Background

Wilcoxon & Simulation

Ranking

Conclusions

Water Quality Monitoringof Maryland’s Tidal Waterways
Rosemary K. Lea ,Christopher V. Rackauckasb ,Annie S. Rossc , Nehemias Ulload ,Graduate Assistant: Sai K. Popurie
Faculty Mentor: Dr. Nagaraj Neerchale
Client: Dr. Brian Smith, Maryland Department of Natural Resources
REU Site: Interdisciplinary Program in High Performance Computing
University of Maryland, Baltimore County, www.umbc.edu/hpcreu

Acknowledgments: NSF, NSA, HPCF, CIRC, UMBC, DNR
aBrown Universityb Oberlin Colleged California State University, Bakersfield

Rosemary Le, Christopher Rackauckas, Annie Ross, Nehemias Ulloa

c Colorado State University

e University of Maryland, Baltimore County

HPC REU

1/16

Background

Wilcoxon & Simulation

Ranking

Conclusions

The Chesapeake Bay
The Chesapeake Bay
Largest estuary in theUnited States
Stretches from Havre deGrace, Maryland toVirginia Beach, Virginia
Houses more than 3,600
species of plants andanimals
Commercial andrecreational resource

Courtesy of Maryland Department of Natural Resources
Rosemary Le, Christopher Rackauckas, Annie Ross, Nehemias Ulloa

Connected to many
tributaries, spanning 5states
HPC REU

2/16

Background

Wilcoxon & Simulation

Ranking

Conclusions

Department of Natural Resources (DNR)

Recognizes that the health of the society and the economy
are dependent on the health of the environment
Strives to preserve, protect, restore, and enhance theenvironment for this and future generations
We want to assist the DNR in analyzing and assessing
the water quality of Maryland’s tidal waterways

Rosemary Le, Christopher Rackauckas, Annie Ross, Nehemias Ulloa

HPC REU

3/16

Background

Wilcoxon & Simulation

Ranking

Conclusions

Monitoring Stations and Parameters
Various types of stations,spanning several decades
38 continuous monitoringstation data from 2011
Readings taken every 15
minutes (majority of stations)
Important Parameters:
Dissolved Oxygen
Turbidity (water clarity)
Chlorophyll (algae growth)
pH (water acidity)

Rosemary Le, Christopher Rackauckas, Annie Ross, Nehemias Ulloa

Courtesy of www.eyesonthebay.net

HPC REU

4/16

Background

Wilcoxon & Simulation

Ranking

Conclusions

What Constitutes “Failure”?

Courtesy of www.eyesonthebay.net

Parameter
D. Oxygen (severe)
Dissolved Oxygen
Turbidity
Chlorophyll
pH

Failure Threshold< 3mg/L< 5mg/L> 7 NTU> 30µg/L< 5.5 or > 8.5Rosemary Le, Christopher Rackauckas, Annie Ross, Nehemias Ulloa

Time Frame
June to September
June to September
April to September
April to September
April to September
HPC REU

5/16

Background

Wilcoxon & Simulation

Ranking

Conclusions

Station Status

Wilcoxon Signed-Rank Test
Nonparametric test that compares the station’s
median to the failure threshold
In terms of a particular parameter, is the station“Good,” “Bad,” or “Borderline?”
Assumes the distribution is symmetricIn the statistic below, Ri denotes the rank of |xi − thresh|
Test Statistic: S =mX[Ri · sign(xi − thresh)]i=1

Rosemary Le, Christopher Rackauckas, Annie Ross, Nehemias Ulloa

HPC REU

6/16

Background

Wilcoxon & Simulation

Ranking

Conclusions

Wilcoxon Results
Wilcoxon Assessment Table (a subset)
Station Name
AnnapolisCIBS
Betterton
Big Annemessex
Bishopville
Budds Landing
Chesapeake Y. Club
Corisca River
Downs Park
Flats
..
.

DO5
Good
Good
Good
Bad
Good
Good
Good
Good
Good
..
.

Rosemary Le, Christopher Rackauckas, Annie Ross, Nehemias Ulloa

DO3
Good
Good
Good
Good
Good
Good
Good
Good
Good
..
.

