National Park Service

U.S. Department of the Interior

Natural Resource Program Center

Variance and Power for Trend Assessment 

of Pilot Data

Integrated Upland Monitoring, Canyonlands National Park

Natural Resource Report NPS/NCPN/NRR—2010/171
ON THE COVER

Upland monitoring site, Canyonlands National Park. NPS photo.
Variance and Power for Trend Assessment 

of Pilot Data

Integrated Upland Monitoring, Canyonlands National Park

Natural Resource Report NPS/NCPN/NRR—2010/171

Prepared by

Dana Witwicki

Northern Colorado Plateau Network

National Park Service

P.O. Box 848

Moab, UT 84532

Editing and Design

Alice Wondrak Biel

Northern Colorado Plateau Network

National Park Service

P.O. Box 848

Moab, UT 84532

January 2010

U.S. Department of the Interior

National Park Service

Natural Resource Program Center

Fort Collins, Colorado
ii Variance and Power for Trend Assessment of Pilot Data: Integrated Upland Monitoring, Canyonlands NP

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Please cite this publication as:

Witwicki, D. 2010. Variance and power for trend assessment of pilot data: Integrated upland monitoring, Canyonlands National Park. Natural Resource Report NPS/NCPN/NRR—2010/171. National 

Park Service, Fort Collins, Colorado.

NPS 164/100865, January 2010
Contents iii

Contents

Figures ....................................................................................................................................v

Tables ......................................................................................................................................v

Abstract ................................................................................................................................vii

Acknowledgements ..............................................................................................................ix

1 Introduction .......................................................................................................................1

2 Survey Design .....................................................................................................................1

2.1 Sampling frame ...................................................................................................................... 1

2.2 Site selection ........................................................................................................................... 1

2.3 Pilot study ............................................................................................................................... 1

2.4 Response variables ................................................................................................................. 2

2.5 Linear models and variance components ............................................................................. 2

2.6 Affordable sample size .......................................................................................................... 3

3 Panel Designs .....................................................................................................................3

4 Analysis ...............................................................................................................................6

4.1 Minimum Detectable Difference ........................................................................................... 6

4.2 Estimating power for trend and precision of status ............................................................ 6

4.3 Effect of panel design ............................................................................................................ 6

4.4 Effect of sampling size ........................................................................................................... 6

4.5 Effect of annual trend ........................................................................................................... 7

4.6 Effect of response type .......................................................................................................... 7

4.7 Discussion ................................................................................................................................ 7

5 Final design ........................................................................................................................8

6 Literature Cited ................................................................................................................10

Appendix A: Power for Trend Figures ................................................................................11

Contents v

Figures

Main report

Figure 3-1. Split-panel designs tested in power analysis. .................................................................................... 4

Figure 3-2. Variations of Design 2 used to analyze sample sizes of 7, 36, and 50 plots per ecological site 

per year............................................................................................................................................................ 5

Figure 5-1. Final split-panel designs for integrated upland monitoring at Canyonlands National Park. ........ 9

Appendix A

Figure A1. Power for trend and standard error of status for each sampling design (Figure 3-1) at 

grassland ecological sites (annual sample size = 12). ................................................................................. 12

Figure A2. Power for trend and standard error of status for each sampling design (Figure 3-1) at 

shrubland ecological sites (annual sample size = 12). ................................................................................ 15

Figure A3. Power for trend and standard error of status for each response variable at grassland 

ecological sites comparing annual sample sizes of 7, 12, 36, and 50 plots per year using Design 2 

(Figure 3-2). ................................................................................................................................................... 18

Figure A4. Power for trend and standard error of status for each response variable at shrubland 

ecological sites comparing annual sample sizes of 7, 12, 36, and 50 plots per year using Design 2 

(Figure 3-2). ................................................................................................................................................... 21

Figure A5. Power for trend for a range of annual increases or decreases in response variables at 

grassland ecological sites using Design 2 (Figure 3-1) and an annual sample size of 12. ....................... 24

Figure A6. Power for trend for a range of annual increases or decreases in response variables at 

shrubland ecological sites using Design 2 (Figure 3-1) and an annual sample size of 12. ...................... 26

Tables

Table 2-1. Ecological sites in Canyonlands NP pilot monitoring. ........................................................................ 1

Table 2-2. Variance components. .......................................................................................................................... 2

Table 2-3. Site, year, and residual variance estimates for responses in grassland and shrubland ecological 

site types for CANY pilot plots. ..................................................................................................................... 3

Table 4-1. Summary of proposed minimum detectable differences (MDD) for each response. ....................... 6

Table 5-1. Ecological site type groupings. ............................................................................................................ 8

Contents vii

Abstract

Power analysis provides an a priori understanding of our ability and confi dence to estimate the condition (i.e., status) of a resource and detect trends in that resource over time. This report describes 

the power analysis conducted by the Northern Colorado Plateau Network to identify an “aff ordable” 

sample size that optimizes tradeoff s between trend and status estimation and overall operational reality 

for its integrated uplands monitoring protocol at Canyonlands National Park (NP). Forty plots were 

monitored at Canyonlands NP for three consecutive years. Key response measurements for (1) understanding the susceptibility of soil to wind and water erosion and (2) detecting shifts in vegetation were 

used in this analysis. For each key response, we estimated the variance separately for shrub and grassland ecological site types, using linear mixed-eff ects models. We also examined power and precision of 

standard error of status for alternative revisit designs and sample sizes, as well as for the ability to detect 

diff erent amounts of annual trend. The operational survey and revisit designs for Canyonlands NP are 

presented in the report. Graphs of power for trend are presented in Appendix A.

Contents ix

Acknowledgements

Many thanks to Steve Garman, former Northern Colorado Plateau Network quantitative ecologist, and 

Tom Philippi, national Inventory and Monitoring quantitative ecologist, for answering questions about 

analyses and providing thoughtful reviews of this document. I would also like to thank Billy Schweiger, 

quantitative ecologist for the Rocky Mountain Network, and Amy Symstad, U. S. Geological Survey 

Ecologist working with the Northern Great Plains Network, for sharing drafts of their own variance and 

power-for-trend assessments and allowing me to adapt their work for the Northern Colorado Plateau 

Network.

Main Report 1

1 Introduction

The Northern Colorado Plateau Inventory and 

Monitoring Network (NCPN) implemented upland monitoring at Canyonlands National Park 

(CANY) during the 2006 fi eld season. Upland 

monitoring was initiated as a three-year pilot 

study to estimate the variance for responses used 

to monitor vital signs. The power analysis described in this report used variance from the pilot study to evaluate the appropriateness of proposed split-panel designs for detecting a trend 

and estimating the precision (or standard error) 

of status for long-term monitoring. 

Power analysis provides an a priori understanding of the ability and confi dence with which one 

can estimate the condition (i.e., status) of an extensive and variable resource and detect trends in 

that resource over time (Gerrodette 1987). Statistical power is the ability to detect an eff ect, given 

that the eff ect actually exists (i.e., the probability 

of not making a Type-II error of failing to detect a 

real trend). This report describes the power analysis conducted by the Northern Colorado Plateau 

Network to identify an “aff ordable” sample size 

that optimizes tradeoff s between trend and status estimation and overall operational reality by 

allocating the sample size into alternative revisit 

designs and determining the maximum number 

of ecological sites among which the sample can 

be divided.

2 Survey Design

2.1 Sampling frame

Survey designs use explicitly mapped areas as 

the sampling frame. For CANY, we used featureextraction modeling to map the target ecological 

sites used to stratify upland monitoring. Ecological sites provide an eff ective way to stratify arid 

upland ecosystems by taking into consideration 

soil geomorphology, landform, and climate, in 

addition to vegetation characteristics. 

The feature-extraction software used fi eld reconnaissance points and spatial data layers to develop rules for where each ecological site occurred 

on aerial photos. It then used those rules to characterize the entire area of interest (i.e., accessible 

areas in Island in the Sky and Needles districts 

of the park). After fi eld verifi cation, the software 

used new data to improve the initial version of the 

map (Garman et al. in review). The resulting map 

included the six ecological sites cover the greatest 

areal extent of CANY (Table 2-1).

2.2 Site selection

A membership design specifi es how sites in a survey design are chosen across space (McDonald 

2003). For CANY, a Generalized Random Tessellation Stratifi ed (GRTS) design (Stevens and 

Olsen 2004) was used to select spatially balanced 

random samples stratifi ed by each target ecological site. In probability-based surveys, such as 

GRTS, the site-selection process allows unbiased 

estimation of both status and, with repeated visits, 

trend (Larsen et al. 1995). Our GRTS design was 

created in R using the “spsurvey” library (Kincaid 

2005, ver. 2.0, available from http://cran.r-project.

org/).

2.3 Pilot study

Using the ordered lists of points produced by 

GRTS, eight plots were established in each of fi ve 

ecological sites for CANY pilot monitoring. (The 

Desert Sand ecological site was not included in 

the pilot study because it had much lower areal 

extent than predicted by soil and ecological site 

maps.) Thirty-one plots were established in 2006, 

and sampled for three consecutive years. The remaining nine plots were established in 2007, and 

sampled for two consecutive years. Plots were 

sampled between April and September each year. 

A broad sampling window was used to capture 

the maximum amount of variation during the 

Table 2-1. Ecological sites in Canyonlands NP pilot 

monitoring.

Ecological 

site # Ecological site name Ecological site type

Total area* 

(ha)

115 Desert Sand 

(sand sagebrush)

Grassland 1,647

118 Desert Sandy Loam 

(fourwing saltbush)

Grassland 1,706

212 Semidesert Sand 

(fourwing saltbush)

Grassland 319

215 Semidesert Sandy Loam 

(fourwing saltbush)

Grassland 621

133 Desert Shallow Sandy Loam 

(blackbrush)

Shrubland 2,212

236 Semidesert Shallow Sandy 

Loam (Utah juniper-pinyon)

Shrubland 2,181

*Total accessible area of ecological site in Island in the Sky and Needles districts of 

Canyonlands NP.
2 Variance and Power for Trend Assessment of Pilot Data: Integrated Upland Monitoring, Canyonlands NP

growing season. In addition, fi eld-crew members 

visited diff erent plots each year, when possible, 

to include the maximum amount of variation between observers. Plots were sampled according 

to the Integrated Upland Monitoring Protocol 

for Park Units in the Northern Colorado Plateau 

Network (Witwicki et al. draft).

Although three years of pilot data from 40 plots 

is a limited data set, it provides a starting point 

for creating a defensible long-term sampling design. Variance and power-for-trend assessments 

will be performed every fi ve years, allowing us to 

analyze the operational sampling design, ensure 

that monitoring goals are being met, and make 

changes to the design as needed.

2.4 Response variables

Response variables examined in this analysis 

were those with potentially important thresholds 

in the target ecological sites. Although threshold 

values have not been defi ned for these ecological 

sites, it is well understood, through conceptual 

models, that biological soil crusts (BSCs) are a 

critical component of these systems, responsible 

for holding the soil in place and preventing erosion by wind or water. Four of the fi ve target ecological sites are dominated by BSCs. 

Key response measurements for understanding 

the susceptibility of soil to wind and water erosion include (1) basal gap size, (2) canopy gap 

size, (3) soil stability, (4) percent cover of BSCs, 

and (5) percent cover of bare soil. Important response measurements for detecting shifts in vegetation include percent cover of (6) shrubs, (7) 

perennial grasses, and (8) annual grasses.

2.5 Linear models and variance 

components

Using the eight response variables described 

above, we developed linear models to estimate 

variance following Larsen et al. (1995; 2001) and 

Urquhart and Kincaid (1999). Residual plots, histograms, and normal QQ (quantile quantile) plots 

were reviewed for each response to determine the 

need for data transformation. Natural-log transformation was used to improve model assumptions of normality and constant variance for all 

responses. Variance components in the model are 

shown in Table 2-2.

