients • The test scores for a class • The sizes of a cancerous tumor for patients

10. Chapter 1 – Section 5 • A treatment is a combination of the values of the factors • Examples of treatments • Giving one medication to one group of patients and a different medication to another • Using one type of fertilizer on a set of plots of corn and a different type of fertilizer on a different set of plots • Playing country music to one group of mice and rap music to another

11. Chapter 1 – Section 5 • The treatment is applied to experimentalunits (people, plants, materials, other objects, …) • When the experimental units are people, we refer to them as subjects • Subjects in an experiment correspond to individuals in a survey

12. Chapter 1 – Section 5 • An example of a designed experiment is to determine whether a new drug, Drug N, is more effective at treating high blood pressure than the existing drug, Drug E • Patients with high blood pressure are given either Drug N or Drug E • The blood pressures are measured one month later

13. Chapter 1 – Section 5 • For this experiment • Factor – the type of drug • Response variable – blood pressure • Treatment – given Drug N or Drug E • Experimental units / subjects – the patients • For this experiment • Factor – the type of drug • Response variable – blood pressure • Treatment – given Drug N or Drug E • Experimental units / subjects – the patients • If patients given Drug N have significantly lower blood pressures than patients given Drug E, we would wish to conclude that Drug N is more effective

14. Chapter 1 – Section 5 • Changes in behavior of subjects • Changes in behavior of subjects • For an experiment comparing a new drug to no treatment at all • If the subject knows that he or she is given a drug, he or she may feel better (the placebo effect) • Changes in behavior of subjects • For an experiment comparing a new drug to no treatment at all • If the subject knows that he or she is given a drug, he or she may feel better (the placebo effect) • For an experiment comparing a new drug to an existing drug • If the subject knows which drug he or she is given, that may change his or her behavior

15. Chapter 1 – Section 5 • To avoid the effects of subject behavior • Subjects not given any medication are often given a placebo such as a sugar tablet • The subjects will not know which treatment they get • To avoid the effects of subject behavior • Subjects not given any medication are often given a placebo such as a sugar tablet • The subjects will not know which treatment they get • To avoid the effects of researcher behavior • The researchers are not told which drug they are administering • To avoid the effects of subject behavior • Subjects not given any medication are often given a placebo such as a sugar tablet • The subjects will not know which treatment they get • To avoid the effects of researcher behavior • The researchers are not told which drug they are administering • When both the subjects and the researchers do not know which treatment, this is called double-blind

16. 3 4 1 2 Chapter 1 – Section 5 • Learning objectives • Define designed experiment • Understand the steps in designing an experiment • Understand the completely randomized design • Understand the matched-pairs design

17. Chapter 1 – Section 5 • Conducting an experiment involves considerable planning • Conducting an experiment involves considerable planning • Planning steps • Conducting an experiment involves considerable planning • Planning steps • Identify the problem • Conducting an experiment involves considerable planning • Planning steps • Identify the problem • Determine the factors • Conducting an experiment involves considerable planning • Planning steps • Identify the problem • Determine the factors • Determine the number of experimental units • Conducting an experiment involves considerable planning • Planning steps • Identify the problem • Determine the factors • Determine the number of experimental units • Determine the level of each factor • Conducting an experiment involves considerable planning • Planning steps • Identify the problem • Determine the factors • Determine the number of experimental units • Determine the level of each factor • Implementation steps • Conducting an experiment involves considerable planning • Planning steps • Identify the problem • Determine the factors • Determine the number of experimental units • Determine the level of each factor • Implementation steps • Conduct the experiment • Conducting an experiment involves considerable planning • Planning steps • Identify the problem • Determine the factors • Determine the number of experimental units • Determine the level of each factor • Implementation steps • Conduct the experiment • Test the claim

18. Chapter 1 – Section 5 • Identify the problem • The first step in planning an experiment (or in most any project at all) is to identify the problem • The identification would include • The general purpose of the experiment • The response variable • The population • This is also referred to as the claim

19. Chapter 1 – Section 5 • Determine the factors • The second step in planning an experiment is to determine the factors to be studied • The factors could be identified • By subject matter experts • By the purpose of the experiment • Using results from previous studies • Factors must be identified as either fixed, controlled, or uncontrolled

20. Chapter 1 – Section 5 • Determine the number of experimental units • In general, the more the experiment units, the more effective the experiment • The number of experimental units • Could be limited by time • Could be limited by money • There are techniques to calculate the number of experimental units (to be covered later)

