Question
In: Statistics and Probability
A factorial experiment with four factors is conducted. Factor A is fixed, and factors B, C...
A factorial experiment with four factors is conducted. Factor A is fixed, and factors B, C and D are random. D is nested under C and C is nested under B. The number of levels is 3, 2, 4 and 3 for A, B, C and D, respectively. There are 3 replicates. Assume the restricted model.
a) Write downs the full linear model for the response including all possible interactions.
b) Find the number of degrees of freedom of all sums of squares
c) Write down the expressions for all expected mean squares.
d) Propose F-tests for the significance of all effects. In case an exact F-test is not possible, propose an approximate F-test.
Solutions
orchestra answered 1 year agoRelated Solutions
The calculations for a factorial experiment involving four levels of factor A, three levels of factor...
The calculations for a factorial experiment involving four
levels of factor A, three levels of factor B, and three
replications resulted in the following data: SST = 272, SSA = 25,
SSB = 24, SSAB = 165.
Set up the ANOVA table and test for significance
using = .05. Show entries to 2 decimals, if necessary.
Round p-value to four decimal places. If your answer is
zero enter "0".
Source of Variation
Sum of Squares
Degrees of Freedom
Mean Square
F...
The calculations for a factorial experiment involving four levels of factor A, three levels of factor...
The calculations for a factorial experiment involving four
levels of factor A, three levels of factor B, and three
replications resulted in the following data: SST = 350, SSA = 46,
SSB = 43, SSAB = 195. Set up the ANOVA table and test for any
significant main effects and any interaction effect. Use α = .01.
Use both p-Value and Critical-Value approaches.
Please state exactly what to type into Excel for anova, and
thank you for your time and...
The calculations for a factorial experiment involving four levels of factor A, three levels of factor...
The calculations for a factorial experiment involving four
levels of factor A, three levels of factor B, and three
replications resulted in the following data: SST = 275, SSA = 26,
SSB = 22, SSAB = 174. Set up the ANOVA table. (Round your values
for mean squares and F to two decimal places, and your
p-values to three decimal places.)
Source
of Variation
Sum
of Squares
Degrees
of Freedom
Mean
Square
F
p-value
Factor A
Factor B
Interaction
Error...
The calculations for a factorial experiment involving four levels of factor A, three levels of factor...
The calculations for a factorial experiment involving four
levels of factor A, three levels of factor B, and three
replications resulted in the following data: SST = 298, SSA = 24,
SSB = 21, SSAB = 195.
Set up the ANOVA table and test for significance
using = .05. Show entries to 2 decimals, if necessary.
Round p-value to four decimal places. If your answer is
zero enter "0".
Source of Variation
Sum of Squares
Degrees of Freedom
Mean Square
F...
The calculations for a factorial experiment involving four levels of factor A, three levels of factor...
The calculations for a factorial experiment involving four
levels of factor A, three levels of factor B, and three
replications resulted in the following data: SST = 278, SSA = 28,
SSB = 24, SSAB = 174. Set up the ANOVA table. (Round your values
for mean squares and F to two decimal places, and your
p-values to three decimal places.)
Source
of Variation
Sum
of Squares
Degrees
of Freedom
Mean
Square
F
p-value
Factor A
Factor B
Interaction
Error...
The calculations for a factorial experiment involving four levels of factor A, three levels of factor...
The calculations for a factorial experiment involving four
levels of factor A, three levels of factor B, and three
replications resulted in the following data: SST = 293, SSA = 22,
SSB = 21, SSAB = 195. Set up the ANOVA table and test for
significance using = .05. Show entries to 2 decimals, if necessary.
If your answer is zero enter "0". Source of Variation Sum of
Squares Degrees of Freedom Mean Square F Factor A Factor B
Interaction...
A factorial experiment involving two levels of factor A and three levels of factor B resulted...
A factorial experiment involving two levels of factor A and
three levels of factor B resulted in the following data.
Factor B
Level 1
Level 2
Level 3
Factor A
Level 1
135
89
76
165
65
94
Level 2
125
128
119
95
106
135
Test for any significant main effects and any interaction. Use
α = 0.05.
Find the value of the test statistic for factor A. (Round your
answer to two decimal places.)
Find the p-value for...
A factorial experiment involving two levels of factor A and three levels of factor B resulted...
A factorial experiment involving two levels of factor A and
three levels of factor B resulted in the following data.
Factor B
Level 1
Level 2
Level 3
Factor A
Level 1
135
93
72
165
69
90
Level 2
125
124
123
95
102
139
Test for any significant main effects and any interaction. Use
α = 0.05.
Find the value of the test statistic for factor A. (Round your
answer to two decimal places.)
Find the p-value for...
a. Tom designed a complete factorial experiment with 2 factors. One factor had 4 levels, the...
a. Tom designed a complete factorial experiment with 2 factors.
One factor had 4 levels, the other had 5 levels. For each
combination of levels of factors, there were 6 replicates. In the
ANOVA table associated with this design, what were the degrees of
freedom of the interaction?
a. 7, b. 12, c. 20, d. 24, e. 30.
b. In the above ANOVA table of the complete factorial
experiment, suppose we want to test the significance of the
main effect...
Consider an experiment with four independent variables: A, B, C, and D. Factor A has 3...
Consider an experiment with four independent variables: A, B, C,
and D.
Factor A has 3 levels and is a between-subjects variable; Factor
B has 2 levels and is a within-subjects variable; Factor C has 2
levels and is a between-subjects variable; Factor D has 3 levels
and is a within-subjects variable.
1. How many “cells” or “conditions” or “groups” are there in
this experiment?
2. If you want to test 10 participants per cell, how many TOTAL
participants will...
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