United States

Department of

Agriculture

Forest Service

Pacific Northwest

Research Station

Research Paper

PNW-RP-533

April 2001

Detecting Response of Douglas-Fir

Plantations to Urea Fertilizer at

Three Locations in the Oregon

Coast Range

Richard E. Miller, Jim Smith, and Harry Anderson
Richard E. Miller is an emeritus scientist and Harry Anderson is a volunteer, U.S.

Department of Agriculture, Forest Service, Pacific Northwest Research Station, 3625

93rd Ave. SW, Olympia, WA 98512-9193; and Jim Smith is a forester, The Timber

Company, Cottage Grove, OR 97424.

Authors
Miller, Richard E.; Smith, Jim; Anderson, Harry. 2001. Detecting response of

Douglas-fir plantations to urea fertilizer at three locations in the Oregon Coast

Range. Res. Pap. PNW-RP-533. Portland, OR: U.S. Department of Agriculture,

Forest Service, Pacific Northwest Research Station. 20 p.

Fertilizer trials in coast Douglas-fir (Pseudotsuga menziesii var. menziesii (Mirb.)

Franco) in the Oregon Coast Range usually indicate small and statistically nonsignificant response to nitrogen (N) fertilizers. Inherently weak experimental designs of past

trials could make them too insensitive to detect growth differences that actually exist.

Ability to detect real differences among treatments should be improved by having

more than two replications per treatment and by using covariance analysis to adjust

observed treatment means for unequal starting conditions among experimental treatments. To demonstrate these assumptions, we used size at fertilization and a prefertilization (calibration) period of growth as covariates when analyzing data from five

coastal plantations. The trials had three to six replications per treatment and calibration

periods of 6 or 7 years. Nitrogen fertilizer was assigned randomly to half the plots at

each location when trees were 16 or 17 years old from seed. Our objectives were to

quantify 4- or 7-year response to N fertilizer and to demonstrate practical means for

detecting response. Effects of fertilization on tree diameter and height, and on basal

area and volume growth per acre were estimated. Among the five nonthinned plantations, observed gross basal area growth was changed by -2 to 13 percent in the

4 or 7 years after fertilization. Observed responses were increased substantially by

covariance analyses at some plantations but decreased at others. Random assignment of three to six plots per treatment did not ensure balanced or comparable plots

for fertilized and nonfertilized treatments.

Keywords: Douglas-fir, Pseudotsuga menziesii, nitrogen, fertilization, urea, tree growth,

stand growth.

Most fertilizer trials in coast Douglas-fir (Pseudotsuga menziesii var. menziesii (Mirb.)

Franco) stands in the Oregon Coast Range indicate small and statistically nonsignificant response to urea or ammonium nitrate. Small response to nitrogen (N) could be

explained by nitrogen sufficiency in this area as suggested by above-average site

quality. Alternatively, weakly replicated experimental designs of past trials could make

them too insensitive to detect differences that actually existed among treatments. We

speculated that ability of field trials to detect real differences among treatments could

be improved by more replications per treatment and by using covariance analysis to

adjust observed treatment means for unequal starting conditions among experimental

treatments. Accordingly, we used stand basal area and volume at fertilization and prefertilization (calibration) growth as covariates when analyzing data from a total of five

plantations at three locations in the Oregon Coast Range. These plantations of 30 halfsib families (from 30 open-pollinated mother trees) had three to six replicate plots per

treatment and a calibration period of 6 or 7 years before fertilization. Nitrogen fertilizer

was assigned randomly to half the plots at each location when trees were 16 or 17

years old from seed. Our objectives were to quantify tree response to N fertilizer and

to demonstrate practical means for detecting response. Effects of fertilization on tree

diameter and height, and on basal area and volume growth per acre, were estimated.

With few exceptions, means of tree and stand attributes before fertilization appeared

similar for fertilized and control groups at the five plantations. Coefficients of variation

expressing variation among replicate plots within fertilized and control groups seldom

exceeded 10 percent.

Abstract

Summary
Tree losses were similar on fertilized and nonfertilized plots in the 4- or 7-year period

after fertilization. Among the five nonthinned plantations, change in quadratic mean

diameter at breast height was accelerated by fertilization at most plantations. Observed (unadjusted) gross basal area growth on fertilized plots in the 4- or 7-year

period ranged from 1.7 percent less to 13.1 percent greater than on nonfertilized plots.

Analysis of variance indicated that mean observed responses of 10 percent or more

were statistically significant (P < 0.10). With covariance adjustment, however, both

absolute and percentage response were decreased at four of five plantations. This

indicates (1) that prefertilization conditions on fertilized plots averaged more favorable

than those on control plots and (2) that using unadjusted means could lead one to

overestimate response at four of the five locations. Of the two covariates, basal area

growth in the 6- to 7-year period before fertilization was more frequently related to

growth than was basal area per acre at fertilization.

We observed small, so-called “negative response” (-1.7 percent) in basal area growth

to 200 lb N/acre at one plantation (with six replications of each treatment). This negative response in both observed and adjusted means, however, was statistically nonsignificant (P = 0.49 or 0.59, respectively); therefore, likely due to chance and validly

interpreted as “no effect” rather than a “negative effect” of fertilization. Although this

interpretation warranted our using one-tail testing, we remained with conventional twotail tests.

Portions of only one plantation were concurrently thinned and fertilized. About 60 percent of live trees before thinning were retained and this included at least two trees of

each half-sib family on each plot. Relative density averaged about 46 before thinning

and 28 after thinning. Thinning removed slightly smaller-than-average trees. When data

of this plantation (set E) were analyzed as a 2 × 2 factorial, (1) the thinning × fertilizing

interaction was nonsignificant so that one could generalize separately about the effects

of thinning and fertilization; (2) mean height growth for all measured trees that survived

the 7-year period was similar for thinned and nonthinned trees; (3) stand basal area

growth in thinned plots was similar to that in nonthinned; (4) yet, periodic annual volume growth of thinned plots averaged 286 cubic feet per acre compared to 355 cubic

feet per acre for nonthinned plots (This shortfall of 68 ft3

/year [19 percent] is the

expected consequence of the reduced basal area growing stock [40 percent) after

thinning]; and (5) N fertilization (200 lb N/acre) increased 7-year basal area growth by 9

percent in both thinned and nonthinned plots.

“Effect size” (ES) relates effect (difference between the treatment means) and the

common variance in the treatment and control distributions (expressed as standard

deviation or variance1/2). In these plantations, ES in observed basal area response to

fertilization ranged from -0.32 to 7.88. Effect sizes of 3.28 or larger in basal area response were statistically significant (P < 0.10). This usually corresponded to 9 percent

or greater increases in basal area growth. Effect sizes were much larger at the Bone

Mountain plantations than at the two Toledo locations because (1) both observed and

adjusted responses were larger and (2) variation in response (residual mean squares)

were consistently smaller. When ES is large, fewer replications are required to detect

significant differences among treatments (reject a “no effect” [or null] hypothesis from

statistical testing).
We demonstrated the potential consequences of assigning only two replications of

each treatment in these stands with minimal variation in tree numbers and stand basal

area. When the two best-stocked plots of the fertilized were arbitrarily matched to the

two poorest stocked control plots (match 1), measured response was inflated. Conversely, response was deflated or negative when the two best stocked control plots

were matched to the two poorest stocked fertilized plots. Among the five plantations,

basal area responses computed from matches 1 and 2 differed by 30 percent to 32-fold

from those observed from using all replicate plots.

To improve detection of response to fertilizers, the following should be attempted:

• Install trials in uniformly stocked and structured stands or, alternatively, group plots

in blocks of similar within-block stocking and structure.

• Install at least three replications to enable covariance analysis and adjustment of

observed means.

• Recognize that a large number of replications of each treatment is necessary to

detect the small response to N fertilization that is characteristic of above-average

site quality stands of coast Douglas-fir.