21. Determine the level of each factor • Three ways to deal with the factors • Control – fix the levels at a constant level (for factors not of interest) • Determine the level of each factor • Three ways to deal with the factors • Control – fix the levels at a constant level (for factors not of interest) • Manipulate – set the levels at predetermined levels (for factors of interest) • Determine the level of each factor • Three ways to deal with the factors • Control – fix the levels at a constant level (for factors not of interest) • Manipulate – set the levels at predetermined levels (for factors of interest) • Randomize – randomize the experimental units (for uncontrolled factors not of interest) • Determine the level of each factor • Three ways to deal with the factors • Control – fix the levels at a constant level (for factors not of interest) • Manipulate – set the levels at predetermined levels (for factors of interest) • Randomize – randomize the experimental units (for uncontrolled factors not of interest) • Randomization decreases the effects of uncontrolled factors, even ones not identified Chapter 1 – Section 5 • Determine the level of each factor • Three ways to deal with the factors

22. Chapter 1 – Section 5 • Conduct the experiment • The subjects are assigned at random to the treatments • When a treatment is applied to more than one experimental unit, this is called replication • Replication is useful for accuracy, to further decrease the effects of uncontrolled factors • Collect and process the data

23. Chapter 1 – Section 5 • Test the claim • This is inferential statistics • Techniques of inferential statistics are studied in chapters 9 through 14

24. 1 2 4 3 Chapter 1 – Section 5 • Learning objectives • Define designed experiment • Understand the steps in designing an experiment • Understand the completely randomized design • Understand the matched-pairs design

25. Chapter 1 – Section 5 • A completelyrandomizeddesignis when each experimental unit is assigned to a treatment completely at random • A completelyrandomizeddesignis when each experimental unit is assigned to a treatment completely at random • An example • A farmer wants to test the effects of a fertilizer • We choose a set of plants to receive the treatment • We randomly assign plants to receive different levels of fertilizer • A completelyrandomizeddesignis when each experimental unit is assigned to a treatment completely at random • An example • A farmer wants to test the effects of a fertilizer • We choose a set of plants to receive the treatment • We randomly assign plants to receive different levels of fertilizer • This has similarities to completely random sampling

26. Chapter 1 – Section 5 • We control as many factors as we can • Amount of watering • Method of tilling • Soil acidity • We control as many factors as we can • Amount of watering • Method of tilling • Soil acidity • Randomization decreases the effects of uncontrolled factors • Rainfall • Sunlight • Temperature

27. Chapter 1 – Section 5

28. 1 2 3 5 4 Chapter 1 – Section 5 • Learning objectives • Define designed experiment • Understand the steps in designing an experiment • Understand the completely randomized design • Understand the matched-pairs design • Understand the randomized block design

29. Chapter 1 – Section 5 • A matched-pairdesignis when the experimental units are paired up and each of the pair is assigned to a different treatment • A matched-pairdesignis when the experimental units are paired up and each of the pair is assigned to a different treatment • A matched pair design requires • Units that are paired (twins, the same person before and after the treatment, …) • Only two levels of treatment (one for each of the pair) • A matched-pairdesignis when the experimental units are paired up and each of the pair is assigned to a different treatment • A matched pair design requires • Units that are paired (twins, the same person before and after the treatment, …) • Only two levels of treatment (one for each of the pair) • An example • A subject before receiving the medication • The same subject after receiving the medication

30. Chapter 1 – Section 5 • Test whether students learn better while listening to music or not • Match students by IQ and gender (to control those factors) • Randomly choose one of each pair (to decrease the effects of other uncontrolled factors • Assign that one to a quiet room and the other to a room with music (the treatment) • Administer the test and analyze the test scores

31. Chapter 1 – Section 5

32. Chapter 1 – Section 5 • An example • We are testing the effects of treatments A, B, and C on soybean plants • Assume that group 1 is treated with A and group 2 is treated with B • Assume that Chemgro plants have higher yields than Pioneer plants • Assume that group 1 has more Chemgro plants (happens because of randomization) than group 2

33. Chapter 1 – Section 5 • If group 1 (treatment A) has higher yields than group 2 (treatment B) • Is this because treatment A is more effective than B? • Is this because there are more Chemgro plants in group 1? • If group 1 (treatment A) has higher yields than group 2 (treatment B) • Is this because treatment A is more effective than B? • Is this because there are more Chemgro plants in group 1? • It is not possible to distinguish • The effects of Treatment A versus B • The effects of Chemgro versus Pioneer • If group 1 (treatment A) has higher yields than group 2 (treatment B) • Is this because treatment A is more effective than B? • Is this because there are more Chemgro plants in group 1? • It is not possible to distinguish • The effects of Treatment A versus B • The effects of Chemgro versus Pioneer • When two effects cannot be distinguished, this is called confounding

34. Summary: Chapter 1 – Section 5 • The planning for designed experiments is crucial to the success of the experiment • A double-blind implementation of experiments reduces the amount of changes in behavior • There are different good methods for assigning treatments to experimental units • Completely random • Matched-pairs • Randomized blocks