The Effects Of Marine Reserves On The Average Density - Management Assignment Help

Assignment Task

Part A: Subtidal surveys

Read the following description of an observational study, and then answer the questions below.

The study was designed to test the effects of marine reserves on the average density of small benthic rocky reef fishes in a standardised habitat, specifically kelp forest at 10 m depth. There were three Locations (namely Leigh, T?wharanui, and Hahei) with a reserve at each. At each Location, six Sites were randomly selected from inside the reserve and six Sites were randomly selected from outside the reserve. At each Site, scuba divers counted fish in eight replicate 5 m by 1 m Transects. The entire survey design was repeated in each of three Years. In each Year, the spatial positions of the Sites were kept constant but the spatial positions of the Transects were varied. There are four factors in this study design: Reserve, Location, Site, and Year.
1. How many total replicates were there across the whole study.[2 marks]

2. Answer the following for each of the four factors: 
a. How many levels are there?[2 marks]
b. Justifying your answer, would you treat the factor as random or fixed?[3 marks]
c. In which other factor (or interaction of factors) is the factor nested (if any)?[3 marks]

3. Which pairs of factors (if any) are crossed?[3 marks] 
Part B: Treatment by Group

The dataset called “Treat.Group.Ass3.csv” is available on Stream. 

An experiment applied a control and two fertiliser treatments (“C”, “T1”, and “T2”) to each of eight groups of plots, with three replicate plots in each group, in a balanced, crossed design. The response variable “Yield” was measured at the end of the experiment. 
1. Write down the model, being sure to define your notation and to articulate any model assumption.[5 marks]

2. With the function aov(), fit an ANOVA model that includesthree terms: Treatment, Group, and the Treatment-Group interaction. Use the output to calculate variance components for the term(s) that you would treat as random effects, and the error term. [5 marks]

3. Show the appropriate F tests for the significance of all three terms in the model. In each case, state the null hypothesis and the conclusion.[4 marks]
4. Fit the equivalent mixed-effects model using the function lme4::lmer(). Show your code and the summary. Are the variance components the same as those given by the ANOVA estimates?[3 marks]

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