We concluded the following from our fertilization trial in five plantations:

1. Coefficients of variation in tree and stand attributes in these plantations before

fertilization were about 5 percent in trees per acre, 15 percent in basal area, and

20 percent in cubic volume, despite the fact that all trees in each plantation (1)

originated from the same half-sib families, (2) were planted at precise tree-to-tree

spacing, and (3) received intensive protection from large animals and weed

competition.

2. Random assignment of three to six plots per treatment did not assure balanced or

comparable plots for fertilized and nonfertilized treatments.

3. Covariance analysis did not consistently reduce experimental error (residual mean

square) or increase effect size.

4. Detection of stand response to fertilization of Douglas-fir on above-average site

quality requires careful planning and execution. Expected response to 200 lb N/acre

is small and experimental error (unaccounted sources of variation) is usually large.
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1

Fertilizer trials in Douglas-fir stands (Pseudotsuga menziesii var. menziesii (Mirb.)

Franco) in the Oregon Coast Range usually indicate small and statistically nonsignificant response to urea or ammonium nitrate fertilizers.1 Small response to nitrogen (N)

in this area could be explained by N sufficiency as suggested by above-average site

quality. The inherently weak experimental design of past trials, however, could make

them too insensitive to detect differences that actually existed among treatments. For

example, most existing trials have only two replicate plots for each treatment, and

stand volume or basal area among plots before fertilization can differ by 20 percent or

more. This creates a risk that control and fertilized treatments may not equally sample

initial differences in site quality and growing stock. Moreover, large differences among

plots in site quality, starting volume, or basal area contribute to large among-plot variation in subsequent tree growth. This variation in growth among replicates inflates the

experimental error term in statistical analyses; consequently, response to fertilization is

less likely to be judged statistically significant or real.

Numerous factors determine statistical “power” or the sensitivity of trials to detect real

differences among treatments (Lipsey 1990). These include (1) the statistical tests

used for analyzing data, (2) choice of alpha level for statistical significance testing, (3)

sample size (the number of replicates or experimental units per treatment), and (4)

“effect size” (the response to treatment relative to its variance). In this report, we examine these factors by using data from five plantations in the Oregon Coast Range.

Our objectives were to detect tree response to N fertilization at these locations and to

demonstrate practical benefits of improved experimental design and of covariance

analysis. We estimated tree and stand response to 200 lb N/acre applied as urea in

four nonthinned plantations. Additionally at the fifth plantation, we compared response

to N in nonthinned plots to response in concurrently thinned plots. The five plantations

had three to six replicate plots per treatment and calibration periods of 6 or 7 years

before fertilization.

Several plantations of half-sib families (from 30 open-pollinated mother trees) were

established in 1972 or 1973 after clearcutting and intensive site preparation at each

of five progeny-test locations on Georgia-Pacific Corporation land. Five plantations at

three of these locations were selected. These three study areas (Toledo North, Toledo

South, and Bone Mountain) provided maximum numbers of trees available from (1)

original planting and (2) replacement plantings in years 1, 2, 3, and later (table 1).

Uniformly planted and intensively managed, these plantations provided an opportunity

to estimate response to N fertilizer in uniform stand conditions. Each plantation contained 6 to 12 plots with the same 30 half-sib families. Families differed among the five

plantations, however. Each plot contained four to five randomly located trees for each

family as noncontiguous (single tree) family subplots. After planting at a 9- by 9- or 9-

by 10-foot spacing within 5- to 10-acre areas surrounded by an 8-foot tall fence, the

1-year-old, container-grown seedlings at each location were subsequently safeguarded

from weeds, disease, and animal damage. These actions and some replacement

planting resulted in uniformly spaced, well-stocked stands at age 16 or 17 years from

seed (figs. 1, 2, 3, and 4).

