1. Section 4.3
Day 3

2. Factors and Levels
Factor: explanatory variable, usually categorical, in a randomized experiment or observational study

3. Factors and Levels
Factor: explanatory variable, usually categorical, in a randomized experiment or observational study
Level: one of the values or categories making up a factor

4. Factors and Levels

5. Factors and Levels

6. Factors and Levels

7. Factors and Levels
Levels

8. Combinations of levels are the ?

9. Treatments

10. If you only have one factor, then the levels and treatments are the same things.

11. For next example, identify:
a) factors
b) levels
c) treatments
d) experimental units
e) response variable

12. A botanist was interested in determining the effects of scheduled watering (three days a week or daily) and the use of fertilizer (no fertilizer, traditional, or organic) in hopes of increasing the heat rating of jalapeño peppers. The botanist conducted his own experiment, assigning each combination of watering schedule and type of fertilizer to three plots at each of four chosen locations that had similar soil and full sun. The average final heat rating for each plot was then recorded at the end of the growing season.

13. For next example, identify:
a) factors
b) levels
c) treatments
d) experimental units
e) response variable

14. A botanist was interested in determining the effects of scheduled watering (three days a week or daily) and the use of fertilizer (no fertilizer, traditional, or organic) in hopes of increasing the heat rating of jalapeño peppers. The botanist conducted his own experiment, assigning each combination of watering schedule and type of fertilizer to three plots at each of four chosen locations that had similar soil and full sun. The average final heat rating for each plot was then recorded at the end of the growing season.

15. For next example, identify:
a) factors
b) levels
c) treatments
d) experimental units
e) response variable

16. A botanist was interested in determining the effects of scheduled watering (three days a week or daily) and the use of fertilizer (no fertilizer, traditional, or organic) in hopes of increasing the heat rating of jalapeño peppers. The botanist conducted his own experiment, assigning each combination of watering schedule and type of fertilizer to three plots at each of four chosen locations that had similar soil and full sun. The average final heat rating for each plot was then recorded at the end of the growing season.

17. For next example, identify:
a) factors
b) levels
c) treatments
d) experimental units
e) response variable

18. Treatments

19. For next example, identify:
a) factors
b) levels
c) treatments
d) experimental units
e) response variable

20. A botanist was interested in determining the effects of scheduled watering (three days a week or daily) and the use of fertilizer (no fertilizer, traditional, or organic) in hopes of increasing the heat rating of jalapeño peppers. The botanist conducted his own experiment, assigning each combination of watering schedule and type of fertilizer to three plots at each of four chosen locations that had similar soil and full sun. The average final heat rating for each plot was then recorded at the end of the growing season.

21. Experimental units are the 72 plots
(assigning each combination of watering schedule and type of fertilizer to three plots at each of four chosen locations)
6(3)(4) = 72

22. For next example, identify:
a) factors
b) levels
c) treatments
d) experimental units
e) response variable

23. A botanist was interested in determining the effects of scheduled watering (three days a week or daily) and the use of fertilizer (no fertilizer, traditional, or organic) in hopes of increasing the heat rating of jalapeño peppers. The botanist conducted his own experiment, assigning each combination of watering schedule and type of fertilizer to three plots at each of four chosen locations that had similar soil and full sun. The average final heat rating for each plot was then recorded at the end of the growing season.

24. Designing Experiments to Reduce Variability
Section 4.4
Designing Experiments to Reduce Variability

25. Why do we perform experiments?

26. To establish cause and effect.
Why do we perform experiments?
To establish cause and effect.

27. What is the fundamental principle of good design for experiments?

28. Random assignment of treatments to experimental units
What is the fundamental principle of good design for experiments?
Random assignment of treatments to experimental units

29. Two Types of Variability

30. Two Types of Variability
1) Between-treatment difference: we want this one because it reveals differences between treatments
--which treatment actually is better

31. Two Types of Variability
1) Between-treatment difference: we want this one because it reveals differences between treatments
2) Within-treatment variability: we do not want this one because it obscures differences between treatments

32. Treatment Made Difference?

33. Between-treatment difference
Probably yes.
All results for short days are higher than for any long day.

34. Treatment Made Difference?

35. Treatment Made Difference?
Not so certain here.

36. Within-treatment variability

37. In order to conclude treatments make a difference, the difference between treatments has to be large enough to overshadow the variation within each treatment.

