In Figure 11.5, we show three combinations of main effects and interactions for a 2 X 2 factorial design. Using the same 2 X 2 structure, with factor A defining the rows and factor B defining the columns, create a set of means that produce each of the following patterns: The main effect for factors A and B, but no interaction. The main effect for factor A and interaction, but no main effect for factor B. The main effect for both factors and interaction (a) Data showing a main effect for factor A but no main effect forfactor B and no interaction.Factor B40OverallM= 20M = 20M = 2030Factor A20Two Levelsof Factor AOverallM = 10M = 10M = 1010OverallOverallM = 15M = 15Factor B(b) Data showing main effects for both factor A and factor B but nointeraction.Factor BTwo Levelsof Factor A40OverallM= 20M= 10M= 3030Factor A20M= 40OverallM = 30M= 2010OverallM = 15OverallM = 35Factor B(c) Data showing no main effect for either factor, but aninteraction.Factor B40OverallM = 15M = 10M = 2030Factor A20OverallM = 15Two Levelsof Factor AM = 20M = 1010OverallM = 15OverallM = 15Factor B

a) The data given showing a main effect for factor A but no main effect for factor B and no…

Answered: In Figure 11.5, we show three…

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

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In Figure 11.5, we show three combinations of main effects and interactions for a 2 X 2 factorial design. Using the same 2 X 2 structure, with factor A defining the rows and factor B defining the columns, create a set of means that produce each of the following patterns:

The main effect for factors A and B, but no interaction.
The main effect for factor A and interaction, but no main effect for factor B.
The main effect for both factors and interaction

(a) Data showing a main effect for factor A but no main effect for
factor B and no interaction.
Factor B
40
Overall
M= 20
M = 20
M = 20
30
Factor A
20
Two Levels
of Factor A
Overall
M = 10
M = 10
M = 10
10
Overall
Overall
M = 15
M = 15
Factor B
(b) Data showing main effects for both factor A and factor B but no
interaction.
Factor B
Two Levels
of Factor A
40
Overall
M= 20
M= 10
M= 30
30
Factor A
20
M= 40
Overall
M = 30
M= 20
10
Overall
M = 15
Overall
M = 35
Factor B
(c) Data showing no main effect for either factor, but an
interaction.
Factor B
40
Overall
M = 15
M = 10
M = 20
30
Factor A
20
Overall
M = 15
Two Levels
of Factor A
M = 20
M = 10
10
Overall
M = 15
Overall
M = 15
Factor B

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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