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

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

Additional Examples

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.

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

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

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 288.9 units.

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

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

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

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

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

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!!!!

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

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

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

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

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

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.

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

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

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

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

Summary and Discussion Practices implemented in Beaty Creek, 2001-2003 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

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# PB94-154820, September, 1993 MINITAB Laboratory 9