NPS Temporal Conference # 1
DESIGNING PANEL SURVEYS
SPECIFICALLY RELEVANT TO NATIONAL PARKS
IN THE NORTHWEST
N. Scott Urquhart
Senior Research Scientist
Department of Statistics
Colorado State University
Fort Collins, CO 80527-1877
NPS Temporal Conference # 2
INFERENCE PERSPECTIVES
 Design Based

Inferences rest on the probability structure
incorporated in the sampling plan
 Completely defensible; very minimal assumptions
 Limiting relative to using auxiliary information
 Model Assisted


Uses models to compliment underlying sampling
structure
Has opportunities for use of auxiliary information
 Model Based (eg: spatial statistics)


Ignores sampling plan
Defensibility lies in defense of model
NPS Temporal Conference # 3
APPROACH OF THIS PRESENTATION
 Use tools from the arena of


Model assisted and
Model based analyses
 To study the performance of


Design based &
Model-assisted analyses
 WHY?

Without models,
 performance evaluations need simulation
 Before substantial data have been gathered

No basis for values to enter into simulation studies
NPS Temporal Conference # 4
STATUS & TRENDS OVER TIME
IN ECOLOGICAL RESOURCES
OF A REGION
MAJOR POINTS
 Regional trend  site trend
 Detection of trend requires substantial elapsed time
 Regional OR intensive site
 Almost all indicators have substantial patterns in
their variability

Design to capitalize on this; don’t fight it.
 Minimize effect of site variability with planned
revisits – specific plans will be illustrated
 Design tradeoffs: TREND vs STATUS
NPS Temporal Conference # 5
REGIONAL TREND  SITE TREND
 The predominant theme of ecology:


Ecological processes
How does a specific kind of ecosystem function
 Energy flows
 Food webs
 Nutrient cycling

Most studies of such functions must be temporally
 Temporally intensive
– What material goes from where to where?
 Consequently spatially restrictive

In this situation: Temporal trend = site trend
NPS Temporal Conference # 6
REGIONAL TREND  SITE TREND
( - CONTINUED)
 The predominant theme of ecology
versus
 A Substantial (any) Agency Focus:

All of an ecological resource
 In an area or region
 Across all of the variability present there

Most government regulations
 Apply to a whole area or region
 Only a few apply to specific sites
 The definition of a “region” certainly depends on what agency
makes the regulation
NPS Temporal Conference # 7
REGIONAL TREND  SITE TREND
( - CONTINUED - III)
 The predominant theme of ecology
versus
 A substantial agency (EPA) focus:

An entire region, like
 Lakes in the Adirondack Mountains
 All lakes in Northeastern US
 All (wadeable) streams the mid-Appalachian Mountains
 Or National Park Service


All riparian areas in Olympic National Park
All riparian areas in National Parks in the
coastal Northwest
NPS Temporal Conference # 8
TREND ACROSS TIME - What is it?
 Any response which changes across time in a
generally


Increasing or
Decreasing
Manner shows trend

Monotonic change is not essential.
 If trend of this sort is present,
it will be detectable as linear trend.

This does NOT mean trend must be linear (examples
follow)
 Any specified form is detectable
 Time = years, here
NPS Temporal Conference # 9
TREND ACROSS TIME - What is it?
(continued)
TREND = YES
TREND = NO; PATTERN = YES
90
90
70
70
50
1989
1991
1993
1995
50
1989
1991
Year
1993
1995
1997
Year
TREND = YES, PATTERN = YES
TREND = NO; PATTERN = YES
400
350
300
300
CARBON DIOXIDE
CONCENTRATION (ppm)
CARBON DIOXIDE
CONCENTRATION (ppm)
350
250
200
150
100
50
0
1955
1965
1975
1985
YEAR
1995
2005
250
200
150
100
50
0
1955
1965
1975
1985
1995
2005
YEAR
NPS Temporal Conference # 10
TREND = NO; PATTERN = YES
DETRENDED CARBON DIOXIDE
CONCENTRATION (ppm)
350
300
TREND
= NO; PATTERN = YES
250
200
150
100
50
0
1955
1965
1975
1985
1995
YEAR
NPS Temporal Conference # 11
TREND DETECTION REQUIRES
SUBSTANTIAL ELAPSED TIME
 IT IS NEARLY IMPOSSIBLE TO DETECT
TREND IN LESS THAN FIVE YEARS. WHY?
var (  ) 
2
2
(
t

t
)
 i
YEARS
2
(
t

t
)
 i
3
4
5
6
7
8
9
10
2
5
10
17.5
28
42
60
82.5
NPS Temporal Conference # 12
BIOLOGICAL INDICATORS HAVE SOMEWHAT
MORE VARIABILITY THAN PHYSICAL
INDICATORS – BUT THIS VARIES, TOO
 Subsequent slides show the relative amount of
variability