Analyses were performed in SAS 9.1 using Proc 

Mixed models. Year and site covariates were 

treated as random eff ects (Urquhart et al. 1998). 

To account for our unbalanced design (e.g., different numbers of revisit years for some plots), 

the restricted maximum likelihood (REML) approach was used to estimate variance and the 

Kenward-Roger method was used to calculate 

degrees of freedom (Spilke et al. 2005). 

Our original intent was to analyze separate models for each response at each ecological site. However, our limited data set resulted in variances of 

0 for year and/or site for more than one-quarter 

of the response variables. To achieve meaningful 

results, we combined all three grassland ecological sites and both shrubland ecological sites into 

ecological site types based on functional group, 

and reanalyzed the data (Table 2-3). For the three 

shrub responses (canopy gap size, crust cover, 

and bare soil cover) that still had a year variance 

of 0, year variances were substituted from the 

grassland ecological site type in order to give a 

more realistic estimate of year variance. Variances were also examined after data were detrended, 

but this altered the variances little and increased 

the number of responses with year variances of 

0. Therefore, the original model was used to estimate variance.

Annual precipitation data from two weather 

stations in CANY were examined to see if estimated variances from the 2006–2008 pilot study 

needed to be further infl ated to be comparable 

with historic variability in annual precipitation. 

Proc Mixed models in SAS were used to estimate 

variance of annual precipitation (1) for the three 

years of the pilot study (2006–2008), and (2) for 

the history of the weather stations (1966–2008). 

Variance of yearly precipitation from 2006 to 

2008 was higher than that for the history of the 

weather stations, so no additional corrections to 

variances were made. 

Table 2-2. Variance components.

Component Description

σ2

Site Variation among sites that is 

consistent across years (e.g., 

variation in vegetation cover 

or soil stability due to soil 

component)

σ2

Year Variation among years that affects 

all sites in the population (e.g., 

regionwide climatic variation)

σ2

Residual Variation specifi c to a site during 

a particular year, including 

measurement error (e.g., erosion 

occurs at a single site due to heavy 

cattle trampling of BSCs).
Main Report 3

2.6 Affordable sample size

The NCPN has determined that the aff ordable 

annual sample size for upland monitoring is approximately 48 plots per park for all large parks 

in the network (Black Canyon of the Gunnison 

National Park and Curecanti National Recreation Area, CANY, Capitol Reef National Park, 

Dinosaur National Monument, and Zion National Park), 24 plots per park for medium-size 

parks (Arches and Bryce Canyon national parks) 

and 3–8 plots for smaller parks (Cedar Breaks and 

Timpanogos Cave national monuments). This is 

based on an estimate of six fi eld-crew members 

monitoring uplands full-time for 12 pay periods.

Although the total annual sample size for CANY 

is 48 plots, an aff ordable sampling size of 12 plots 

per year per ecological site was used to evaluate 

split-panel designs (see Figure 3-1). One of the 

designs was used to evaluate the eff ect of using 

diff erent sample sizes (see Figure 3-2).

3 Panel Designs

A serious concern of sampling arid/semiarid upland vegetation and soils is that sites may become 

fatigued if sampled too often. The most likely 

scenario of site fatigue at CANY is increased soil 

loss caused by repeated trampling of BSCs in 

monitoring plots. Our goal is to disturb plots as 

little as possible and to avoid monitoring the effects of our presence at plots as much as possible. 

As such, designs that revisit the same sites each 

year were not considered for upland monitoring. 

Instead, we investigated split-panel designs that 

rest plots for 2–7 years between revisits. We also 

wanted to sample some sites two years in a row 

to understand year-to-year variation of shrub and 

annual grass cover. The four designs considered 

for NCPN upland monitoring in CANY are displayed in Figure 3-1. 

As per MacDonald (2003), the numerical notation of a panel design indicates the number of 

consecutive years of sampling followed by the 

number of consecutive years of rest for plots in 

each type of panel. For example, Design 1, notated as (2-3),(1-4), calls for 2 consecutive years of 

sampling followed by 3 consecutive years of rest 

for plots in panels 1–5, and 1 year of sampling followed by 4 years of rest for plots in panels 6–10.

A preliminary analysis determined that split-panel designs, like those shown in Figure 3-1, provided better precision of status and higher power 

to detect trend in early years by allocating more 

plots to panels where plots were visited for only 

one consecutive year (e.g., panels 6–10 in Design 

1) than to panels where plots were visited for two 

consecutive years (e.g., panels 1–5 in Design 1). 

Therefore, all four designs analyzed in this power 

analysis were structured in this way. Design 2 was 

used to examine the eff ect of diff erent sample 

sizes and annual trends (Figure 3-2).

When selecting an operational sampling design, 

it is important that the sampling frame be large 

enough to include all of the proposed unique 

plots in a design. For example, it would not be 

feasible to select Design 3 (99 unique plots) to 

monitor ecological site 212, due to the low areal 

extent of this ecological site in CANY (only 319 

ha predicted by our map; Table 2-1) and a high 

sampling-frame error (only 1⁄4 of plots have been 

correctly predicted by the map in this ecological 

site). 

Table 2-3. Site, year, and residual variance 

estimates for responses in grassland and 

shrubland ecological site types for CANY pilot 

plots.

