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

Expert Solution

Sol:


Related 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...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT