Project - Hazardous Waste and Statistical Analysis
Materials
copyrighted, March 2002 by Greg Langkamp and Joe Hull
| Notes to the Instructor |
Exercise # 6 links the topics of normal distributions with hazardous waste. In this exercise, the students were presented with hazardous waste production data from the Federal EPA's Biennial Reporting System, the only nationwide, uniform database on hazardous waste generation and management (see student background information). The exercise focused on just the hazardous waste categorized and monitored under the Resource Conservation and Recovery Act (RCRA). RCRA waste, such as lead and toluene, is assigned to one of 500 federal hazardous waste codes. Statewide data can be found in the Biennial Reporting System (BSR) database at the Right-to-Know website:http://www.rtk.net/rtkdata.html.
We pre-selected for the students 12 populous states, and identified the most populous counties (about 30 per state), to ensure a reasonably-sized sample and ensure that counties reported data for most years. We provided 1990 population data for every county in the 12 states, taken from a US census web site (http://www.census.gov/population/censusdata/90den_stco.txt). Therefore, much of the "grunt work" was done in advance for the students, however the alternative would have been extremely time consuming and would have diverted the focus away from the mathematical and environmental analysis.
Each group of students is presented with a data sheet (see data sheet for
Illinois given at the bottom of this page). We have
students inspect the data and make observations. Because
the RCRA waste production sometimes fluctuate wildly (up to two orders of
magnitude) from biennium to biennium the students calculated the mean RCRA
waste production over the 8 year period for each of the 30 counties in their
state. The county-by-county mean
data is fairly skewed for each state. Our goal was to obtain hazardous waste
data that showed an approximately normal distribution, but with outliers. Students
progressively work towards obtaining a normal distribution by computing per
capita waste production, and then afterwards, transforming the data using
logarithms. Finally, students investigate a regulatory scheme based upon z-scores.
A few additional notes for the instructor:
1. As with all data,
the reliability and meaning of the RCRA waste production values should be
questioned immediately. Note Madison County, where waste generated increased
from 48 kilotons in 1989 to 9.5 Megatons in 1991, a factor of 200. The
students should be asked to identify such variability among the data, comment
on or explain its possible origins, and draw a tentative conclusion about
reliability.(See question #2) The EPA web site also discusses data reliability.
2. The students normalize the RCRA waste generation data by population,
and then by also logging the data. We introduce normalization specifically
in lecture; most students grasp the concept intuitively when it involves population
density. However, other examples of normalizations that don't involve
people need to be introduced, as many students do not readily grasp the very
general applicability of normalization.
3. We came up with an enforcement/regulatory theme ("sticks and carrots") for this waste exercise, which is carried throughout. The enforcement rubric allowed us to introduce a utilitarian aspect to the mathematical analysis at all major steps in this exercise; how would you punish and reward polluters? The students create increasingly more sophisticated punishment/reward schemes, including one that uses z-scores. Are these schemes mathematically sound?
4.
How does the federal, state, county or local government punish and/or reward
polluters? Are their enforcement schemes mathematically sound?
These are tie-in questions that could be addressed in lecture.
See Data Set #003 for individual state data and more instructor suggestions.
| Student Background Information | top of page |
Hazardous waste is any waste that may be considered toxic, flammable
(i.e. burns readily), corrosive, reactive or explosive. Many types of businesses
produce hazardous waste. Some are small businesses such as dry cleaners,
auto repair shops, hospitals, and photo processing centers. Others are larger
firms which may generate large quantities of hazardous waste, such as chemical
manufacturers, electroplating companies, and petroleum refineries.
The Resource Conservation and Recovery Act (RCRA) is the main Federal law that regulates hazardous and other wastes to ensure that they are managed properly. RCRA waste is solid waste assigned a federal hazardous waste code and regulated by RCRA either because it was managed subject to RCRA permitting standards or because it was shipped subject to RCRA hazardous transportation requirements. EPA has a list of specific hazardous wastes, defined by 504 different waste codes. Not all hazardous waste is RCRA waste.
Information on hazardous wastes comes from the Federal EPA's Biennial Reporting System (BRS). BRS contains data from Hazardous Waste Report Forms submitted by regulated hazardous waste generators and handlers. BRS represents the only nationally consistent reporting of information on hazardous waste generation and management activities in the United States. Although the information collected is not designed to measure environmental impact, it is the most comprehensive source available for information on the management and generation of hazardous wastes. The data are collected every other year.
Some hazardous wastes are not picked up in the BRS database. Hazardous wastes that are generated in the home, like mineral spirits and old paint, are not regulated by the federal RCRA program. In addition, not all hazardous waste generators are required to report, some waste is exempted from regulation, and some waste is regulated under other environmental statutes (particularly at the state level). Some facilities may fail to report.
RCRA data for this project were taken from the original BRS database. This database is no longer posted on the EPA’s website, but can be accessed through the Right To Know Network website: http://www.rtk.net/ The 1990 county population data is taken from a US census web site http://www.census.gov/population/censusdata/90den_stco.txt.
| Project # 6 | top of page |
Name _______________________ Name____________________________
RCRA data: 1991=L1, 1993=L2, 1995=L3, 1997=L4
Population data = L5
Compute "mean RCRA waste" for each county, and store the results in list L6. Transfer the mean values to the data sheet. What are the units of measure for the mean?
2. Analyze the data
Find the county with the biggest change in RCRA waste generation from
one biennium to the next: which county, how much waste one year, how much
in the next report? What is the percent change from one biennium to the next?