38. In order to conclude treatments make a difference, the difference between treatments has to be large enough to overshadow the variation within each treatment.
We want a large mean difference and a low variability.

39. In order to conclude treatments make a difference, the difference between treatments has to be large enough to overshadow the variation within each treatment.
We want a large mean difference and a low variability.
If the mean difference is near zero, the treatments did not make a difference.

40. 3 Basic Designs for Experiment
1) Completely Randomized Design
2) Randomized Paired Comparison Design
3) Randomized Block Design

41. Completely Randomized Design
Treatments randomly assigned to units without restriction
Treatment groups should be about equal in size

42. Randomized Paired Comparison Design
1) using matched pairs: pairs of similar units are randomly assigned different treatments

43. Randomized Paired Comparison Design
1) using matched pairs: pairs of similar units are randomly assigned different treatments
2) using repeated measures: each treatment is assigned in random order to each unit

44. Blocking
Process of setting up an experiment by dividing the units into groups (blocks) of similar units and then assigning treatments at random within each block
What does blocking help control in the experiment?

45. Blocking
Process of setting up an experiment by dividing the units into groups (blocks) of similar units and then assigning treatments at random within each block
Blocking used primarily to reduce the
within-treatment variation

46. Blocking

47. Which of the three designs do you think is least suitable?
What makes this design less effective than the other two designs?

48. Which of the three designs do you think is least suitable?
Completely randomized design is the least suitable.
What makes this design less effective than the other two designs?

49. Which of the three designs do you think is least suitable?
Completely randomized design is the least suitable.
What makes this design less effective than the other two designs?
All of the individual variability remains as
nothing is done to reduce the within-treatment
variation.

50. Page 274, P29

51. Page 274, P29
a. randomized paired comparison with repeated measures

52. Page 274, P29
b. randomized paired comparison with matched pairs

53. Page 274, P29
c. randomized paired comparison with matched pairs because there may be a residual effect of one or both of the drugs—that is, the drug does not clear out of the bloodstream in the time allowed between treatments

54. Blocking in an experimental design is used
primarily to
A.eliminate the need for random assignment
B.reduce confounding
C.reduce the within-treatment variation
D.eliminate the need for replication
E.reduce the between-treatment variation

55. Blocking in an experimental design is used
primarily to
A.eliminate the need for random assignment
B.reduce confounding
C.reduce the within-treatment variation
D.eliminate the need for replication
E.reduce the between-treatment variation

56. The three components of a well-designed experiment are
A. comparison, randomization, and double- blindness
B. comparison, randomization, and replication
C. comparison, replication, and simple random sampling
D. randomization, replication, and homogeneity
E. comparison, randomization, and homogeneity

57. The three components of a well-designed experiment are
A. comparison, randomization, and double- blindness
B. comparison, randomization, and replication
C. comparison, replication, and simple random sampling
D. randomization, replication, and homogeneity
E. comparison, randomization, and homogeneity

58. When the effects of two variables on a
response variable cannot be distinguished from
each other, the variables are said to be
A. biased
B. blocked
C. confounded
D. stratified
E outliers

59. When the effects of two variables on a
response variable cannot be distinguished from
each other, the variables are said to be
A. biased
B. blocked
C. confounded
D. stratified
E outliers

60. What is the main difference between an observational study and an experimental study?

61. What is the main difference between an observational study and an experimental study?
In an experiment, treatments are randomly assigned to the subjects under study.
In an observational study, the conditions of interest (treatments) are already built in to the subjects.

62. Page 276, E33

63. Page 276, E33
The modified SAT study is a completely randomized design, where each student is randomly assigned to one of two groups, one group for each treatment.

64. Page 276, E33
The modified SAT study is a completely randomized design, where each student is randomly assigned to one of two groups, one group for each treatment.
Experimental units: high school students who want to take the special course

65. Page 276, E33
Factor and levels: The only factor is course taking behavior, and the levels are course or no course

66. Page 276, E33
Factor and levels: The only factor is course taking behavior, and the levels are course or no course
Treatments: course or no course (control)
Only one factor so levels and treatments ar the same

67. Page 276, E33
Factor and levels: The only factor is course taking behavior, and the levels are course or no course
Treatments: course or no course (control)
Response variable: SAT score

68. Page 276, E33
Factor and levels: The only factor is course taking behavior, and the levels are course or no course
Treatments: course or no course (control)
Response variable: SAT score
Blocks: none

69. Questions?
Read through Activity 4.4a on pages before class tomorrow