Response

Variance

Site Year Residual

Grassland type

Basal gap 0.71500 0.00449 0.04046

Canopy gap 0.67380 0.00141 0.02264

Soil stability 0.01314 0.00462 0.02384

Crust cover 0.01175 0.01246 0.03330

Bare soil cover 0.14390 0.28190 0.79940

Shrub cover 0.70600 0.01194 0.02806

Perennial grass cover 0.49130 0.05793 0.05028

Annual grass cover 0.00802 0.02491 0.06480

Shrubland type

Basal gap 0.10470 0.00315 0.03779

Canopy gap 0.05868 0 0.00917

Soil stability 0.09466 0.00172 0.01884

Crust cover 0.59920 0 0.30530

Bare soil cover 0.21440 0 0.59920

Shrub cover 0.10670 0.01245 0.08471

Perennial grass cover 0.15880 0.00024 0.01417

Annual grass cover 0.00167 0.00426 0.01116
4 Variance and Power for Trend Assessment of Pilot Data: Integrated Upland Monitoring, Canyonlands NP

Design 1 (2-3),(1-4).

Panel

Year

1 2 3 4 5 6 7 8 9 10

1 33 33

2 33 33

3 33 33

4 33 3 3

5 3 33 3

6 6 6

7 6 6

8 6 6

9 6 6

10 6 6

45 unique plots

12 plots per ecological site per year

Design 2 (2-5),(1-6).

Panel

Year

1 2 3 4 5 6 7 8 9 10

1 33 33

2 33 3 3

3 33 3

4 3 3

5 3 3

6 3 3

7 3 33

8 6 6

9 6 6

10 6 6

11 6

12 6

13 6

14 6

63 unique plots

12 plots per ecological site per year Design 3 (2-7),(1-8).

Panel

Year

1 2 3 4 5 6 7 8 9 10

1 33 3

2 3 3

3 3 3

4 3 3

5 3 3

6 3 3

7 3 3

8 3 3

9 3 33

10 6 6

11 6

12 6

13 6

14 6

15 6

16 6

17 6

18 6

99 unique plots

12 plots per ecological site per year

Design 4 (2-7),(1-2).

Panel

Year

1 2 3 4 5 6 7 8 9 10

1 33 3

2 3 3

3 3 3

4 3 3

5 3 3

6 3 3

7 3 3

8 3 3

9 3 33

10 666 6

11 666

12 666

45 unique plots

12 plots per ecological site per year

Figure 3-1. Split-panel designs tested in power analysis.
Main Report 5

Design 2c (2-5),(1-6).

Panel

Year

1 2 3 4 5 6 7 8 9 10

1 12 12 12 12

2 12 12 12 12

3 12 12 12

4 12 12

5 12 12

6 12 12

7 12 12 12

8 26 26

9 26 26

10 26 26

11 26

12 26

13 26

14 26

266 unique plots

50 plots per ecological site per year

Figure 3-2. Variations of Design 2 used to analyze sample sizes of 7, 36, and 50 plots per ecological site per year.

Design 2a (2-5),(1-6).

Panel

Year

1 2 3 4 5 6 7 8 9 10

1 22 22

2 22 2 2

3 22 2

4 2 2

5 2 2

6 2 2

7 2 22

8 3 3

9 3 3

10 3 3

11 3

12 3

13 3

14 3

35 unique plots

7 plots per ecological site per year

Design 2b (2-5),(1-6).

Panel

Year

1 2 3 4 5 6 7 8 9 10

1 99 99

2 99 99

3 99 9

4 9 9

5 9 9

6 9 9

7 9 99

8 18 18

9 18 18

10 18 18

11 18

12 18

13 18

14 18

189 unique plots

36 plots per ecological site per year
6 Variance and Power for Trend Assessment of Pilot Data: Integrated Upland Monitoring, Canyonlands NP

4 Analysis

4.1 Minimum Detectable Difference

The minimum detectable diff erence (MDD) is 

the annual rate of change in trend that a design 

can detect. For log-transformed responses, such 

as those described here, this equates to a proportional change or annual percent increase or 

decrease. A 10% annual increase equates to a 

172% total increase over 10 years, or an increase 

in bare-soil cover from 5.4% in 2006 to 14.7% in 

2016. The annual rate is equivalent to the slope of 

the regression line in a linear model.

The minimum detectable diff erence for a trend 

should be ecologically relevant and can be determined by using thresholds of ecological sites, 

if known. Because no threshold values have been 

determined for target ecological sites in CANY, 

we attempted to determine ecologically meaningful annual increases or decreases for each 

response variable based on the pilot plot means 

and extremes, change over a 10-year period, and 

professional judgment (Table 4-1). Cover of vegetation types and bare soil required at least 10% 

change per year for meaningful ecological changes to occur. Changes in all other soil-related variables were meaningful at a 2–5% rate of annual 

change. Because MDD’s for the selected responses will also vary by ecological site, we strongly 

considered the most conservative estimates when 

selecting an MDD for a response.

4.2 Estimating power for trend and 

precision of status

Power to detect a specifi ed trend and precision of 

status were estimated using an unpublished function written by Tom Kincaid (U.S. Environmental 

Protection Agency, Corvallis, Oregon) for R. This 

function uses MDD, variance components, desired Type 1 error (alpha), the selected panel design, and two additional correlation values (site.

rho = 1; year.rho = 0) set to these default values 

based on Urquhart et al. (1993). We set alpha = 

0.10 and examined power for trend and standard 

error of status over a 20-year time frame. We used 

a less-conservative alpha because we do not want 

to risk missing trends that may be important to 

park managers.

4.3 Effect of panel design

In Designs 1–4 (Figure 3-1), each response in each 

ecological site type was compared using an annual sample size of 12 and the appropriate MDD 

(Figures A1 & A2 in Appendix A). In general, all 

four split-panel designs performed similarly. For 

some responses, Design 3 provided lower power 

in early years, and Designs 1 and 4 provided higher power in early years.

4.4 Effect of sampling size

Samples sizes of 7, 12, 36, and 50 plots per year 

were compared for each response in each ecological site type using Design 2 (see Figure 3-2) 

Table 4-1. Summary of proposed minimum detectable differences (MDD) for each response.

