Question

Consider a two-way ANOVA with two levels for factor A, four levels for factor B, and four replicates in each of the 88 cells, with SSA=25, SSB=30, SSE=120, and SST=280. Complete parts (a) through (d).

a) Form the ANOVA summary table and fill in all values in the body of the table.

b) At the 0.01 level of significance, is there an effect due to factor A?

c) At the 0.01 level of significance, is there an effect due to factor B?

d) At the 0.01 level of significance, is there an interaction effect?

Answer #1

a)

Source | SS | df | MS | F | p vlaue |

Factor A | 25 | 1 | 25.00 | 5.71 | 0.0250 |

Factor B | 30 | 3 | 10.00 | 2.29 | 0.1044 |

Interaction | 120 | 3 | 40.00 | 9.14 | 0.0003 |

error | 105 | 24 | 4.38 | ||

total | 280 | 31 |

b)

as p value for factor A is higher than 0.01 ; effect due to factor A is not significant.

c)

as p value for factor B is higher than 0.01 ; effect due to factor B is not significant.

d)

as p value for interaction is lower than 0.01 ; effect due to interaction is significant.

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= 248, SSA= 22,
SSB= 21, SSAB= 155.
Set up the ANOVA table and test for significance using alpha=
.05 . Show entries to 2 decimals, if necessary. If the answer is
zero enter “0”.
Source of Variation
Sum of Squares
Degrees of Freedom
Mean Square
F
p-value
Factor A
Factor B
Interaction
Error
Total

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 = 291, SSA = 20,
SSB = 24, 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...

A two-way analysis of variance experiment with no interaction is
conducted. Factor A has three levels (columns) and Factor
B has six levels (rows). The results include the following
sum of squares terms:
SST = 390.8 SSA = 238.5 SSE =
69.9
a. Construct an ANOVA table. (Round
intermediate calculations to at least 4 decimal places. Round
"SS" to 2 decimal places, "MS" to 4 decimal
places, "F" to 3 decimal places.)
b. At the 10% significance level, can you...

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 = 284, SSA = 29,
SSB = 24, SSAB = 176. 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 B, and three
replications resulted in the following data: SST = 282, SSA =
28,SSB = 23, SSAB = 173. 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
?
?
?
?
?...

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=286, SSA=24,
SSB=22, SSAB=185..
Set up the ANOVA table and test for significance using a=.05.
Show entries to 2 decimals, if necessary. If the answer is zero
enter “0”.
Source of Variation
Sum of Squares
Degrees of Freedom
Mean Square
F
p-value
Factor A
Factor B
Interaction
Error
Total
The -value for Factor A is...

A two-way analysis of variance experiment with no interaction is
conducted. Factor A has three levels (columns) and Factor
B has seven levels (rows). The results include the
following sum of squares terms:
SST = 346.9 SSA = 196.3 SSE =
79.0
a. Construct an ANOVA table. (Round
intermediate calculations to at least 4 decimal places. Round
"SS" to 2 decimal places, "MS" to 4 decimal
places, "F" to 3 decimal places.)
Source
SS
df
MS
F
p-value
Rows
Columns...

The following observations were obtained when conducting a
two-way ANOVA experiment with no interaction.
Click here for the Excel Data File
Factor A
Factor B
1
2
3
4
X¯¯¯jX¯j for Factor
B
1
3
4
3
5
3.750
2
8
10
9
8
8.750
3
12
16
14
13
13.750
X−iX−i for Factor A
7.667
10.000
8.667
8.667
X¯¯¯¯¯¯¯ = 8.7500X¯¯ = 8.7500
a. Calculate SST, SSA,
SSB, and SSE. (Round intermediate
calculations to at least 4 decimal places....

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: ,STT = 261, SSA=21,
SSB=22, SSAB=165
Set up the ANOVA table and test for significance using a=.05 .
Show entries to 2 decimals, if necessary. If the answer is zero
enter “0”.
Source of Variation
Sum of Squares
Degrees of Freedom
Mean Square
F
p-value
Factor A
Factor B
Interaction
Error
Total
The -value for...

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 = 269, SSA = 26,
SSB = 21, SSAB = 171. 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...

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