DATA QUALITY and ANALYSIS Strategy for Monitoring Post-fire Rehabilitation Treatments Troy Wirth and David Pyke USGS – Biological Resources Division Forest and Rangeland Ecosystem Science Center Corvallis, Oregon U.S. Department of Interior U.S. Geological Survey Supported by USGS - BLM Interagency Agreement #HAI040045

Data Quality Assess the ability of the data to determine treatment success Assess the ability of the data to determine treatment success Ability to achieve high data quality will depend on variability Ability to achieve high data quality will depend on variability Calculate data quality variables Calculate data quality variables Confidence intervals (precision) Confidence intervals (precision) Alpha (p-value) & beta levels Alpha (p-value) & beta levels Sample size estimation Sample size estimation

Confidence Intervals Construct a simple confidence interval around data to determine precision of estimate Construct a simple confidence interval around data to determine precision of estimate The narrower the confidence interval, the more precise the estimate The narrower the confidence interval, the more precise the estimate Must specify the alpha level Must specify the alpha level Alpha level, or type I error is the probability of declaring there is no difference when there is. Alpha level, or type I error is the probability of declaring there is no difference when there is. Specifies the width of the confidence interval (1 – alpha) Specifies the width of the confidence interval (1 – alpha)

From Elzinga et al. 1998

Confidence Intervals

Sample Size Estimation Equations which estimate the number of samples required to meet your sampling objective Equations which estimate the number of samples required to meet your sampling objective For single populations (quantitative objective) For single populations (quantitative objective) Confidence level (Type I error rate) Confidence level (Type I error rate) Confidence interval width Confidence interval width For detecting difference between two populations For detecting difference between two populations Confidence levels (Type I and II error rate) Confidence levels (Type I and II error rate) Minimum detectable change Minimum detectable change Iterative process Iterative process

Single Population Sample Size Calculate sample size estimate for each parameter of interest Calculate sample size estimate for each parameter of interest Result will depend on variability of data Result will depend on variability of data For example, using equation for single population: For example, using equation for single population: = sample size required = alpha level for specified level of confidence = standard deviation = desired precision level (absolute term)

Single Population Sample Size Estimation Example Alpha = 0.1 Alpha = 0.1 X = 18.5 % cover of perennial grass X = 18.5 % cover of perennial grass S = 4.9 % cover S = 4.9 % cover d = (18.5*0.2) = 3.7 d = (18.5*0.2) = 3.7 Initial sample = 5 Initial sample = 5 Need 3 more samples (precision achieved 4.7)

Improving Data Quality In order to increase data quality (achieve sample size) you need to: In order to increase data quality (achieve sample size) you need to: Reduce standard deviation (variability) Reduce standard deviation (variability) Increase the number of samples Increase the number of samples In order to reduce sample size estimates without more samples you can: In order to reduce sample size estimates without more samples you can: Increase alpha (less confidence) Increase alpha (less confidence) Increase precision or MDC (detect a larger difference) Increase precision or MDC (detect a larger difference)

Graphical Analysis Using Confidence Intervals Compare treatment results to quantitative objectives or control areas Compare treatment results to quantitative objectives or control areas Several types of analysis to fit your situation Several types of analysis to fit your situation Types of graphical analysis: Types of graphical analysis: Comparison of treatment to quantitative standard Comparison of treatment to quantitative standard Seeded plants vs. quantitative standard Seeded plants vs. quantitative standard All plants at treatment plots change from time 1 to time 2 All plants at treatment plots change from time 1 to time 2 Comparison of two populations (seeded/unseeded) Comparison of two populations (seeded/unseeded) Treatment vs. control Treatment vs. control Treatment vs. control (change from time 1 to time 2) Treatment vs. control (change from time 1 to time 2)

Flowchart for Graphical Analysis Density

Graphical Analysis (comparison to a standard) Specify quantitative objective Specify quantitative objective Determine desired alpha level and precision Determine desired alpha level and precision Collect data at treatment plots Collect data at treatment plots Graph mean with confidence interval of desired width (typically 80 or 90%) Graph mean with confidence interval of desired width (typically 80 or 90%) Graphically compare to quantitative standard to determine which situation exists Graphically compare to quantitative standard to determine which situation exists Need mean, standard deviation, and n Need mean, standard deviation, and n Use ES&R Equation spreadsheet to help Use ES&R Equation spreadsheet to help

Graphical Analysis (comparison to a quantitative objective) Quantitative objective: 5 plants/m 2 Quantitative objective: 5 plants/m 2 Alpha level: 0.1 (90% Confidence Interval) Alpha level: 0.1 (90% Confidence Interval) X = 7 plants/m 2 X = 7 plants/m 2 S = 1.3 plants/m 2 S = 1.3 plants/m 2 N = 5 N = 5

D: The sample mean is above the quantitative objective, but the lower limit of the confidence interval is below the objective. Comparison to a Quantitative Objective

C: The sample mean is above the objective but the lower confidence limit is below the objective. Comparison to a Quantitative Objective