Response MDD 

(annual trend)

Mean (min–max) Range Current status After 10 years*

Basal gap size 2–5% increase 427 cm (70–2,996 cm) 522 cm (86–3,659 cm) 0–5,000 cm

Canopy gap size 2–5% increase 228 cm (45–1,659 cm) 279 cm (55–2,026 cm) 0–5,000 cm

Soil stability 2–5% decrease 3.4 (1.1–5.8) 2.8 (0.9–4.7) 1–6

BSC cover 2% decrease 58.3% (0.2–90.5%) 47.7 (0.2–74.1%) 0–100%

Bare soil cover 10% increase 5.4% (0–47.7%) 14.7% (0–>100%) 0–100%

Shrub cover 10% increase 9.1% (0–20.3%) 24.7% (0–55.2%) 0–100%

Perennial grass cover 10% decrease 4.3% (0–24.7%) 1.6% (0–9.1%) 0–100%

Annual grass cover 20–25% increase 0.2% (0–2.3%) 1.5% (0–17.0%) 0–100%

*calculation uses lowest value for each row in the MDD (annual trend) column 
Main Report 7

and the appropriate MDD. For most responses, 

increasing sample size caused power for trend to 

increase and standard error of status to decrease 

for sample sizes of up to 36 plots (Figures A3 & 

A4 in Appendix A). Sample sizes above 36 plots 

provided little additional improvement in power 

for trend or standard error of status.

4.5 Effect of annual trend

A range of annual trends was compared for each 

response in each ecological site type using Design 2 and an annual sample size of 12 (Figures 

A5 & A6 in Appendix A). For responses with 

MDDs of 2–5% (basal and canopy gaps, soil stability, and percent crust cover), annual trends of 

2%, 5%, and 10% were compared. For responses 

with MDDs of 10–20% (percent cover of bare 

soil, shrubs, perennial grass, and annual grass), 

annual trends of 5%, 10%, and 20% were compared. Most response variables in each ecological site type reached 80% power within 10 years. 

The exceptions were percent cover of bare soil 

and crust, which took approximately 13–25 years 

to reach a power of 80%. Varying MDD did not 

aff ect the standard error of status, so these results 

are not presented. 

4.6 Effect of response type

Responses generally displayed acceptable levels 

of power for trend and standard error of status 

for the sampling designs, sample sizes, and rates 

of annual trend examined in this analysis. The 

most problematic responses were percent cover 

of bare soil and of crust. These two responses 

tended to take longer to reach a power of 80% 

and had higher standard errors of status than the 

other responses. It is likely that the high variance 

in these responses is primarily a result of measurement error. Methods of estimating bare soil 

and crust cover have been changed since pilot 

sampling, and we are optimistic that these changes will result in greater repeatability between observers. Using the pilot data to select a sampling 

design should give us a conservative estimate of 

power and standard error of status for percent 

bare soil and crust. 

4.7 Discussion

The diff erences between the split-panel designs 

tested were relatively minor, which was unsurprising, given the similarity between the designs. 

Any of these designs would probably be appropriate for upland monitoring in CANY. A more 

diffi cult question, however, is which annual sample size is appropriate for each ecological site. It is 

clear from the results presented here that for most 

responses, there is little to be gained by using an 

annual sample size of more than 36 plots, because 

at some point between 12 and 36, no signifi cant 

improvements in trend and standard error of status are seen when plots are added. 

Because the gains from increasing annual sample 

size seem relatively minor, and considering the 

aff ordable sample size, it may be more benefi cial 

overall to monitor additional ecological sites in 

CANY than to implement the optimum sample 

size for a few of the ecological sites. The response 

that would appear to benefi t most from increasing sample size is crust cover in the shrubland 

ecological site type (Appendix A, Figure A4-G.). 

However, the pilot data may be infl ating variance 

of this response, because the two ecological sites 

combined for the shrubland ecological site type 

have very diff erent amounts of crust cover. Ecological site 236 has high amounts of crust cover, 

while the soil surface in ecological site 133 is composed primarily of gravels, with small amounts of 

crust between the rocks. 

Increasing the rest time between revisits from two 

to seven years resulted in a fairly minor increase 

in the time required to detect trend, and an extremely small decrease in standard error of status 

(Appendix A, Figures A1 & A2). There was a fouryear delay in detecting trend in the worst-case 

scenario, but 80% power was reached by Year 7 

(Appendix A, Figure A1-K.). We feel that the (2-

5),(1-6) design (Design 2) is probably the best 

compromise for sampling uplands in CANY. Due 

to the sensitivity of BSCs to repeated trampling, 

we must consider whether repeated trampling at 

a lower total number of unique plots would be 

preferable to the impact of creating additional 

trails and new trampling to get a greater total 

number of unique plots.

When we are able to expand these analyses to include simulations and numerous additional years 

of data, we may see meaningful changes and need 

to alter the revisit design. While we do not expect 

this to happen, a key advantage of a GRTS design 

is the ability to recast the panel membership of 

existing sites into new structures.
8 Variance and Power for Trend Assessment of Pilot Data: Integrated Upland Monitoring, Canyonlands NP

5 Final design

The fi nal split-panel design for integrated upland 

monitoring at CANY will be based on Design 2, 

but modifi ed to sample aggregated ecological site 

types. The six original target ecological sites will 

be combined into three ecological site types: grassland, blackbrush, and pj/blackbrush (Table 5-1).

We will use the sampling frames of all four original target grassland ecological sites but combine 

them into a single grassland sampling frame. Any 

of the four grassland ecological sites will be monitored if it occurs anywhere within the grassland 

sampling frame. This will give us a diff erent number of plots for each grassland ecological site, but 

these numbers should represent the area of each 

ecological site across the landscape. 

Ecological site information will be recorded for 

each plot and used in trend analyses; however, 

annual reports will summarize data by ecological 

site type. This sampling strategy was chosen due 

to the similarity of grassland ecological sites and 

the low areal extent of two of the grassland ecological sites. 

The fi nal design, outlined in Figure 5-1, calls for 

the following:

• Sampling 48 upland monitoring plots per 

year using the rotating split-panel designs.

• Establishing 252 plots over a seven-year period. 

