INSTAT, CAS, UPLBSTAT 162: EXPERIMENTAL DESIGNS
Stat 162
Experimental Designs
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STAT 162: Experimental Designs - Exercises and Questions, Quizzes of Statistics
A series of exercises and questions related to experimental designs in statistics. It covers topics such as blocking, randomized complete block design (rcbd), latin square design (lsd), and factorial experiments. The questions are designed to test understanding of key concepts and principles in experimental design, making it a valuable resource for students studying statistics.
Typology: Quizzes
2022/2023
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Stat 162
Experimental Designs
For numbers 1 to 3 : A doctor wants to test the effectiveness of the three brands of headache drug (A, B and C) based on time (in minutes) of relief. There were 16 patients with chronic headache problems available for the experiment. These patients are from different age groups, thus, the doctor decided to impose blocking to account the such differences. The following are ages of patients: 20 , 39 , 33 , 23 , 45 , 41 , 25 , 26 , 56 , 58 , 43 , 48 , 37 , 51 , 34 , 55.
- Which of the following form the best blocks for the experiment? I. Block 1 : 20 , 39 , 33 , 23 , 25 , 26 , 37 , 34 Block 2 : 45 , 41 , 56 , 58 , 43 , 48 , 51 , 55 II. Block 1 : 20 , 39 , 33 , 58 , 43 , 48 , 51 , 55 Block 2 : 45 , 41 , 56 , 23 , , 25 , 26 , 37 , 34 A. I only B. II only C. Both I and II D. Neither I nor II
For numbers 1 to 3 : A doctor wants to test the effectiveness of the three brands of headache drug (A, B and C) based on time (in minutes) of relief. There were 16 patients with chronic headache problems available for the experiment. These patients are from different age groups, thus, the doctor decided to impose blocking to account the such differences. The following are ages of patients: 20 , 39 , 33 , 23 , 45 , 41 , 25 , 26 , 56 , 58 , 43 , 48 , 37 , 51 , 34 , 55.
- What is the experimental design of this experiment? A. Two-Factor Factorial Experiment in RCBD B. Two-Factor Factorial Experiment in CRD C. One-way Experiment in RCBD D. One-way Experiment in CRD
4. Which of the following is(are) true about RCBD?
I. Variability within blocks is removed from the experimental
error.
II. It is considered when the set of units has a predictable pattern
of variability.
A. I only B. II only C. Both I and II D. Neither I nor II
6. Which of the following is(are) TRUE if the relative efficiency of
RCBD over CRD is 200 %?
I. CRD is more efficient by 100 % than RCBD with the same
number of replicates.
II. RCBD is 200 % more efficient than CRD with the same number
of replicates.
A. I only B. II only C. Both I and II D. Neither I nor II
7. Which of the following is(are) TRUE about the Latin Square
Design?
I. It takes care of two gradients of the same direction by using
two-dimensional blocking of experimental materials.
II. The number of treatment levels must be equal to the number
of rows and columns in the layout.
A. I only B. II only C. Both I and II D. Neither I nor II
9. Which of the following illustrate(s) a possible layout of LSD
with subsampling with 3 treatment levels and 2 subsamples, if
each box in the layout represents one experimental unit?
A. I only B. II only C. Both I and II D. Neither I nor II
10. Which of the following is(are) TRUE if the relative efficiency of
LSD over CRD is 50 %?
I. There is no gain in precision from blocks.
II. LSD is 50 % more efficient than CRD.
A. I only B. II only C. Both I and II D. Neither I nor II
For numbers 12 to 15 : A factorial experiment laid out in CRD was conducted to determine the effects of types of vaccine (V) and body part (P) where the vaccine was administered on the area of blister (cm 2 ) on the rabbit skin. Included in the experiment are the three types of vaccine (V 1 , V 2 and V 3 ) and two randomly selected body part (P 1 and P 2 ). Each treatment combination was applied to four rabbits.
- The expected mean squares of the interaction is _____. A. 𝜎!"
B. 4 𝜎!"
C. 𝜎$
- 𝜎!"
D. 𝜎$
- 4 𝜎!"
For numbers 12 to 15 : A factorial experiment laid out in CRD was conducted to determine the effects of types of vaccine (V) and body part (P) where the vaccine was administered on the area of blister (cm 2 ) on the rabbit skin. Included in the experiment are the three types of vaccine (V 1 , V 2 and V 3 ) and two randomly selected body part (P 1 and P 2 ). Each treatment combination was applied to four rabbits.
- The F-ratio for testing the effects of body parts is _______. A. MSP/MSE B. MSP/MSV C. MSP/MS(VxP) D. MS(VxP)/ MSP
For numbers 12 to 15 : A factorial experiment laid out in CRD was conducted to determine the effects of types of vaccine (V) and body part (P) where the vaccine was administered on the area of blister (cm 2 ) on the rabbit skin. Included in the experiment are the three types of vaccine (V 1 , V 2 and V 3 ) and two randomly selected body part (P 1 and P 2 ). Each treatment combination was applied to four rabbits.