Fitting a Linear Mixed Model - Efficacy of Different Strains of Rhizobia - Statistics Assessment Answer

Statistics Assessment Answer

To study the efficacy individual clover seeds were planted in small pottles set out on trays in a controlled environment. After a week they were inoculated with the rhizobia. The pottles were then watered regularly and the clover plants were allowed to grow. After a few weeks, the plants were harvested and the amount of dry matter above ground was measured. Each tray had a complete set of the treatments which are the different rhizobia as well as a positive and negative control, so the trays can be treated as blocks in the experiment.

The symbiotic potential is calculated from the harvested dry weight adjusted for the amount that the plants would be expected to grow without any treatment (the negative control) and then as a ratio of the average of the TA1 treatment which is a commonly used commercial strain of rhizobia.

The ideal would be to find some strains that perform as well as the positive control as then the need for additional fertilizer is negated.

The data are in a file called SPTrial.csv.

1. Import the data and draw some graphs to show the important features.

2. Fit a simple analysis of variance model to the data and discuss the general conclusions. (Note I do NOT want a list of all of the possible comparisons that are significant)

3. Fit a random effects model with the Trays as the random effect and the Treatments as fixed effects.

4. Discuss the random effects:-

   1. Do the Trays explain a useful amount of the total variability?

   2. Do you believe that it is reasonable to assume that the variability of the Trays can be modeled by a Normal distribution?

   3. Calculate the simple means for each Tray and compare the rankings with the random effects.

5. The row and column variables can be used to draw a graph of the pottles colored by the residuals to investigate any spatial variability in the results. We would be concerned if there were any areas with high or low residuals. Draw a graph and discuss the spatial distribution of the residuals.

6. What overall conclusions would you draw from the experiment? Are there any strains that appear to be better than TA!?

QUESTION 2

FITTING A GENERALISED LINEAR MIXED MODEL

An experiment was carried out to test the efficacy of various lures to attract wasps to traps. Seven lures were tested along with a commercially available wasp bait and a control of no lure. Six replicates in blocks were set up and the counts of wasps trapped after a certain length of time is recorded. The data are in the file “Trial4.csv”

Lure 1 is known to work well and the others six (Lures 2 to 7) are simpler versions of the Lure 1 which would be cheaper to produce.

1. Use appropriate graphs of the data and discuss what results might be expected from the data.

   1. Do you think there are any Block effects?

2. Fit a Generalised Linear model to the data with fixed effects for both Treatment and Block.

   1. Justify the distribution used for the response variable.

   2. Discuss the model fitted, include comments on the model fit, significance of any effects and residual analysis.

3. Fit a Generalised Linear model to the data with a fixed effect for Treatment and a random effect for Block.

   1. Discuss the model fitted, include comments on the model fit, significance of any effects and residual analysis.

4. Discuss differences between the two models, which do you think better models the data, why do you choose this model.

5. What are the main conclusions from the trial, are they the same for both models? Discuss any differences if there are any.

6. Fit a simpler model using the linear model or analysis of variance functions to the log of the counts. Show the output for your model. How does it vary from the GLM fitted above?

Choose two different multiple comparison procedures, compare the means for a sensible factor. Discuss the results from the two multiple comparisons.

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