• Allowing 5–6 years of rest after sampling to 

give biological soil crust time to recover.

• Preferentially placing plots used in the threeyear pilot study (2006–2008) in panels 6 and 

14, to allow the maximum amount of rest after the initial three years of monitoring. 

Park managers received an outline of the design 

in May 2009, and were given the opportunity to 

provide feedback. Full operational monitoring of 

uplands in CANY began in June 2009.

Table 5-1. Ecological site type groupings.

Ecological site 

type Ecological site name

Grassland

(4,293 ha)

Desert Sand (sand sagebrush) 

Desert Sandy Loam (fourwing saltbush) 

Semidesert Sand (fourwing saltbush) 

Semidesert Sandy Loam (fourwing saltbush) 

Blackbrush

(2,212 ha)

Desert Shallow Sandy Loam 

(blackbrush) 

Pinyon-Juniper/

Blackbrush

(2,181 ha)

Semidesert Shallow Sandy Loam 

(Utah juniper-pinyon) 
Main Report 9

Final design for shrubland (blackbrush 

and PJ/blackbrush) ecological sites 

(2-5),(1-6).

Panel

Year

1 2 3 4 5 6 7 8 9 10

1 33 33

2 33 3 3

3 33 3

4 3 3

5 3 3

6 3 3

7 3 33

8 6 6

9 6 6

10 6 6

11 6

12 6

13 6

14 6

63 unique plots sampled for each ecological site over 7 years

12 plots per ecological site per year

Final design for grassland ecological sites 

(2-5),(1-6).

Panel

Year

1 2 3 4 5 6 7 8 9 10

1 66 66

2 66 66

3 66 6

4 6 6

5 6 6

6 6 6

7 6 66

8 12 12

9 12 12

10 12 12

11 12

12 12

13 12

14 12

126 unique plots sampled over 7 years 

24 plots per year among all four target grassland ecological sites

Figure 5-1. Final split-panel designs for integrated upland 

monitoring at Canyonlands National Park.
10 Variance and Power for Trend Assessment of Pilot Data: Integrated Upland Monitoring, Canyonlands NP

6 Literature Cited

Garman, S. L., D. Witwicki, and A. Wight. In review. Mapping ecological sites for long-term 

monitoring in national parks. Proceedings of 

the 9th Biennial Conference of Research on 

the Colorado Plateau.

Gerrodette, T. 1987. A power analysis for detecting trends. Ecology 68(5):1364–1372.

Larsen, D. P., T. M. Kincaid, S. E. Jacobs, and N. 

S. Urquhart. 2001. Designs for evaluating 

local and regional scale trends. BioScience 

51:1069–1078. 

Larsen, D. P., N. S. Urquhart, and D. L. Kugler. 

1995. Regional scale trend monitoring of 

indicators of trophic conditions of lakes. 

Water Resources Bulletin 31(1):117–140. 

MacDonald, T. L. 2003. Review of environmental monitoring methods: survey designs. 

Environmental Monitoring and Assessment 

85:277–292.

Spilke, J., H. P. Piepho, and X. Hu. 2005. Analysis 

of unbalanced data by mixed linear models 

using the MIXED procedure of the SAS system. Journal of Agronomy and Crop Science 

191:47–54.

Stevens, D. L., and A. R. Olsen. 2004. Spatially 

balanced sampling of natural resources. 

Journal of the American Statistical Association 99(465):262–278.

Urquhart, N. S., and T. M. Kincaid. 1999. 

Designs for detecting trend from repeated 

surveys of ecological resources. Journal of 

Agricultural, Biological, and Environmental 

Statistics 4:404–414.

Urquhart, N. S., W. S. Overton, and D. S. Birkes. 

1993. Comparing sampling designs for the 

monitoring of ecological status and trends: 

Impact of temporal patterns. Pages 71–85 in

V. Barnet and K. F. Turkman, eds., Statistics 

for the environment. London, U.K.: John 

Wiley and Sons.

Urquhart, N. S., S. G. Paulsen, and D. P. Larsen. 

1998. Monitoring for policy-relevant regional trends over time. Ecological Applications 8:246–257.

Witwicki, D. L., S. L. Garman, H. Thomas, A. 

Wight, R. H. Weissinger, T. E. O’Dell, and M. 

E. Miller. Draft integrated upland monitoring protocol for the park units in the Northern Colorado Plateau Network. National 

Park Service, Inventory and Monitoring Program, Northern Colorado Plateau Network, 

Moab, Ut.
Appendix A: Power for Trend Figures 11

Appendix A

Power for Trend Figures
12 Variance and Power for Trend Assessment of Pilot Data: Integrated Upland Monitoring, Canyonlands NP

Number of Years

0 5 10 15 20

SE of Status

0.0

0.2

0.4

0.6

0.8

1.0

Number of Years

0 5 10 15 20

SE of Status

0.0

0.2

0.4

0.6

0.8

1.0

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

Design 1 

Design 2

Design 3

Design 4

A

 

Number of Years

0 5 10 15 20

SE of Status

0.0

0.2

0.4

0.6

0.8

1.0

D

 

Design 1 

Design 2

Design 3

Design 4

B

 

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

Design 1 

Design 2

Design 3

Design 4

C

 Design 1 

Design 2

Design 3

Design 4

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

Design 1 

Design 2

Design 3

Design 4

E

 

Design 1 

Design 2

Design 3

Design 4

F

 

Basal gap size

2% annual increase

Canopy gap size

2% annual increase

Soil stability

2% annual decrease

Figure A1. Power for trend and standard error of status for each sampling design (Figure 3-1) at grassland ecological sites 

(annual sample size = 12). Responses include basal and canopy gap size, soil stability, and percent cover of biological soil 

crusts, bare soil, shrubs, perennial grass, and annual grass.
Appendix A: Power for Trend Figures 13