Turbidity
Good
Good
Good
Good
Good
Good
Good
Good
Good..
.
HPC REU

Chlorophyll
BadGoodGoodBad
Bad
Bad
Bad
BadGood..
.
7/16

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Wilcoxon & Simulation

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Conclusions

Simulation
The Wilcoxon Test assumes the distribution is symmetric, but
not all parameters are distributed as such
Assesses the validity of the Wilcoxon’s Test and the effect ofviolating assumption of symmetry

Rosemary Le, Christopher Rackauckas, Annie Ross, Nehemias Ulloa

HPC REU

8/16

Background

Wilcoxon & Simulation

Ranking

Conclusions

Gamma Distributions
Gamma distributions with rate = 1 and various shape values

Rosemary Le, Christopher Rackauckas, Annie Ross, Nehemias Ulloa

HPC REU

9/16

Background

Wilcoxon & Simulation

Ranking

Conclusions

Simulation Results

Wilcoxon Type I Error
Wilcoxon test applied to samples drawn from the gamma
distribution before and after log-transformation
BeforePPratePP

shape2
4
10
50
100

PPPP
P

After

1

10

1

10

0.87370.50540.17160.03040.02040.86920.50420.17010.01450.01280.21830.10030.04070.01310.01160.2207
0.09770.03350.02970.0205Rosemary Le, Christopher Rackauckas, Annie Ross, Nehemias Ulloa

HPC REU

10/16

Background

Wilcoxon & Simulation

Ranking

Conclusions

Ranking of Stations

Ranking of Stations
In order to rank stations, one must perform a comparison
between each pair of stations to see whether the stations are
significantly differentThis results in n2 tests where n is the number of stations
In order to control for Type I Error over the whole study,
multiple comparison tests must be used

Rosemary Le, Christopher Rackauckas, Annie Ross, Nehemias Ulloa

HPC REU

11/16

Background

Wilcoxon & Simulation

Ranking

Conclusions

Tukey Test

Tukey Test
Tukey’s Test is a commonly used multiple comparison test
It performs multiple ANOVA’s using a test statistic q in theStudentized Range Distribution
Being based on ANOVA tests, it is designed to test means
One can use proportions to make a Tukey-like test ofproportions by using a variance transformation
qqq
X
X +1
10
p = 2 arcsin n+1 + arcsin n+1 , SE = n410.35+ n410.35
A +0.5
B +0.5
Test Statistic: q =pA0 −pB0
SE

where X is the number of readings above the threshold and n is
the number of observations in the sample (station).
Rosemary Le, Christopher Rackauckas, Annie Ross, Nehemias Ulloa

HPC REU

12/16

Background

Wilcoxon & Simulation

Ranking

Conclusions

Bonferroni

Bonferroni’s Adjustment
Bonferroni’s method is to adjust α for alln2



tests

The probability that there is a false-positive in events A or B
is p(A) + p(B)Thus since there are n2 tests, by dividing α by n2 we getthat the total probability of a Type 1 Error is α
Therefore the adjustment is simply to let α = αn0 where α0 is(2)the chosen α

Rosemary Le, Christopher Rackauckas, Annie Ross, Nehemias Ulloa

HPC REU

13/16Background

Wilcoxon & Simulation

Ranking

Conclusions

Benjamini-Hochberg
The Benjamini-Hochberg Method
While the Bonferroni method uses the traditional Type I Error
definition, the Benjamini-Hochberg method uses what’s
known as the Familywise Type I Error
Familywise Type I Error: The probabily of ”false discoveries”
α is the fraction of tests with false-positive rejections
The method is as follows:
1

Sort the p-values p(1) . . . p(m) where m is the number of tests

2kFinding the largest k such that p(k) ≤ mα3

Reject p(1) . . . p(k) .

Rosemary Le, Christopher Rackauckas, Annie Ross, Nehemias Ulloa

HPC REU

14/16

Background

Wilcoxon & Simulation

Ranking

Conclusions

Oxygen (5mg/L) — Ranking of continuous monitoring stations
with respect to its Percent Failure (% Fail) , the Tukey Test (TT),the Bonferroni Test (Bonf), Benjamini-Hochberg Method (BH),
and the Bayesian Ranking Method (BRM).
Station Name

% FailTT

Bonf% FailMean

Betterton
Havre de Grace
Flats..
.

000.0001..
.

1
11..
.

111..
.

1
13..
.

452..
.

Little Monie
Masonville (bottom)
Goose (bottom)

0.80210.80400.8981363638363638363638373638

Rosemary Le, Christopher Rackauckas, Annie Ross, Nehemias Ulloa

BH

HPC REU

15/16

Background

Wilcoxon & Simulation

Ranking

Conclusions

Conclusions
Conclusions
Wilcoxon— The Bay and its tributaries appear to be in goodcondition for all parameters except chlorophyll
Simulation— Log-transformation of the data substantiallyreduces Type I error, however the error is still large
Ranking—The Bonferonni Adjustment appears to be themost conservative grouping method while theBenjamini-Hochberg Method appears to be the least

References
For complete details of all our projects, please see
the Project Technical Report:
HPCF–2012–12 www.umbc.edu/hpcf > Publications.
For more information about the parameters and stations,please visit: www.eyesonthebay.net
Rosemary Le, Christopher Rackauckas, Annie Ross, Nehemias Ulloa

HPC REU

16/16