WORTH: 15% of class mark
FORMAT: Answers to the questions posed below, maximum of 10 pages
DUE: January 27, 2017. A hard copy is due at the beginning of class. Late assignments will not be accepted.
RETURN: I will have these marked for you by February 3, 2017.
Readings
- Required reading: Hornung RW and Reed LD. Estimation of average concentration in the presence of non-detectable values. Applied Occupational and Environmental Hygiene 1990;5:46-51 (Hornung & Reed)
- Required reading: Finkelstein MM, Verma DK. Exposure estimation in the presence of non-detectable values: Another look. American Industrial Hygiene Association Journal 2001;62:195-198 (Finkelstein & Verma)
You will need the following files to do this assignment
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File to Download
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What is in the File
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.xls file for the Radon Data
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The .xls file on that page includes the exposure data that you will use for the rest of the course.
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Spreadsheet program for the MLE method, written by Finkelstein and Verma, 2001, and described in their article cited above. This version has been expanded to fit the radon data.
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An explanation of how to use the spreadsheet program by Finkelstein and Verma, 2001.
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For your assignment, please answer the following questions
1. First consider the following overview questions about censored data:
a. What are “censored” data?
b. What are typical reasons in occupational or environmental hygiene that data might be left-censored?
c. What are the usual methods for dealing with left-censored data and what are the problems with these methods?
d. What are situations in occupational or environmental hygiene when data might be right-censored?
(4 marks)
2. Based on the arguments presented in the article by Hornung and Reed and the course dataset, what value would you substitute for each non-detectable value to estimate the mean concentration?
Please indicate the reasons for your choice, including a description of the methods described by Hornung and Reed, and the methods and results of the calculations/analyses you did to come to your conclusion.
(3 marks)
3. Use the methods presented in the article by Finkelstein and Verma to calculate the geometric mean and geometric standard deviation of the concentrations using “maximum likelihood methods”. (Use the MLE LOD Template.xls with the course data).
How does this geometric mean and geometric standard deviation compare with the ones that would be estimated using L/2 and L/√2 as suggested in Hornung and Reed?
Based on the Finkelstein and Verma method and the Hornung and Reed method, what substitute value would you use for data below detection limits in the dataset? Please explain your rationale.
(3 marks)
For questions 4 through 7, first substitute your chosen value for the concentrations that were below detection limits.
4. Use your statistics program to plot two frequency distributions and two Q-Q plots for the concentration data:
- one untransformed and
- one log-transformed (logarithms to the base e)
Make sure that your histograms have at least 50 “intervals” and that all plots are properly labelled.
(2 marks)
5. Use your statistics program to determine the arithmetic mean, log mean, geometric mean, arithmetic standard deviation, log standard deviation, and geometric standard deviation of the concentration data. (Please describe your methods and show your formulae.)
(2 marks)
6. Use your statistics program to do a Shapiro-Wilks goodness of fit test for normality of the concentration data, both untransformed and log-transformed. Indicate the meaning of the result.
(2 marks)
7. Do you think the data approximate a log-normal distribution? Why and/or why not? Please consider all possible arguments.
(4 marks)
