Assignment 5

Due Date

Friday, February 17, 2012

Data Source

The data for this assignment are from Michael Crawlely's web site.

Overview

The data are the results of a toxicology bioassay. Crawley (2002) describes the experiment as follows (p. 532). "Three products (A, B, and C) were applied to batches of insects in circular arenas. The initial numbers of insects (n) varied between 15 and 24. The insecticides were each applied at 17 different doses, varying on a log scale from 0.1 to 1.7 units of active ingredient per square metre. The number of insects found dead after 24 hours ("dead") was counted.

Questions

1. Fit a model that allows each insecticide product to have its own dose-response relationship. Is there evidence that the dose-response relationship varies by product?
2. Is it valid here to use the residual deviance to assess the fit of this model? If so, carry out the test. What are your conclusions?
3. Can the model of Question 1 be simplified further? For instance, does it appear that all three products are different from each other? If not, try simplifying the model by collapsing two of the products into a single category. Fit the model with your new "product" variable.
4. Formally test whether the simplification you carried out in Question 3 can be justified statistically.
5. Graph your final model on a probability scale along with the data. Clearly show the individual dose-response curves of the remaining "products" in your model.
6. Construct odds ratios that allow you to compare how dosage affects the response. Calculate the odds ratios separately for each "product" and interpret your result.
7. Report 95% confidence intervals for the odds ratios in Question 6.

Cited reference

Crawley, Michael J. 2002. Statistical Computing: An Introduction to Data Analysis Using S-Plus. Wiley, New York.

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