Use the following description for Questions 1-2: Assume we design a statistical study where 10 participants try 3 chocolate types (A, B,C) in randomized order for 7 days, i.e., each participant tries 3 types of chocolate (A, B,C) in randomized order every day for 7 days. We are interested in testing if the chocolate type impacts taste preference (response variable, on a scale 0-10). Question 1: What type of study design would you recommend for this study? What is/are the factors? What is/are the block(s)? A.) Latin squares design with two factors and one block. Factors are the Chocolate type (3 levels: A, B, C) and Participant (10 levels: representing 10 participants). Block is Day (7 levels: representing days). B.) Latin squares design with one factor and two blocks. Factor is the Chocolate type (3 levels: A, B, C). Blocks are Participant (10 levels: representing 10 participants) and Day (7 levels: representing days). C.) Latin squares design with two factors and one block. Factors are the Chocolate type (3 levels: A, B, C) and Day (7 levels: representing days). Block is Participant (10 levels: representing 10 participants). D.) Latin squares design with one factor and two blocks. Factor is the Day (7 levels: representing days). Blocks are Chocolate type (3 levels: A, B, C) and Participant (10 levels: representing 10 participants). Question 2: Consider the study design we used in the Question above. Is the following statement true or false: "This study design is an incomplete block design because not all levels of the factor(s) are represented in each block" A.) True B.) False QUESTION 3: Imagine an experiment with a factor that has 9 levels (e.g., coffee made with coffee beans from 9 different countries) and for each level, there are 20 different participants who provide their taste preference. The mean square of the factor representing between factor (coffee) level variation is 40.0 and the mean square of the error (residual) representing within factor (coffee) level variation is 10.0. What would the F test statistic be? A.) 40 B.) 4
Use the following description for Questions 1-2:
Assume we design a statistical study where 10 participants try 3 chocolate types (A, B,C) in
randomized order for 7 days, i.e., each participant tries 3 types of chocolate (A, B,C) in randomized
order every day for 7 days. We are interested in testing if the chocolate type impacts taste preference
(response variable, on a scale 0-10).
Question 1:
What type of study design would you recommend for this study? What is/are the factors? What is/are the block(s)?
A.) Latin squares design with two factors and one block. Factors are the Chocolate type (3 levels: A, B, C) and Participant (10 levels: representing 10 participants). Block is Day (7 levels: representing days).
B.) Latin squares design with one factor and two blocks. Factor is the Chocolate type (3 levels: A, B, C). Blocks are Participant (10 levels: representing 10 participants) and Day (7 levels: representing days).
C.) Latin squares design with two factors and one block. Factors are the Chocolate type (3 levels: A, B, C) and Day (7 levels: representing days). Block is Participant (10 levels: representing 10 participants).
D.) Latin squares design with one factor and two blocks. Factor is the Day (7 levels: representing days). Blocks are Chocolate type (3 levels: A, B, C) and Participant (10 levels: representing 10
participants).
Question 2:
Consider the study design we used in the Question above. Is the following statement true or false:
"This study design is an incomplete block design because not all levels of the factor(s) are represented in
each block"
A.) True
B.) False
QUESTION 3:
Imagine an experiment with a factor that has 9 levels (e.g., coffee made with coffee beans from 9 different countries) and for each level, there are 20 different participants who provide their taste preference. The mean square of the factor representing between factor (coffee) level variation is 40.0 and the mean square of the error (residual) representing within factor (coffee) level variation is 10.0.
What would the F test statistic be?
A.) 40
B.) 4
C.) 0.4
D.) 20
E.) 2
F.) 0.2
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