B: The sample mean is below the quantitative objective, but the upper limit of the confidence interval is above the objective. Comparison to a Quantitative Objective

A: The sample mean and confidence interval (CI) fall below the objective. Conclude that the objective has not been met. Comparison to a Quantitative Objective

Graphical Analysis (Treatment v. Control) Confidence interval of the difference between the treatment and control Confidence interval of the difference between the treatment and control Uses the difference between the means of two treatments and constructs a single CI using the variance from both estimates (SE) Uses the difference between the means of two treatments and constructs a single CI using the variance from both estimates (SE) A mean of 0 represents no difference between the two treatments A mean of 0 represents no difference between the two treatments Express the quantitative objective as an absolute value or as a multiple of the control. Express the quantitative objective as an absolute value or as a multiple of the control. Use the mean and CI to make a determination of treatment effect Use the mean and CI to make a determination of treatment effect

Graphical Analysis (Treatment v. Control) Using the ESR monitoring spreadsheet Using the ESR monitoring spreadsheet Specify the desired alpha level Specify the desired alpha level Enter the mean, standard deviation, and N from the data collected at the treatment and control plots Enter the mean, standard deviation, and N from the data collected at the treatment and control plots Specify the level of quantitative objective (multiple of control or absolute difference) Specify the level of quantitative objective (multiple of control or absolute difference) Make interpretation based on graphical analysis of the CI of the difference between the two treatments Make interpretation based on graphical analysis of the CI of the difference between the two treatments

Graphical Analysis (Treatment v. Control) Quantitative objective: twice that of control plot (2) – note that because it is a CI of difference the original amount is subtracted from quantitative objective Quantitative objective: twice that of control plot (2) – note that because it is a CI of difference the original amount is subtracted from quantitative objective Alpha level: 0.1 (90% Confidence Interval) Alpha level: 0.1 (90% Confidence Interval) Control Control X = 2.0 X = 2.0 S = 0.5 S = 0.5 N = 7 N = 7 Treatment Treatment X = 4.9 X = 4.9 S = 0.9 S = 0.9 N = 7 N = 7

Treatment vs. Control A: The mean and confidence interval for the difference between the two means is completely above the level of ecological significance (5 plants/m 2 ).

B: The difference of the mean between is above the level of ecological significance, but the lower confidence limit for the difference is below the level of ecological significance. Treatment vs. Control

C: The difference between the two means is below the level of ecological significance, but the upper confidence limit for the difference is above the level of ecological significance. Treatment vs. Control

D: The mean and confidence interval of the difference is below the level of ecological significance. Conclude that there is no ecologically significant difference between the control and treatment plots. Treatment vs. Control

E: The mean of the difference is above zero, but the lower confidence limit is below 0 (no difference) and the upper confidence limit is above 5 plants/m 2. Treatment vs. Control

F: The mean of the difference is above 0, but the lower confidence limit is below 0 and the upper confidence limit is below the level of ecological significance. Treatment vs. Control

Flowchart for Graphical Analysis Density

Graphical Analysis (Treatment vs. Control T2-T1) Confidence interval of the difference in change between two time periods between treatment and control Confidence interval of the difference in change between two time periods between treatment and control Uses the difference between the change in the means of treatment and control and constructs a single CI using the variance from both estimates (SE) Uses the difference between the change in the means of treatment and control and constructs a single CI using the variance from both estimates (SE) A mean of 0 represents no difference in change between the two treatments A mean of 0 represents no difference in change between the two treatments Express the quantitative objective as an absolute value or as a multiple of the control. Express the quantitative objective as an absolute value or as a multiple of the control. Use the mean and CI to make a determination of treatment effect Use the mean and CI to make a determination of treatment effect

Appears that there is a difference in year three when there actually was not. Accounting for initial difference in the degree of change

B: The difference of the mean between is above the level of ecological significance, but the lower confidence limit for the difference is below the level of ecological significance. Change in Treatment vs. Control

Graphical Analysis (Treatment at two time periods, T2-T1) Confidence interval of the change between the two time periods Confidence interval of the change between the two time periods Treats the two time periods as paired, reducing variability Treats the two time periods as paired, reducing variability A mean of 0 represents no change between the two time periods A mean of 0 represents no change between the two time periods Express the quantitative objective as the desired change between the two different time periods Express the quantitative objective as the desired change between the two different time periods Use the mean and CI compared to the quantitative objective to make a determination of success Use the mean and CI compared to the quantitative objective to make a determination of success

Paste graphs directly into reports and describe quantitative results e.g. Perennial Grass Density The density of perennial grasses is significantly greater in the treatment plots as compared to the control plots. We are 90% confident that the difference is between 1.06 to 4.54 plants/m 2 greater than the control plots with a mean of 2.8 plants/m 2 ) Reporting

Reporting Link reports back to quantitative objectives Link reports back to quantitative objectives Re-assess whether objectives were reasonable and possible reasons for success and failure. Re-assess whether objectives were reasonable and possible reasons for success and failure. Make recommendations for future improvements to implementation and monitoring Make recommendations for future improvements to implementation and monitoring