Ordered by the amount of residual variability: least to
most (aquatic responses)











Acid Neutralizing Capacity
Ln(Conductance)
Ln(Chloride)
pH(Closed system)
Secchi Depth
Ln(Total Nitrogen)
Ln(Total Phosphorus)
Ln(Chlorophyll A)
Ln( # zooplankton taxa)
Ln( # rotifer taxa)
Maximum Temperature
And others, both
aquatic and
terrestrial
NPS Temporal Conference # 13
IMPORTANT COMPONENTS OF VARIANCE
 POPULATION VARIANCE:
2
( SITE
)
2
(

 YEAR VARIANCE:
YEAR )
2
(

 RESIDUAL VARIANCE:
RESIDUAL )
NPS Temporal Conference # 14
IMPORTANT COMPONENTS OF VARIANCE
( - CONTINUED)
2
 POPULATION VARIANCE: ( SITE
)

Variation among values of an indicator (response) across
all sites in a park or group of related parks, that is, across
a population or subpopulation of sites
NPS Temporal Conference # 15
IMPORTANT COMPONENTS OF VARIANCE
( - CONTINUED II)
2
(

 YEAR VARIANCE:
YEAR )

Concordant variation among values of an indicator
(response) across years for ALL sites in a regional
population or subpopulation

NOT variation in an indicator across years at a single site

Detrended remainder, if trend is present
 Effectively the deviation away from the trend line (or other
curve)
NPS Temporal Conference # 16
IMPORTANT COMPONENTS OF VARIANCE
( - CONTINUED - III)
 Residual component of variance

Has several contributors

Year*Site interaction
2
( RESIDUAL
)
 This contains most of what ecologists would call year to year
variation, i.e. the site specific part

Index variation
 Measurement error
 Crew-to-crew variation (minimize with documented protocols
and training)
 Local spatial = protocol variation
 Short term temporal variation
NPS Temporal Conference # 17
SOURCE OF DATA FOR ESTIMATES OF
COMPONENTS OF VARIANCE
 EMAP Surface Waters:
Northeast Lakes Pilot 1991 - 1994
 About 450 observations



Over four years
Including about 350 distinct lakes
Design allowed estimation of several residual
components
NPS Temporal Conference # 18
COMPOSITION OF TOTAL VARIANCE - NE LAKES
Acid Neutralizing Capacity
LAKE COMPONENT OF VARIANCE
Ln(Conductance)
Ln(Chloride)
pH(Closed system)
Secchi Depth
Ln(Total Nitrogen)
Ln(Total Phosphorus)
Ln(Chlorophyll A)
YEAR
Ln( # zooplankton taxa)
Ln( # rotifer taxa)
Maximum Temperature
0.00
RESIDUAL COMPONENT OF VARIANCE
0.20
0.40
0.60
0.80
1.00
PROPORTION OF VARIANCE
NPS Temporal Conference # 19
SOURCE OF COMPONENTS OF
VARIANCE FROM NW HABITAT
Oregon Department of Fisheries and Wildlife – stream habitat survey
 GRADIENT: Stream gradient measured on site
 WIDTH: Wetted stream width
 ACW: Active Channel
 ACH: Active Channel Height
 UNITS100: Number of distinct habitat units per 100 meters of stream length
 NOPOOLS: Number of pools in the surveyed reach
 POOLS100: Number of pools per 100 meters
 PCTPOOL: % of reach length in pools
 PCTFINES: % stream substrate that is sand or finer particle size
 PCTGRAVEL: % of stream stubstrate that is gravel sized particles
 RIFSNDOR: % of riffle stream length that is sand or finer particle size
 RIFGRAV: % of riffle stream length that is gravel sized particles
 SHADE: % stream channel shaded
 LOG(PIECESLWD +0.01): Number of pieces of large woody debris per 100 meters.
 LOG(VOLUMELWD +0.01): Volume of large woody debris (m^3/100 meters)
 RESIDPD: Volume of residual pools (pools remaining if streamflow stopped)
NPS Temporal Conference # 20
COMPOSITION OF TOTAL VARIANCE NW HABITAT
Ln(Conductance)
LAKE COMPONENT OF VARIANCE
pH(Closed system)
LOG(VOLUME L WD)
% Shaded
% Riffle fine
% Fines
Pools per 100m
UNITS100
YEAR
Active Channel Width
Gradient
RESIDUAL COMPONENT OF VARIANCE
0.00
0.10
PROPORTION OF VARIANCE
NPS Temporal Conference # 21
SOURCE OF COMPONENTS OF
VARIANCE FROM GRAND CANYON
 Grand Canyon Monitoring and Research Center

