1. Chapter 10 Analysis of Covariance
BAE 5333 Applied Water Resources Statistics
Biosystems and Agricultural Engineering Department
Division of Agricultural Sciences and Natural Resources
Oklahoma State University
Source
Dr. Dennis R. Helsel & Dr. Edward J. Gilroy
2006 Applied Environmental Statistics Workshop
and
Statistical Methods in Water Resources

2. Analysis of Covariance Application
Are there more than one regression line?
Are they parallel?
Do they have the same intercept?

3. Additional Examples

4. Analysis of Covariance (ANCOVA)
Technique that is between ANOVA and regression.
Similar to regression with dummy variables.
Covariate
Uncontrolled variable that influences the response but does not interact with any of the other factors being tested.
Removes variation due to covariate, which provides a more precise analysis
If not used, will be reflected in the error term.

5. Two Types of Explanatory Variables
Regression Analysis
Using Dummy Variables
Two Types of Explanatory Variables
Continuous Variable X
Y = b0 + b1 X
Models the relationship with Y
Binary (indicator) variable GROUP
GROUP = 0 or 1
Indicates a group assignment
0 = Winter
1 = Summer

6. Testing for a Shift in Intercept (Assuming Two Parallel Lines)
Y = b0 + b1 X + b2 GROUP
Winter: Group = 0 b2*GROUP = 0
Summer: Group = 1 b2*GROUP = b2
Null Hypothesis
b2 = 0
Alternative Hypothesis
b2 ≠ 0
Y = bo + b1X when GROUP=0 (winter)
Y = bo + b1X +b2 when GROUP=1 (summer)
Or Y = (bo + b2) + b1X
b2 is the shift in the intercept

7. MINITAB Output Conc = b0 + b1 Flow + b2 WET/DRY
Group = WET/DRY
All coefficients are significant at α=0.05, i.e. there is an effect of wet vs. dry weather on flow.
Dry conditions reduce CONC by units.

8. Testing for Different Slopes (Assuming Equal Intercepts)
Y = b0 + b1 X + b3 GROUP X
Null Hypothesis
b3 = 0
Alternative Hypothesis
b3 ≠ 0
Y = bo + b1X when GROUP=0 (winter)
Y = bo + b1X + b3X when GROUP=1 (summer)
Or Y = bo + (b1 + b3) X
b3 is the shift in the slope

9. Testing for Different Slopes and Intercepts
Y = b0 + b1 X + b2 GROUP + b3 GROUP X
Null Hypothesis
b2 = 0 and/or b3 = 0
Alternative Hypothesis
b2 ≠ 0 and/or b3 ≠ 0
Y = bo + b1X GROUP=0 (winter)
Y = bo + b1X + b2 + b3X GROUP=1 (summer)
Or Y = (bo + b2) + (b1 + b3) X

10. Paired Watershed Study
ANCOVA Application
Paired Watershed Study
Paired Watershed Study - tool used to evaluate how land use change effects water quality in a treatment watershed while accounting for climatic variation with a control watershed.
A calibration period is used to establish a relationship between the watersheds and is then compared to the treatment period relationship.
If a significant difference can be found between the two relationships, we can calculate the difference in slopes and/or intercepts.
Treatment Watershed
Control Watershed

11. Paired Watershed Analysis To Evaluate Phosphorus in Beaty Creek, Oklahoma
Andrew Lyon and Daniel Storm
Biosystems and Agricultural Engineering
Oklahoma State University
Treatment Watershed
Control Watershed

12. Eucha–Spavinaw Basin Problem
Poultry production principle industry
2,000 poultry houses produce 85 million birds annually, which produce 100,000 tons of poultry litter (1500 tons P)
Of 48,000 kg/yr of P entering Lake Eucha, 50% comes from runoff from poultry litter applied to permanent pastures and elevated STP.
Centrifugal spreader

13. Eucha–Spavinaw Basin Problem
Poultry House Locations
and Soil Test P Levels
Land Cover
Poultry house complex of 3 houses to 15 houses, note concentration near Decatur on Arkansas side.
Phosphorus Mass Balance Issue!!!!