Number of Years

0 5 10 15 20

SE of Status

0.0

0.2

0.4

0.6

0.8

1.0

Number of Years

0 5 10 15 20

SE of Status

0.0

0.2

0.4

0.6

0.8

1.0

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

Design 1 

Design 2

Design 3

Design 4

G

Number of Years

0 5 10 15 20

SE of Status

0.0

0.2

0.4

0.6

0.8

1.0

J

 

Design 1 

Design 2

Design 3

Design 4

H

 

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

Design 1 

Design 2

Design 3

Design 4

I

 

Design 1 

Design 2

Design 3

Design 4

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

Design 1 

Design 2

Design 3

Design 4

K

 

Design 1 

Design 2

Design 3

Design 4

L

 

Crust cover

2% annual decrease

Bare soil cover

10% annual increase

Shrub cover

10% annual increase

Figure A1, cont.
14 Variance and Power for Trend Assessment of Pilot Data: Integrated Upland Monitoring, Canyonlands NP

Number of Years

0 5 10 15 20

SE of Status

0.0

0.2

0.4

0.6

0.8

1.0

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

Design 1 

Design 2

Design 3

Design 4

M

 

Number of Years

0 5 10 15 20

SE of Status

0.0

0.2

0.4

0.6

0.8

1.0

P

 

Design 1 

Design 2

Design 3

Design 4

N

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

Design 1 

Design 2

Design 3

Design 4

O

Design 1 

Design 2

Design 3

Design 4

Perennial grass cover

10% annual decrease

Annual grass cover

20% annual increase

Figure A1, cont.
Appendix A: Power for Trend Figures 15

Number of Years

0 5 10 15 20

SE of Status

0.0

0.2

0.4

0.6

0.8

1.0

Number of Years

0 5 10 15 20

SE of Status

0.0

0.2

0.4

0.6

0.8

1.0

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

Design 1 

Design 2

Design 3

Design 4

A

 

Number of Years

0 5 10 15 20

SE of Status

0.0

0.2

0.4

0.6

0.8

1.0

D

 

Design 1 

Design 2

Design 3

Design 4

B

 

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

Design 1 

Design 2

Design 3

Design 4

C Design 1 

Design 2

Design 3

Design 4

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

Design 1 

Design 2

Design 3

Design 4

E Design 1 

Design 2

Design 3

Design 4

F

 

Basal gap size

2% annual increase

Canopy gap size

2% annual increase

Soil stability

2% annual decrease

Figure A2. Power for trend and standard error of status for each sampling design (Figure 3-1) at shrubland ecological sites 

(annual sample size = 12). Responses include basal and canopy gap size, soil stability, and percent cover of biological soil 

crusts, bare soil, shrubs, perennial grass, and annual grass.
16 Variance and Power for Trend Assessment of Pilot Data: Integrated Upland Monitoring, Canyonlands NP

Number of Years

0 5 10 15 20

SE of Status

0.0

0.2

0.4

0.6

0.8

1.0

Number of Years

0 5 10 15 20

SE of Status

0.0

0.2

0.4

0.6

0.8

1.0

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

Design 1 

Design 2

Design 3

Design 4

G

 

Number of Years

0 5 10 15 20

SE of Status

0.0

0.2

0.4

0.6

0.8

1.0

J

 

Design 1 

Design 2

Design 3

Design 4

H

 

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

Design 1 

Design 2

Design 3

Design 4

I

 

Design 1 

Design 2

Design 3

Design 4

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

Design 1 

Design 2

Design 3

Design 4

K

 

Design 1 

Design 2

Design 3

Design 4

L

 

Crust cover

2% annual decrease

Bare soil cover

10% annual increase

Shrub cover

10% annual increase

Figure A2, cont.
Appendix A: Power for Trend Figures 17

Number of Years

0 5 10 15 20

SE of Status

0.0

0.2

0.4

0.6

0.8

1.0

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

Design 1 

Design 2

Design 3

Design 4

M

 

Number of Years

0 5 10 15 20

SE of Status

0.0

0.2

0.4

0.6

0.8

1.0

P

 

Design 1 

Design 2

Design 3

Design 4

N

 

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

Design 1 

Design 2

Design 3

Design 4

O

 

Design 1 

Design 2

Design 3

Design 4

Perennial grass cover

10% annual decrease

Annual grass cover

20% annual increase

Figure A2, cont.
18 Variance and Power for Trend Assessment of Pilot Data: Integrated Upland Monitoring, Canyonlands NP

Number of Years

0 5 10 15 20

SE of Status

0.0

0.2

0.4

0.6

0.8

1.0

Number of Years

0 5 10 15 20

SE of Status

0.0

0.2

0.4

0.6

0.8

1.0

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

n=7

n=12

n=36

n=50

A

 

Number of Years

0 5 10 15 20

SE of Status

0.0

0.2

0.4

0.6

0.8

1.0

n=7

n=12

n=36

n=50

D

 

B

 

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

n=7

n=12

n=36

n=50

C

 

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0 E

 

F

 

n=7

n=12

n=36

n=50

n=7

n=12

n=36

n=50

n=7

n=12

n=36

n=50

Basal gap size

2% annual increase

Canopy gap size

2% annual increase

Soil stability

2% annual decrease

Figure A3. Power for trend and standard error of status for each response variable at grassland ecological sites comparing 

annual sample sizes of 7, 12, 36, and 50 plots per year using Design 2 (Figure 3-2). Responses include basal and canopy gap 

size, soil stability, and percent cover of biological soil crusts, bare soil, shrubs, perennial grass, and annual grass.
Appendix A: Power for Trend Figures 19

Number of Years

0 5 10 15 20

SE of Status

0.0

0.2

0.4

0.6

0.8

1.0

Number of Years

0 5 10 15 20

SE of Status

0.0

0.2

0.4

0.6

0.8

1.0

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

n=7

n=12

n=36

n=50

G

 

Number of Years

0 5 10 15 20

SE of Status

0.0

0.2

0.4

0.6

0.8

1.0

J

 

H

 

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0 I

 

