Statistical Tools for Analysis. Anne McFarland Texas Institute for Applied Environmental Research (TIAER) Tarleton State University

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1 Statistical Tools for Analysis Anne McFarland Texas Institute for Applied Environmental Research (TIAER) Tarleton State University

2 Monitoring Objectives Focus Watershed Scale Evaluating BMP Effectiveness Quantifying Load Reductions

3 Concentrations & Loads Concentrations represent a point in time Instantaneous effect Units generally mg/l Loads represent a mass over time Cumulative effects Units generally lbs/yr or kg/yr

4 Concentrations to Loads Concentration (mg/l) Load (kg or lbs/day) Need Flow (cfs) or Volume (ft 3 /day)

5 Upstream Downstream

6 Concentration to Load Concentration (mg/l) to Load (lbs/day) ** KNOW YOUR UNITS ** (concentration, mg/l) * (28.32 L/ft 3 ) * (volume, ft 3 /day) = mg/day (mg/day)/(1,000,000 kg/mg) = kg/day (kg/day)*( lbs/kg) = lbs/day Units and Conversion Factors

7 Concentration to Load Bacteria Concentrations (cfu/100 ml) or (MPN/100 ml) Loads (cfu or MPN/day) ** See Examples in Handout **

8 What if loads are not important? Do you still need flow?

9 Flow vs Concentration Example: Largely nonpoint source contributions North Bosque near Valley Mills

10 Flow vs Concentration Example: Largely point source contributions North Bosque below Stephenville

11 Measures of Central Tendency Mean or Average = (sum of values)/n Median = midpoint or mean of the two middle values Mode = most frequent value

12 Measures of Central Tendency Where subscript i = individual observation c = concentration w = weighting factor or flow associated with the concentration

13 Flow-Weighted Average Example: Concentration (mg/l) Flow (cfs) Flow-wtd Avg = [(0.45*10) + (2.30*0.01) + (0.75*15)] ( ) = 0.63 mg/l Average (not flow-wtd) = 1.17 mg/l

14 Event Mean Concentration EMC = average pollutant concentration over the duration of a storm event EMC = total pollutant loading per event total runoff volume per event = n VV ii CC ii i=1 Where V = runoff volume over time i C = concentration at time i n = number of samples

15 Flow in Statistical Analyses Flow used as: Weighting factor for concentrations in comparing Means (t-tests) Example: T-test comparing concentrations at two stations Weighting factor (flow), gives more emphasis to concentrations at high than at low flows

16 Flow in Statistical Analyses Flow used as: Covariate in Analysis of Covariance (ANCOVA) for evaluating BMPs ANCOVA combines analysis of variance and regression analysis in comparing treatments Covariate (flow) an observed continuous variable that influences measured results that are not related to the treatment

17 Flow in Statistical Analyses Flow used as: Flow-adjustment variable for trend analysis Trend analysis evaluates changes over time Want to control for hydrologic changes in evaluating changes in concentration over time

18 Normal Data Distributions Log

19 Measures of Central Tendency Geometric Mean = average of logarithmic values of a data set converted back to a real (base 10) number Geometric Mean = Antilog[(log(X i )+ log(x n ))/n of base 10 log Can also be calculated as:

20 Geometric Mean Why use it with bacteria data? Bacteria data are quite variable (can grow exponentially under the right conditions) Geometric mean is not overly influenced by a few very large values Example Dataset E. coli Sample (MPN/ Number 100 ml) Average 159 Geomean 43

21 Exploratory Data Analysis Become familiar with your data Graph it Develop summaries Plot relationships (if appropriate)

22 Exploratory Data Analysis Data Plots Hog Creek Assessing Water Quality Management Plan Implementation in the Middle and South Bosque River and Hog Creek Watershed, TIAER Report PR1104

23 Exploratory Data Analysis Explore the Distribution of the Data Types of plots

24 Exploratory Data Analysis Box-and-Whisker Plots * Outlier Upper outer fence = Q3 +1.5(IQR) Lower inner fence = Q1 +1.5(IQR)

25 Test Parametric Assumptions Normality Shaprio-Wilks Statistic Equal Variances Hartley s F-test Independence Autocorrelation (correlation with time) Seasonality (correlograms)

26 Exploratory Data Analysis Are data transformations needed? Water Quality and Flow Data Generally follow a log distribution Log or Ln Transformation If transformed, parametric assumptions need to be tested on the transformed data.

