2. What are the two purposes for Randomized Block Designs? Increase precision of estimates of treatment differences, and power for detecting differences in treatments Broaden the basis for conclusions

3. Exercise 3

4.  - Expected Difference in treatment means σ - standard deviation in experimental units Block 1 Block 2 Block 3 Block 4

5. Why are replicates within a block usually not recommended? Replicates require larger blocks of experimental units → more heterogeneity among experimental units in a block

7. A. B. use randomized block design and randomize the four treatments to four flowers within each type

13. What if there is an interaction between block and treatment? That means differences in treatments depend on the block! Can we draw general conclusions if that is the case? Treatment MS must be significantly larger than error (which is equivalent to interaction in this case) if we want to draw general conclusions!

14. removing treatment differences

26. response was the activity level of the enzyme EROD in the liver. Example

32. Golf Magazine June 2006

33. (a)Define Objectives Determine if tee height affects golf driving distance (b) Identify sources of variation  tee height  Golfer and ability level  brand ball  club  wind speed  repeat swings

34. c) Choose rule to assign experimental units to treatment factors Complete Block Design  Blocks will be Golfers (takes into account differences in ability levels and clubs)  Treatment Factor tee height, each golfer will hit 5 balls from each tee height in a randomized order d) Measurements to be made: 1) distance 2) whether or not ball is on fairway “accuracy” Expected difficulties: miss hit balls may not be representative. Solution 1) use low handicap golfers, 2) warm up 3) use more than 5 balls and don’t count miss hits

38. What if there is an interaction between block and treatment? That means differences in treatments depend on the block! Can we draw general conclusions if that is the case? Treatment MS must be significantly larger than error (which is equivalent to interaction in this case) if we want to draw general conclusions!

40. RCB Design nitrogen timing on wheat Treatment: Timing of Nitrogen application Blocks: Irrigation gradient

41. Latin Square 5  5 Latin-Square laid out in Bettgelert Forest 1929. Study the effects of exposure On 1)Sitka spruce 2) Norway spruce 3)Japanese larch 4) European larch 5) Pinus contorta

42. In LSD every treatment occurs in every row and column Also every row occurs in every column and vise versa

43. . Treatment Factor is tire design: types A, B, C, D Objective to study how different tire designs affect tread life

44. One Blocking Factor is type of car Because tires wear at different rates on different type cars Economy car Luxury Car SUV Muscle Car

45. Another Blocking factor is Tire Position Speed of tire wear also depends on tire position on the car Left Front Right Front Left Rear Right Rear

46. Why not include interactions?

48. Therefore Use a Latin Square Design Tire Position CarLeft FRight FLeft RRight R EconomyABCD LuxuryBCDA SuvCDAB MuscleDABC Ignoring Column Blocks this is a RCB in Rows Ignoring Rows this is a RCB in columns

53. Example Dairy Cow Experiment Treatment is Diet: Response is Milk Yield 1. Row Block is Cow 2. Column Block is period Calfing------------> Milk Yield Diet 1 Diet 2 Diet 3

56. United States The FDA considers two products bioequivalent if the 90% CI of the relative mean Cmax, AUC(0-t) and AUC(0-∞) of the test (e.g. generic formulation) to reference (e.g. innovator brand formulation) should be within 80.00% to 125.00% in the fasting state. Although there are a few exceptions, generally a bioequivalent comparison of Test to Reference formulations also requires administration after an appropriate meal at a specified time before taking the drug, a so-called "fed" or "food-effect" study. A food-effect study requires the same statistical evaluation as the fasting study, described above.

60. Blocks - Homogeneous Groups of Experimental Units Reduce variance of experimental error RE RBF Conclusions apply to population represented by all blocks Latin Square Design