Such extreme changes in hazard waste production do not seem reasonable, maybe the numbers are in error. But maybe not! Give one reasonable explanation why RCRA waste generation might change so much in one biennium.
Use your TI-83+ to make a frequency histogram of the mean RCRA waste values. (For review information, consult Chapter 3 in your text.) Sketch the histogram on graph paper. Label axes appropriately.
Are the mean RCRA waste values normally distributed? How can you easily tell without doing any computations?
Compute the mean and standard deviation of the mean RCRA waste values. Use the TI-83+ for assistance.
Is the standard deviation less than, equal to, or greater than the mean?
In your opinion, is the standard deviation "small", "medium" or "large"? Explain briefly.
Compute the following 7 numbers:
Do any of the 7 numbers come out negative? ___________ If so, do these numbers have any physical meaning, can you have negative mean RCRA waste in reality? What do the negative numbers tell you?
Sometimes there are data
that seem to be "way out of bounds." These numbers can be accurate
or they can be caused by error. In either case they tend to dominate the
calculations. Statisticians call these numbers outliers; outliers
are numbers that lie more than 3 standard deviations away from the mean.
Are there any outliers in your mean RCRA waste values? If so, what are the
names of the counties?
3. Per Cap Waste
The EPA hires you as a consultant, to impose fines on counties that are
"environmentally bad." Your supervisor suggests that counties
that generate the most RCRA waste should be fined the most. Discuss why this
system might not be fair.
Another method of fines is to punish the people, not the counties. In other words, fine the counties that have the highest mean RCRA waste per capita (per person). Compute the mean RCRA waste per capita for each county. Convert the result so that the units are in pounds per person. (Note: 1 ton = 2000 pounds) Store the final result in L7 and record on the data sheet.
Use your TI-83+ to make a frequency histogram of the per capita mean RCRA waste values. Sketch the histogram on separate graph paper. Label axes appropriately.
What is the mean of the mean per capita RCRA waste? What is the standard deviation? (Use correct symbols when writing values.)
Is the standard deviation large, medium or small compared to the mean?
Measuring spread in skewed
data using standard deviation is problematic because standard deviation is
often many times bigger than the mean. Has normalization by population "improved"
the standard deviation of the data? In other words, is the per capita waste
data less skewed than the unnormalized waste values?
4. Transform the data
When data are skewed to the right, we can often make the distribution
more symmetrical by logging the data. Do this now: log the mean per capita
RCRA values for each county, and store the results in list L8. Record the
logged values on your data sheet. Then sketch a frequency histogram of the
logged values. Include units and labels.
How does the histogram
of the transformed data (log of the per capita mean RCRA values) compare to
the two histograms that you sketched previously?
Compute the mean and standard deviation for the transformed data. Include units of measure.
Is the standard deviation less than, equal to, or greater than the mean?
Is the standard deviation "small", "medium" or "large", as compared to the mean? Explain briefly.
For the transformed data, calculate the 7 numbers:
Use these 7 numbers to determine if the transformed data are normally distributed. Show work.
5. Carrots and Sticks
You have transformed the county data into a distribution that is closer to
normal. Now you come up with the following idea to impose waste fines.
Based on the transformed data, impose the highest fines on counties that lie
more than 3 standard deviations above the mean, impose moderate fines on counties
that lie between 2 and 3 standard deviations above the mean, impose small
fines on counties that lie between 1 and 2 standard deviations above the mean,
and very small fines for those counties between the mean and 1 standard deviation
above the mean. On your data sheet, under the column "st. dev. category",
indicate which counties are in the categories: ">3", "2
to 3", "1 to 2", or "0 to 1".
To reward counties that produce the least amount of RCRA waste per person, you will give waste credits that can be sold in the market. On your data sheet, for those counties whose RCRA wastes are below the mean, mark categories "<-3", "-3 to -2", "-2 to -1", and "-1 to 0".
Now you get good results with this penalty and reward system. Overall, polluters are given monetary incentives to improve their standard deviation score. In fact, you suggest that all states take up your system. Your boss likes the idea, but she has some questions:
Is it possible that in
some state most of the counties would be in the "above 3" or "below
-3" categories? This could be seen as politically "heavy handed",
with lots of money flowing back and forth in fines and credits. What is your
answer?
How would this system
work with a state like South Dakota , whose mean per capita RCRA waste is
very low? Won't most of the counties in South Dakota be getting pollution
credits?
You've convinced your boss that this system will work, but now she has a third question. When two counties lie in the same standard deviation category they are penalized or rewarded the same, even if their mean RCRA waste per capita numbers are different. Is there some way to refine the rewards and incentives so that there is a continuous scale?
A continuous scale can be based on "z-scores" for each county. A z-score is a number that indicates how many standard deviations each county lies above or below the mean. Z-scores are computed with the simple formula:
Here x is each county's
logged per capita mean RCRA waste, xbar is the mean of logged per capita wastes,
and s is the standard deviation. The z-scores are positive if the county
lies above the mean, and negative if they lie below. Fill out the last column
on the data sheet with the z-score for each county; round to 2 decimal places
of accuracy.
Your boss thinks your z-score idea is great. She now gives you enough money to impose fines and give credits. She suggests a $100,000 fine or credit per z-score (fines for positive z-scores, credits for negative z-scores). Will your agency lose money, earn money, or break even? Explain in detail.