Effects of Glen Canyon Dam on the near River Habitat
in the Grand Canyon
 At various heights above the river
 Height is measured as the height of the river’s water
at various flow rates
 Eg: 15K cfs, 25K cfs, 35K cfs, 45K cfs & 60K cfs
 Using first two years’ data

Mike Kearsley – UNA
 Design = spatially balanced

With about 1/3 revisited
NPS Temporal Conference # 22
COMPOSITION OF TOTAL VARIANCE
GRAND CANYON -- NEAR RIVER VEGETATION
Richness - 60K cfs
Richness - 45K cfs
SITE COMPONENT OF
VARIANCELAKE COMPONENT
YEAR
RESIDUAL COMPONENT OF VARIANCE
Richness - 35K cfs
Richness - 25K cfs
Richness - 15K cfs
Veg - 60K cfs
Veg - 45K cfs
Veg - 35K cfs
Veg - 25K cfs
0.00
0.20
0.40
0.60
0.80
PROPORTION OF VARIANCE
1.00
NPS Temporal Conference # 23
ALL VARIABILITY IS OF INTEREST
 The site component of variance is one of the major
descriptors of the regional population
 The year component of variance often is small to
small to estimate. It is a major enemy for detecting
trend over time.
If it has even a moderate size, “sample size” reverts to the
number of years.
 In this case, the number of visits and/or number of sites
has no practical effect.

NPS Temporal Conference # 24
ALL VARIABILITY IS OF INTEREST
( - CONTINUED)
 Residual variance characterizes the inherent
variation in the response or indicator.
 But some of its subcomponents may contain useful
management information

CREW EFFECTS ===> training
 VISIT EFFECTS ===> need to reexamine definition of
index (time) window or evaluation protocol
 MEASUREMENT ERROR ===> work on
laboratory/measurement problems
NPS Temporal Conference # 25
DESIGN TRADE-OFFS: TREND vs STATUS
 How do we detect trend in spite of all of this
variation?
 Recall two old statistical “friends.”


Variance of a mean, and
Blocking
NPS Temporal Conference # 26
DESIGN TRADE-OFFS: TREND vs STATUS
( - CONTINUED)
 VARIANCE OF A MEAN:
var (mean) 
2
m

Where m members of the associated population have
been randomly selected and their response values
averaged.

Here the “mean” is a regional average slope, so "2"
refers to the variance of an estimated slope ---
NPS Temporal Conference # 27
DESIGN TRADE-OFFS: TREND vs STATUS
( - CONTINUED - II)
 Consequently
var (mean) 
 Becomes
2
m
1
2
var (regional mean slope) 
m  ( ti  t ) 2
 Note that the regional averaging of slopes has the
same effect as continuing to monitor at one site for a
much longer time period.
NPS Temporal Conference # 28
DESIGN TRADE-OFFS: TREND vs STATUS
( - CONTINUED - III)
 Now, 2, in total, is large.
 If we take one regional sample of sites at one time,
and another at a subsequent time, the site
component of variance is included in 2.
 Enter the concept of blocking, familiar from
experimental design.

Regard a site like a block

Periodically revisit a site

The site component of variance vanishes from the
variance of a slope.
NPS Temporal Conference # 29
NOW PUT IT ALL TOGETHER
 Question: “ What kind of temporal design should
you use for Northwest National Parks?
 We’ll investigate two (families) of recommended
designs.


All illustrations will be based on 30 site visits per year, as
Andrea recommended.
General relations are uninfluenced by number of sites
visited per year, but specific performance is.
 We’ll use the panel notation Trent set out.
NPS Temporal Conference # 30
RECOMMENDATION OF
FULLER and BREIDT
 Based on the Natural Resources Inventory (NRI)

Iowa State & US Department of Agriculture
 Oriented toward soil erosion &
 Changes in land use
 Their recommendation
MATH RECOME…
 Pure panel = [1-0] = “Always Revisit”
100%
50%
0%
50%
 Independent = [1-n] = “Never Revisit”
 Evaluation context


No trampling effect – remotely sensed data
No year effects
 Administrative reality of potential variation in
funding from year to year
NPS Temporal Conference # 31
TEMPORAL LAYOUT OF [(1-0), (1-n)]
YEAR
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
[1-0]
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
[1-n]
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
NPS Temporal Conference # 32
FIRST TEMPORAL DESIGN FAMILY
 30 site visits per year
[1-0]
30
20
10
0
[1-n]
0
10
20
30
ALWAYS
REVISIT
NEVER
REVISIT
NPS Temporal Conference # 33
POWER TO DETECT TREND
FIRST TEMPORAL DESIGN FAMILY
NO YEAR EFFECT
1
30:0
20:10
10:20
0:30
0.8
POWER
Always
Revisit
0.6
0.4
0.2
0
0
5
10
15
Never
Revisit
20
YEARS
NPS Temporal Conference # 34
POWER TO DETECT TREND
FIRST TEMPORAL DESIGN FAMILY,
MODEST (= SOME) YEAR EFFECT
1
30:0
20:10
10:20
0:30
POWER
0.8
0.6
0.4
0.2
0
0
5
10
15
20
YEARS
NPS Temporal Conference # 35
POWER TO DETECT TREND
FIRST TEMPORAL DESIGN FAMILY
BIG (= LOTS) YEAR EFFECT
1
30:0
20:10
10:20
0:30
POWER
0.8
0.6
0.4
0.2
0
0
5
10
15
20
YEARS
NPS Temporal Conference # 36
FOREST INVENTORY ANALYSIS (FIA)
HAS A SYSTEMATIC SPATIAL DESIGN
WITH [1-9]
YEAR
1
FIA
X
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
X
21
X
 Doesn’t match up well with [1-0] and [1-n]
 We need to investigate alternatives
NPS Temporal Conference # 37
SERIALLY ALTERNATING TEMPORAL
DESIGN [(1-3)4 ] SOMETIMES USED BY
EMAP
YEAR
1
FIA
X
[(1-3)4 ]
X
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
21
X
X
X
X
X
X
NPS Temporal Conference # 38
X
SERIALLY ALTERNATING TEMPORAL
DESIGN [(1-3)4 ] SOMETIMES USED BY
EMAP
YEAR
1
FIA
X
[(1-3)4 ]
X
2
3
4
5
6
7
8
9
10
11
X
X
X
…
X
X
X
…
X
X
X
X
…
…
X
 Unconnected in an experimental design sense

…
Very weak design for estimating year effects, if present
NPS Temporal Conference # 39
SPLIT PANEL [(1-4)5 , --- ]
YEAR
1
FIA
X
[(1-4)5 ]
X
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
21
X
X
 AGAIN, Unconnected in an experimental design
sense

