Question
In: Statistics and Probability
A split-plot experiment was conducted in a completely randomized design with whole-plot treatments as a 2x2...
A split-plot experiment was conducted in a completely randomized design with whole-plot treatments as a 2x2 factorial (factors A and B) and the subplot treatments as three levels of factor C. There are four whole-plot replicants per whole plot treatment. Assume all treatment effects were fixed and include all interactions between factors.
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Write the linear model for the experiment. Identify each of the model effects/components and list the number of levels for each effect. Make sure to specify which effects are random and which are fixed.
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Create the ANOVA table for the experiment, just including the name of the source, degrees of freedom, and expected mean squares
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Write out the appropriate F-ratio for each of the treatment effects and all interactions.
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PS：Part b of homework 5 was proving a little more difficult than intended. For some of the ANOVA tables in chapter 14 slides I added a column for the expected MS to make part of the question a little easier. In your solutions you'll want to replace any letters with their values if the problem gives them. If the problem doesn't, just use the notation.
Solutions
orchestra answered 1 year agoRelated Solutions
A split-plot experiment was conducted in a completely randomized design with whole-plot treatments as a 2x2...
A split-plot experiment was conducted in a completely randomized
design with whole-plot treatments as a 2x2 factorial (factors A and
B) and the subplot treatments as three levels of factor C. There
are four whole-plot replicants per whole plot treatment. Assume all
treatment effects were fixed and include all interactions between
factors.
1. Write the linear model for the experiment. Identify each of
the model effects/components and list the number of levels for each
effect. Make sure to specify which...
True or False 1. In a completely randomized experimental design with 10 treatments, if the sample...
True or False
1. In a completely randomized experimental design with 10
treatments, if the sample size (n) is 40 and α = 0.05, then tukey’s
critical value is qα = 4.82.
2. The Chi-Square distribution is a right-skewed distribution
that is dependent on two degrees of freedom (the numerator df and
the denominator df).
An irrigation experiment was conducted in a randomized complete block design in a Lavencia orange grove....
An irrigation experiment was conducted in a randomized complete
block design in a Lavencia orange grove. Six irrigation treatments
were used in eight blocks of trees. The data below are the weight
in pounds of harvested fruit from each plot.
a. Consider the flood irrigation method to be the standard
practice. Use the Dunnett method to test the difference between the
flood irrigation and each of the other methods
b. Calculate the F-statistic assuming a completely randomized
one-way design. How...
Case Study: Applying a Completely Randomized Design (Detecting Changes in Consumer Comfort) In a study conducted...
Case Study: Applying a Completely Randomized Design
(Detecting Changes in Consumer Comfort)
In a study conducted to investigate browsing activity by
shoppers, each shopper was initially classified as a nonbrowser,
light browser, or heavy browser. For each shopper, the study
obtained a measure to determine how comfortable the shopper was in
a store. Higher scores indicated greater comfort. Suppose the
following data were collected:
Nonbrowser
Light
Browser
Heavy Browser
4
5
5
5
6
7
6
5
5
3
4 ...
The following data are from a completely randomized design.
You may need to use the appropriate technology to answer this
question.
The following data are from a completely randomized design.
Treatment
A
B
C
162
142
126
142
157
123
166
123
138
144
142
140
148
137
150
168
157
127
Sample
mean
155
143
134
Sample
variance
135.6
166.0
108.4
(a)
Compute the sum of squares between treatments.
(b)
Compute the mean square between treatments.
(c)
Compute the sum of squares due to error.
(d)
Compute the...
Given data from a completely randomized design experiment: Treatment 1 = {3.8, 1.2, 4.1, 5.5, 2.3}...
Given data from a completely randomized design experiment:
Treatment 1 = {3.8, 1.2, 4.1, 5.5, 2.3}
Treatment 2 = {5.4, 2.0, 4.8, 3.8}
Treatment 3 = {1.3, 0.7, 2.2}
a.) Calculate the treatment means and variances for each of the
3 treatments above.
b.) Use statistical software to complete the ANOVA table.
Source
df
SS
MS
F
Treatment
Error
Total
c.) In words, what is the null and alternative hypotheses for
the ANOVA F-test?
d.) Test the null hypothesis that...
i.Briefly describe the three methods of CRD( completely randomized design) , RCBD(randomized complete block design), FD(factorial design)....
i.Briefly describe the three methods of CRD(
completely randomized design) , RCBD(randomized complete block
design), FD(factorial design). You can present this part using
Table or Figure. ii.What are the similarities and differences
between CRD( completely randomized design , RCBD(randomized
complete block design), FD(factorial design)? You can present
this part using Table or Figure.
Data is collected from a completed randomized design for comparing two treatments A and B: A:...
Data is collected from a completed randomized design for
comparing two treatments A and B:
A: 25, 24, 22
B: 27, 30, 29
The experimenter is interested in finding out if treatment B is
better than treatment A. Find the p-values using both the
randomization test and the t-test and then make a conclusion (alpha
= 0.05)
Students in a business statistics course performed a completely randomized design to test the strength of...
Students in a business statistics course performed a completely
randomized design to test the strength of four brands of trash
bags. One-pound weights were placed into a bag, one at a time,
until the bag broke. A total of 24 bags, 6 for each brand, were
used. The data in the accompanying table give the weight (in
pounds) required to break the trash bags. Brand 1 Brand 2 Brand 3
Brand 4 31 42 34 22 40 36 38 16...
The following data are from a completely randomized design. In the following calculations, use α =...
The following data are from a completely randomized design. In
the following calculations, use α = 0.05 (level of
significance)
Treatment 1
Treatment 2
Treatment 3
63
82
69
47
72
54
54
88
61
40
66
48
sample mean
51
77
58
sample variance
96.67
97.34
81.99
a. Use analysis of variance to test for a significant difference
among the means of the three treatments.
b. Use Fisher’s LSD procedure to determine which means are
different.
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