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0 K

 

L

 

n=7

n=12

n=36

n=50

n=7

n=12

n=36

n=50

n=7

n=12

n=36

n=50

n=7

n=12

n=36

n=50

n=7

n=12

n=36

n=50

Crust cover

2% annual decrease

Bare soil cover

10% annual increase

Shrub cover

10% annual increase

Figure A3, cont.
20 Variance and Power for Trend Assessment of Pilot Data: Integrated Upland Monitoring, Canyonlands NP

Number of Years

0 5 10 15 20

SE of Status

0.0

0.2

0.4

0.6

0.8

1.0

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

n=7

n=12

n=36

n=50

M

Number of Years

0 5 10 15 20

SE of Status

0.0

0.2

0.4

0.6

0.8

1.0

P

 

N

 

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0 O

 

n=7

n=12

n=36

n=50

n=7

n=12

n=36

n=50

n=7

n=12

n=36

n=50

Perennial grass cover

10% annual decrease

Annual grass cover

20% annual increase

Figure A3, cont.
Appendix A: Power for Trend Figures 21

Number of Years

0 5 10 15 20

SE of Status

0.0

0.2

0.4

0.6

0.8

1.0

Number of Years

0 5 10 15 20

SE of Status

0.0

0.2

0.4

0.6

0.8

1.0

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

n=7

n=12

n=36

n=50

A

 

Number of Years

0 5 10 15 20

SE of Status

0.0

0.2

0.4

0.6

0.8

1.0

n=7

n=12

n=36

n=50

D

 

B

 

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

n=7

n=12

n=36

n=50

C

 

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0 E

 

F

 

n=7

n=12

n=36

n=50

n=7

n=12

n=36

n=50

n=7

n=12

n=36

n=50

Basal gap size

2% annual increase

Canopy gap size

2% annual increase

Soil stability

2% annual decrease

Figure A4. Power for trend and standard error of status for each response variable at shrubland ecological sites comparing 

annual sample sizes of 7, 12, 36, and 50 plots per year using Design 2 (Figure 3-2). Responses include basal and canopy gap 

size, soil stability, and percent cover of biological soil crusts, bare soil, shrubs, perennial grass, and annual grass.
22 Variance and Power for Trend Assessment of Pilot Data: Integrated Upland Monitoring, Canyonlands NP

Number of Years

0 5 10 15 20

SE of Status

0.0

0.2

0.4

0.6

0.8

1.0

Number of Years

0 5 10 15 20

SE of Status

0.0

0.2

0.4

0.6

0.8

1.0

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

n=7

n=12

n=36

n=50

G

 

Number of Years

0 5 10 15 20

SE of Status

0.0

0.2

0.4

0.6

0.8

1.0

J

 

H

 

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0 I

 

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0 K

 

L

 

n=7

n=12

n=36

n=50

n=7

n=12

n=36

n=50

n=7

n=12

n=36

n=50

n=7

n=12

n=36

n=50

n=7

n=12

n=36

n=50

Crust cover

2% annual decrease

Bare soil cover

10% annual increase

Shrub cover

10% annual increase

Figure A4, cont.
Appendix A: Power for Trend Figures 23

Number of Years

0 5 10 15 20

SE of Status

0.0

0.2

0.4

0.6

0.8

1.0

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

n=7

n=12

n=36

n=50

M

 

Number of Years

0 5 10 15 20

SE of Status

0.0

0.2

0.4

0.6

0.8

1.0

P

 

N

 

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0 O

 

n=7

n=12

n=36

n=50

n=7

n=12

n=36

n=50

n=7

n=12

n=36

n=50

Perennial grass cover

10% annual decrease

Annual grass cover

20% annual increase

Figure A4, cont.
24 Variance and Power for Trend Assessment of Pilot Data: Integrated Upland Monitoring, Canyonlands NP

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

2% increase

5% increase

10% increase

A. Basal gap size

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

2% increase

5% increase

10% increase

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

2% decrease

5% decrease

10% decrease

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

2% decrease

5% decrease

10% decrease

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

5% increase

10% increase

20% increase

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

5% increase

10% increase

20% increase

A. Basal gap size

C. Soil stability

E. Bare soil cover

B. Canopy gap size

D. Crust cover

F. Shrub cover

Figure A5. Power for trend for a range of annual increases or decreases in response variables at grassland ecological sites 

using Design 2 (Figure 3-1) and an annual sample size of 12. Responses include basal and canopy gap size, soil stability, and 

percent cover of biological soil crusts, bare soil, shrubs, perennial grass, and annual grass.
Appendix A: Power for Trend Figures 25

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

5% decrease

10% decrease

20% decrease

G. Perennial grass cover

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

5% increase

10% increase

20% increase

H. Annual grass cover

G. Perennial grass cover H. Annual grass cover

Figure A5, cont.
26 Variance and Power for Trend Assessment of Pilot Data: Integrated Upland Monitoring, Canyonlands NP

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

2% increase

5% increase

10% increase

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

2% increase

5% increase

10% increase

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

2% decrease

5% decrease

10% decrease

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

2% decrease

5% decrease

10% decrease

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

5% increase

10% increase

20% increase

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

5% increase

10% increase

20% increase

A. Basal gap size

C. Soil stability

E. Bare soil cover

B. Canopy gap size

D. Crust cover

F. Shrub cover

Figure A6. Power for trend for a range of annual increases or decreases in response variables at shrubland ecological sites 

using Design 2 (Figure 3-1) and an annual sample size of 12. Responses include basal and canopy gap size, soil stability, and 

percent cover of biological soil crusts, bare soil, shrubs, perennial grass, and annual grass.
Appendix A: Power for Trend Figures 27

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

5% decrease

10% decrease

20% decrease

Number of Years

0 5 10 15 20

Power for Trend

0.0

0.2

0.4

0.6

0.8

1.0

5% increase

10% increase

20% increase

G. Perennial grass cover H. Annual grass cover

Figure A6, cont.

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