Question

An experiment has a single factor with four groups and two values in each group.

a. How many degrees of freedom are there in determining the among-group variation?

b. How many degrees of freedom are there in determining the within-group variation?

c. How many degrees of freedom are there in determining the total variation?

Answer #1

An experiment has a single factor with five groups and three
values in each group. In determining the among-group variation,
there are 4 degrees of freedom. In determining the within-group
variation, there are 20 degrees of freedom. In determining the
total variation, there are 24 degrees of freedom. Also, note that
SSA= 96, SSW=160, SST=256, MSA=24, MSW=8, and
FSTAT=3.
Complete parts (a) through (d).Click here to view page 1 of
the F table.
a. Construct the ANOVA summary table and...

Consider an experiment with six groups, with two values in each.
For the ANOVA summary table shown to the right, fill in all the
missing results.
Source Degrees of Freedom Sum of
Squares Mean Square (Variance) F
Among groups c−1=? SSA=? MSA=2424
FSTAT=?
Within groups n−c=? SSW=7272 MSW=?
Total n−1=? SST=?
Complete the ANOVA summary table.

You conduct a one-factor ANOVA with 6 groups and 5 subjects in
each group (a balanced design) and obtain F=2.67F=2.67. Find the
requested values.
dfbetween=
dfwithin=
You intend to conduct an ANOVA with 5 groups in which each group
will have the same number of subjects: n=25n=25. (This is referred
to as a "balanced" single-factor ANOVA.)
What are the degrees of freedom for the numerator?
d.f.(treatment) =
What are the degrees of freedom for the denominator?
d.f.(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= 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...

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
?
?
?
?
?...

Part of an ANOVA table involving 8 groups for a study is shown
below.
Source of
Variation
Sum of
Squares
Degrees of
Freedom
Mean
Square
F
Between
Treatments
126
_____?
_____?
_____?
Within
Treatments
240
_____?
_____?
(Error)
Total
_____?
67
Complete all the missing values in the above table and fill in
the blanks.
Use α = 0.05 to determine if there is any significant
difference among the means of the eight groups.

There are four treatment groups in the experiment, with 13
lizards within each treatment
T1: Brown lizard, brown leaf
T2: Brown lizard, green leaf
T3: Green lizard, green leaf
T4: Green lizard, brown leaf
Of the categorical variables and their interactions, which is
more biologically important(e.g, which explains more of the
variation in the response variable)? Calculate the percent of
variation explained by each variables
----------------------------------------------------------------------------
Mean of Fitness
Brown leaves
Green leaves
Brown lizard
8.088210
7.157375
Green lizard
9.053549...

A researcher conducted a two-factor research study using two
levels of factor A and four levels of factor B with a separate
sample of n = 6 subjects in each of the eight treatment conditions
(cells). The following table summarizes the results of the
analysis, but it is not complete. Fill in the missing values.
(Hint: Start with the df values)
Source
SS
df
MS
Between Treatments
620
____
Factor A
____
____
____
F A = ____
...

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