Analyzing a Design - Analysis of Covariance - Dealing with Pseudoreplication - Statistics Assignment Help

Assignment Task:

Statistics Assignment Help

Q1. Identifying and Analyzing a Design
Two plots of land were used for an experiment to evaluate the effects on sweet corn plants of the timing of nitrogen application to the soil (early, optimum or late) and two levels of nitrification inhibitor (none, .5 lb/acre). The inhibitor delays conversion of ammonium forms of nitrogen into a more mobile nitrate form to reduce leaching losses. The nitrogen was supplied as pulse-labelled 15N through a drip irrigation system. The response is the percentage of 15N taken up by the plants. The results are in the file Nitrogen.csv, with variables:

 plot    field plot (1 or 2)
 timing of  nitrogen application to the soil (early, optimum or late)
 inhibitor whether the inhibitor was applied (yes or no)

a)    Identify and describe the experimental design.
b)    Describe briefly how the principles of control, randomization and replication would have been applied in this experiment.
c)    Examine an appropriate anova table and interaction plot. What would you conclude?
d)    Carry out any further analysis you deem appropriate, and summarize your findings
e)    The response here is a percentage. Some would suggest using the inverse-sine square root transform sin-1?(y/100) for this

Q2. Unbalanced/Incomplete Design  

With reference to the situation in 

Q1, suppose that one of the experimental units is destroyed by pests, so that the response is missing. Explain how the analysis would be affected. As part of your answer, give the form of the anova table (sources and degrees of freedom). Under what circumstances would the loss of two experimental units lead to an incomplete design? Explain, and give the anova table for this case.

Q3. Analysis of Covariance
Consider again your data from the experiment on sheep in Q1. Previously the animals were placed in blocks based on their weights. Now try an alternative analysis in which the initial live weight of the sheep is used as a covariate, rather than as a blocking variable. Give a full summary of the results and compare with the previous analysis. Detail briefly the advantages and disadvantages of each approach.

Q4. Dealing with Pseudoreplication
The file Bacteria.csv contains the results from an experiment to determine the effects of two soil treatments on the density of bacteria found on the leaf surfaces of sugarbeet. Six plants were grown in an environmental chamber, three in Soil type 1 and three in Soil type 2. Ten samples were taken from each of the six plants. For each sample, a fixed biomass of leaf was homogenised, and a fixed volume of a designated dilution spread on a plate. The bacterial density was then assessed by counting the number of colonies for each plate. The scientists who conducted the experiment have produced the following analysis

Q5. Identifying and Analyzing a Design 
An experiment was carried out to test the effect on egg weight of including molasses in the diet of laying hens at four concentrations (0, 70, 140 and 210 g kg-1). Four groups, each of 48 birds, received each diet in turn, in different orders, for a period of four weeks. Data for the first two weeks after changing diets were discarded. The file Molasses.csv gives the mean egg weight for each group on each diet (based on weighing eggs on weekdays each day of weeks 3 and 4 in each period). 
a)    Identify and describe the experimental design.
b)    Why were the data for the first two weeks of each period discarded?
c)    How would the randomization have been done?
d)    Is there evidence that adding molasses to the diet depresses egg weight? If so, could the relationship be linear?
e)    Assuming that smaller eggs are undesirable, what level of molasses can be safely used in laying hen diets without causing any depression in egg weight? Discuss.

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