14. Eucha–Spavinaw Basin History
1997 – City of Tulsa and OCC water quality study found both lakes were nutrient enriched, which lead to excess algal production
1999 – Under EPA Section 319 program, OCC began to implement Best Management Practices (BMPs) in Beaty Creek basin (off-site watering and heavy use areas for cattle, pasture improvement, fencing off of riparian areas, etc.)
December 2001 – City of Tulsa files suite against six poultry integrators and City of Decatur, AR for polluting Tulsa’s water resources
Watershed team supervised by the court-appointed special master

15. Eucha–Spavinaw Basin History
2003 – Out of court settlement resulted in $7.5 million payment from poultry industry to City of Tulsa
During 2003 a full moratorium on litter application in the basin
From 2004 to 2008 at least 1/3 of litter must be transported out of basin
Anyone who uses litter must have approved nutrient management plan
Producers and Ranchers
Court approved watershed management team develop plans

16. Paired Watershed Approach History
1950’s – Inception of approach, primarily used to evaluate effect of forestry practices in Northwest
1980’s – Paired Watershed Studies began to be employed to evaluate BMP effects in agricultural settings
1993 – U.S. EPA adopted a uniform paired watershed study design, approach became the most appropriate for documenting BMP effects over relatively short time periods

17. Paired Watershed Approach Conditions of Use
Requires two watersheds
Control and Treatment
Requires two Periods of study
Calibration and Treatment
Control Watershed has constant management during total duration of study
Treatment Watershed undergoes a change in management during the treatment period, such as implementing BMPs

18. Paired Watershed Approach Conditions of Use
Data are collected in both watersheds
Initial conditions (calibration)
After BMP implementation (treatment)
Two periods are compared
Assumes a quantifiable relationship exists in water quality between the two watersheds
When a change is made in one of the watersheds, then a new relationship will exist
A much shorter period of record can be used compared to using one site

19. Paired Watershed Approach Conditions of Use
Does not assume water quality is the same in each watershed
Assumes both watersheds respond in a predictable manner due to experiencing the same weather
Controls weather influence and other environmental factors, which is the primary reason to use the paired watershed study approach
ANCOVA used to test significance between periods
Regression Analysis is used to quantify differences between periods, if any exists.

20. Paired Watershed Approach Limitations
Basins should be close in proximity to assume they experience the same weather
Basins hydrology should be similar
Bedrock and surficial geology
Slope
Soils
Land cover and landuse
Size

21. Study Results Previous OCC Study
August 1999 OCC began a project to document BMP effectiveness in Beaty Creek Basin
Paired watershed study design used with Little Saline Creek Basin as the calibration watershed
Calibration period: Sept 1999 to Sept 2000
Treatment period: Sept 2003 to Sept 2004
Published in 2005, 14% reduction total P
Practices included riparian management, buffer and filter strips, streambank stabilization, animal waste storage facilities, pasture establishment and management, heavy use areas for cattle production and instillation of septic systems (OCC 2005). Specifically in the Beaty Creek basin, implemented BMPs included protecting 330 acres of riparian area by installing 34 off-site watering facilities and establishing 9.4 miles of fencing. They improved pastures on 7,135 acres in the watershed by reducing nutrient runoff through prescribed grazing strategies, implemented nutrient management plans, and planting 1,683 acres of pasture that was formerly either cropland or poorly vegetated pasture (OCC 2005). Other BMPs were implemented in the basin by the Natural Resource Conservation Service (NRCS) EQIP program. The NRCS only tracks dollars spent on BMP implementation on a county level and not a watershed level, so quantifying the amount spent from this program in the Beaty and Spavinaw Creek basin is very difficult.
Beaty Creek = Treatment
Little Saline Creek = Control

22. Study Methods Build upon existing OCC project
Use full two year calibration and treatment periods
Beaty Creek was paired with Little Saline Creek
Calibration period: Sept 1999 to Sept 2001
Treatment period: Sept 2003 to Sept 2005

23. Study Results Periods were significantly different at the 0.086 level
31% reduction in total P
Due to BMPs, reduced poultry litter application, and possibly other unknown influences

24. Summary and Discussion
Practices implemented in Beaty Creek,
OCC implemented BMPs
NRCS EQIP implemented BMPs
Reduction in poultry litter application, i.e. litter exported out of basin
Analysis showed a 31% total P reduction, 9/2003 to 9/2005 (treatment period)
Actual total P load increased during treatment period
A cause and effect link between BMPs and water quality cannot be shown as all the factors that affect the response to the treatment were not controlled.
An association relationship between these practices and water quality allows us to infer that the reduction in stream total P was likely the result of these activities

25. MINITAB Laboratory 9 Reading Assignment
Chapter 11 Multiple Linear Regression
Section 8 Analysis of Covariance
(pages 316 to 322)
Statistical Methods in Water Resources
by D.R. Helsel and R.M. Hirsch
Paired Watershed Study Design
EPA# 841F93009, NTI# PB , September, 1993
MINITAB
Laboratory 9