27 Statistical Designs Major Statistical Designs for Watershed Studies: Single Watersheds Before/After or Upstream/Downstream Trend or Step Trend Analysis Paired Watersheds Before-After-Control-Impact (BACI)

28 Single Watershed Before/After Temporal Before and After Practice Implementation Source Diagram: NRCS, NWQH

29 Single Watershed Before/After Statistical Approach Two Sample t-test comparing means Before and After Assumes samples random, independent, normally distributed and with equal variances Wilcoxon Rank Sum Test (nonparametric) Source Diagram: NRCS, NWQH

30 Single Watershed Before/After Statistical Approach Assumes similar climate and hydrology between the Before and After periods Monitoring covariates, such as flow, can aid in adjusting for differences Source Diagram: NRCS, NWQH

31 Single Watershed Above/Below Spatial Above and Below Practice Location (upstream/downstream) Source Diagram: NRCS, NWQH

32 Single Watershed Above/Below Statistical Approach Paired t-test of above and below observations Observations are independent Difference in paired observations normally distributed Sign Test and Signed Rank Test (nonparametric) Observations still need to be independent, but normal distribution not required

33 Single Watershed Above/Below One of the Disadvantages Differences may be do to inherent differences within the watershed and not the practice

34 Single Watershed Above/Below Before monitoring helps account for inherent differences within the watershed Before Monitoring After Monitoring No Practice Source Diagram: NRCS, NWQH

35 Paired Watersheds Paired watershed or BACI approach (Before-After-Control-Impact) Two (or more) Watersheds Involves a Calibration & Treatment period At least one watershed serves as a control

36 Paired Watersheds Calibration period (monitor both without practice, treated identically) Calibration Period Source Diagram: NRCS, NWQH

37 Paired Watersheds Treatment period (implement practice on one, treat control as in calibration period, and monitor both) Treatment Period Source Diagram: NRCS, NWQH

38 Paired Watersheds Calibration Period Treatment Period Source Diagram: NRCS, NWQH

39 Evaluating BMPs Paired Watershed or BACI (Before-After-Control-Impact) Average storm flow or storm volume used as covariate nonpoint source contributions (volume will vary with each runoff event)

40 Paired Watershed Approach Source: J.D. Hewlett Principles of Forest Hydrology. The University of Georgia Press.

41 Paired Watersheds Statistical Approach ANOCOVA analysis of covariance Requires develop of a significant regression relationship between control and treatment watersheds during both calibration and treatment periods

42 Paired Watersheds Controlling Phosphorus in Runoff from Long-term Dairy Waste Application Fields. AWRA, 2004 McFarland and Hauck

43 Paired Watersheds Controlling Phosphorus in Runoff from Long-term Dairy Waste Application Fields. AWRA, 2004 McFarland and Hauck

44 Detecting Water Quality Changes Before & After BMP Implementation Garry L. Grabow, Jean Spooner, Laura A. Lombardo, and Daniel E. Line (1998 & 1999) NCSU Water Quality Group Biological and Agricultural Engineering Department NWQEP NOTES Newsletter J. C. Clausen and J. Spooner Paired Watershed Study Design. Office of Water, U.S. Environmental Protection Agency, Washington, DC. EPA 841-F p

45 Paired Watersheds Disadvantages Assumes there is a quantifiable relationship in water quality between the two watersheds Parametric assumptions may be violated Variances in water quality data unlikely to be equal between time periods Data may not be normally distributed Data may not be independent (serially correlated)

46 Trend Analysis

47 Trend Analysis Lots of available methods, but most have limited application because Datasets have Censored data (< values) Have data gaps Are not normally distributed Are not independent (serial correlation and/or seasonality)

48 Statistical Approach Trend Stations Seasonal Kendall test (preferred method) Nonparametric test, so data do not need to be normally distributed Can accept censored data (< values) Can accept some data gaps Can deal with seasonality

49 Trend Analysis Additional Considerations: Changes in analytical methods over time Changes in reporting limits over time Limit of Quantitation (LOQs, < or leftcensored values) Influences from flow or hydrologic variability

50 Trend Analysis Dataset Preparation Evaluate & adjust for variability in reporting limits Check for seasonal influences and use seasonal tests, if appropriate Evaluate & adjust for variability in flow

51 Computer Program for the Kendall Family of Trend Tests By Dennis R. Helsel, David K. Mueller, and James R. Slack

52 Statistical Data Analysis Look at your data Make sure it meets parametric assumptions or use nonparametric tests Consider the need for data transformations (Log or Ln) Flow adjust, if needed Consider seasonality or correlation with time

53 Major References USDA-NRCS Chapter 4, Statistical Designs. In: National Handbook of Water Quality Monitoring. ent.aspx?content=17843.wba Helsel & Hirsch Statistical Method in Water Resources. USGS, Techniques for Water- Resource Investigations. ew.html