Matches better with FIA
 Still a very weak design for estimating year effects, if
present
NPS Temporal Conference # 40
X
SPLIT PANEL [(1-4)5 ,(2-3)5 ]
YEAR
1
FIA
X
[(1-4)5 ]
X
2
3
4
5
6
7
8
9
X
12
13
14
15
16
17
18
19
20
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
21
X
X
X
X
11
X
X
[(2-3)5 ]
10
X
X
X
X
X
X
X
X
This Temporal Design IS connected
Has three panels which match up with FIA
NPS Temporal Conference # 41
X
X
X
SECOND TEMPORAL DESIGN FAMILY
 30 site visits per year
[1-4]
30
20
10
0
[2-3]
0
5
10
15
NPS Temporal Conference # 42
POWER TO DETECT TREND
SECOND TEMPORAL DESIGN FAMILY
NO YEAR EFFECT
1
30:0
20:5
10:10
0:15
POWER
0.8
0.6
0.4
0.2
0
0
5
10
YEARS
15
20
NPS Temporal Conference # 43
POWER TO DETECT TREND
SECOND TEMPORAL DESIGN FAMILY
SOME YEAR EFFECT
1
30:0
20:5
10:10
0:15
POWER
0.8
0.6
0.4
0.2
0
0
5
10
YEARS
15
20
NPS Temporal Conference # 44
POWER TO DETECT TREND
SECOND TEMPORAL DESIGN FAMILY
LOTS OF YEAR EFFECT
1
30:0
20:5
10:10
0:15
POWER
0.8
0.6
0.4
0.2
0
0
5
10
YEARS
15
20
NPS Temporal Conference # 45
COMPARISON OF POWER TO DETECT TREND
DESIGN 1 & 2 = ROWS
YEAR EFFECT
NONE
SOME
1
0.8
0.8
0.6
0.4
POWER
0.8
POWER
POWER
LOTS
1
1
0.6
0.6
0.4
0.4
0.2
0.2
0.2
0
0
0
5
10
15
20
0
0
YEARS
0
5
10
15
5
10
15
20
15
20
YEARS
20
1
1
0.8
0.8
0.8
0.6
0.6
0.6
0.4
0.2
POWER
1
POWER
POWER
YEARS
0.4
0.2
0
0.2
0
0
5
10
YEARS
15
20
0.4
0
0
5
10
YEARS
15
20
0
5
10
YEARS
NPS Temporal Conference # 46
POWER TO DETECT TREND
VARYING YEAR EFFECT AND TEMPORAL
DESIGN
1
TEMPORAL DESIGN 2
0.8
NONE
POWER
TEMPORAL DESIGN 1
0.6
SOME
0.4
LOTS
0.2
0
0
5
10
15
20
YEARS
NPS Temporal Conference # 47
STANDARD ERROR OF STATUS
TEMPORAL DESIGN 1, NO YEAR EFFECT
0.5
SE STATUS
0.4
TOTAL OF 30
SITES
0.3
30:0
20:10
10:20
0:30
0.2
110 SITES
VISITED BY
YEAR 5
0.1
0
0
5
10
410 SITES
VISITED BY
YEAR
20
15
YEARS
NPS Temporal Conference # 48
20
STANDARD ERROR OF STATUS
TEMPORAL DESIGN 1, SOME YEAR EFFECT
0.5
30:0
20:10
10:20
0:30
SE STATUS
0.4
0.3
0.2
0.1
0
0
5
10
15
YEARS
NPS Temporal Conference # 49
20
STANDARD ERROR OF STATUS
TEMPORAL DESIGN 1, LOTS OF YEAR EFFECT
0.5
SE STATUS
0.4
0.3
0.2
30:0
20:10
10:20
0:30
0.1
0
0
5
10
15
YEARS
NPS Temporal Conference # 50
20
STANDARD ERROR OF STATUS
TEMPORAL DESIGN 2, NO YEAR EFFECT
0.5
SE STATUS
0.4
30:0
20:5
10:10
0:15
TOTAL OF
75 SITES
0.3
0.2
0.1
TOTAL OF
150 SITES
0
0
5
10
15
YEARS
NPS Temporal Conference # 51
20
STANDARD ERROR OF STATUS
TEMPORAL DESIGN 2, SOME YEAR EFFECT
0.5
30:0
20:5
10:10
0:15
SE STATUS
0.4
0.3
0.2
0.1
0
0
5
10
15
YEARS
NPS Temporal Conference # 52
20
STANDARD ERROR OF STATUS
TEMPORAL DESIGN 2, LOTS OF YEAR EFFECT
0.5
30:0
20:5
10:10
0:15
SE STATUS
0.4
0.3
0.2
0.1
0
0
5
10
15
YEARS
NPS Temporal Conference # 53
20
SO WHAT?
Regardless of evaluation circumstances,
 Trend
detection improves the more the same sites are
revisited
 Status estimation improves as the number of distinct sites
visited increases
 Temporal design 2 is better than temporal design 1 in
relevant cases

Its power is only slightly influenced by split between panels
NPS Temporal Conference # 54
METADATA
 Really important for your successors

Like your grandchildrens’ generation
 I’ll comment about this later in the conference if you
want me to
NPS Temporal Conference # 55
FUNDING ACKNOWLEDGEMENT
The work reported here today was developed under the STAR Research Assistance
Agreement CR-829095 awarded by the U.S. Environmental Protection Agency (EPA) to
Colorado State University. This presentation has not been formally reviewed by EPA. The
views expressed here are solely those of presenter and STARMAP, the Program he
represents. EPA does not endorse any products or commercial services mentioned in this
presentation.
This research is funded by
U.S.EPA – Science To Achieve
Results (STAR) Program
Cooperative
# CR - 829095
Agreement
NPS Temporal Conference # 56
TEMPORAL DESIGN 1
ALWAYS REVISIT
TIME PERIOD ( ex: YEARS)
PANEL 1 2 3 4 5 6 7 8 9 10 11 12 13 ...
1
X X X X X X X X X X X X X
NPS Temporal Conference # 57
TEMPORAL DESIGN 2:
NEVER REVISIT
PANEL
1
2
3
4
5
6
7
8
9
1 2
X
X
TIME PERIOD ( ex: YEARS)
3 4 5 6 7 8 9 10 11 12 13 ...
X
X
X
X
X
X
X
NPS Temporal Conference # 58
TEMPORAL DESIGN 3:
AUGMENTED SERIALLY ALTERNATING
TIME PERIOD ( ex: YEARS)
PANEL 1 2 3 4 5 6 7 8 9 10 11 12 13 ...
0
X X X X X X X X X X X X X
1
X
X
X
X
2
X
X
X
3
X
X
X
4
X
X
X
NPS Temporal Conference # 59
TEMPORAL DESIGN 4: SPLIT PANEL
SERIALLY ALTERNATING
PLUS SERIALLY ALTERNATING WITH CONSECUTIVE YEAR REVISITS
PANEL
1
1A
2
2A
3
3A
4
4A
TIME PERIOD ( ex: YEARS)
1 2 3 4 5 6 7 8 9 10 11
X
X
X
X X
X X
X X
X
X
X
X X
X X
X X
X
X
X
X X
X X
X
X
X
X X
X X
12 13 ...
X
X
X
X
X X
NPS Temporal Conference # 60
DESIGN EFFECT
1
A
POWER for TREND
0.8
0.6
DESIGNS 1, 3, & 4
0.4
DESIGN 2
0.2
0
0
5
10
TIME ( = YEARS )
15
NPS Temporal Conference # 61
20
LAKE EFFECT; DESIGNS 2 & 4
VAR LAKE = 1, 2, 5
POWER for TREND
1
B
0.8
0.6
DESIGN 4
ALL VARIANCES
0.4
1
2
0.2
DESIGN 2
LAKE VAR = 5
0
0
5
10
15
TIME ( = YEARS )
NPS Temporal Conference # 62
20
YEAR EFFECT - DESIGNS 2 & 4
1
C
YEAR EFFECT
0, 0.05, 0.10
TOP CURVES FOR 0.00
POWER for TREND
0.8
0.6
0.4
DESIGN 2
DESIGN 4
0.2
0
0
5
10
15
TIME ( = YEARS )
NPS Temporal Conference # 63
20
STANDARD ERROR (STATUS)
STANDARD ERROR OF ESTIMATED STATUS ALL DESIGNS
0.4
D
DESIGN 1
0.2
DESIGN 2
DESIGNS 3 & 4
0
0
5
10
15
TIME ( =Years )
NPS Temporal Conference # 64
20
SIZE OF TREND EFFECT: DESIGN 4
1
E
POWER for TREND
0.8
l = 0.03
l = 0.02
0.6
l = 0.015
0.4
l = 0.01
0.2
0
0
5
10
15
20
TIME ( = YEARS )
NPS Temporal Conference # 65
SAMPLE SIZE EFFECT - DESIGN 4
1
F
POWER for TREND
0.8
n = 240
0.6
n = 120
0.4
n = 60
0.2
0
0
5
10
TIME ( = YEARS )
15
NPS Temporal Conference # 66
20
SECCHI DEPTH
1.2
A
1
3% PER YEAR
0.8
1% PER YEAR
0.6
0.4
0.2
0
0
5
10
TIME ( = YEARS )
15
NPS Temporal Conference # 67
ln ( CHLOROPHYLL a )
POWER for TREND
1
A
0.8
3% PER YEAR
0.6
0.4
1% PER YEAR
0.2
0
0
5
10
15
TIME ( = YEARS )
NPS Temporal Conference # 68
20
ln(TOTAL PHOSPHORUS)
1
A
POWER for TREND
0.8
0.6
3% PER YEAR
0.4
0.2
1% PER YEAR
0
0
5
10
15
20
TIME ( = YEARS )
NPS Temporal Conference # 69
ln( NUMBER ZOOPLANKTON TAXA)
1
POWER for TREND
0.8
0.6
3% PER YEAR
0.4
0.2
1% PER YEAR
0
0
5
10
15
TIME ( = YEARS )
NPS Temporal Conference # 70
20