Introduction

Methods

1 Miller, R.E.; Hazard, J.W.; Bruce, D. 1991. Response

of western Oregon stands to nitrogen fertilizer. Interagency Agreement PNW 88-557. Portland, OR. On file

with: Forestry Sciences Laboratory, 3625 93rd Ave. SW,

Olympia, WA 98512.
2

Table 1—Description of three study locations installed by Georgia-Pacific Corporation in the Oregon

Coast Range

Plot size

Site index a Plots per

Area Sets Soil series a (50 yr) plantation Fertilizedb Measured

Ft No. – – – – – Acres – – – – –

Toledo:

North E, F Blachy silty clay loam 126 12 0.314 0.225

South A Elsie silt loam 143 10 .243 .169

Coquille:

Bone Mountain A, B Preacher loam 127 6 .212 .147

a According to soil survey maps and reports.

b 200 lb N/acre ÷ 0.46 = 435 lb urea/acre.

A

B

Figure 1—Aerial view of the Toledo North (A) and

Toledo South (B) study areas when trees were about

6 years old.
3

Figure 3—Portions of the Toledo South plantation after 1989 growing season; tree age 17 years

from seed.

Figure 2—Portions of the Toledo North plantations after 1989 growing season; tree age 17 years

from seed.
4

Figure 4—Aerial view of the Bone Mountain plantations after 1980 growing season; tree age 7 years

from seed. Sets A and B are in the left half of the more uniform, lower block of trees.

Fertilization and

Thinning

Tree Measurement

The three study areas, each with one or two study plantations, are located on level to

gently sloping topography with well-drained soil series weathered from sedimentary

(Preacher), alluvium (Elsie), or basic igneous and sedimentary rock (Blachly). Effective

rooting depth of modal (characteristic) profiles is 60 inches or more. Mean site index

(50-year base age) ranged between 126 and 143 feet (table 1).

A fertilization treatment was assigned randomly to half the plots in each plantation.

Urea fertilizer providing 200 lb N/acre was uniformly spread over assigned plots in

spring 1990 (table 1). To ensure uniformity of applications, the gross plot area was

quartered with string, then the total fertilizer for each plot was weighed and volumetrically allocated to four large containers, each containing the fertilizer for a quarter-plot.

Fertilizer in each large container was transferred to four smaller buckets for application.

Contents of two buckets were spread uniformly over each quarter-plot; then the fertilizer in the remaining two buckets was spread over the same quarter-plot, but at right

angles to the direction of the first spread. Cool weather and showers in the 2 weeks

after fertilization probably minimized potential losses from urea volatilization.

Only portions of the set E plantation at Toledo North were thinned. Six of the 12 plots

were thinned before the 1990-growing season. About 60 percent of the trees were

retained after thinning. Hence, effects of concurrent thinning and fertilization, alone

and in combination, could be analyzed as a 2 x 2 factorial design (three replications

per treatment).

Diameter at breast height (d.b.h.) of all trees in interior subplots (0.169 to 0.225 acres)

was measured with a steel tape. Trees for measurement were identified with numbered

aluminum tags at breast height (4.5 ft) and were pruned to 6-foot height to provide safe

access and more reliable measurement of d.b.h. to nearest 0.1 inch. Total height of

100 or more trees per plot was measured initially at age 16 or 17 years by either
5

height-measuring poles or clinometers (to the nearest foot). Four years later (7 years

later at set E, Toledo North), about 60 trees per plot were measured with clinometers.

Buffer areas around interior plots contained only one row of trees. Although wider buffers were desirable, interior subplots would have been smaller so that fewer trees

would have been available for evaluating effects of fertilization.

Stand basal area growth before and after fertilization was calculated from d.b.h. measurements. Total bole volume (total stem volume above a 6-in stump) was estimated

for each tree using a general volume equation (Bruce and DeMars 1974) accessed

by measured d.b.h. and either measured height or estimated height from a heightdiameter equation specific to each plot and year. The height equation was of the form,

H = a - b (1/d.b.h.). Periodic mean annual growth and mortality in basal area and cubic

volume were computed by summing individual tree data.

Effects of fertilization on height and diameter growth of surviving trees, and on change

in tree numbers, basal area, and volume per acre were estimated and compared by

analysis of variance (ANOVA) and by covariance analyses (SAS 1988). Growth before fertilization, and tree and stand statistics at fertilization were used separately as

covariates. Thereby, we computed adjusted means of growth and response.

With few exceptions, means of tree and stand attributes before fertilization were similar

for fertilized and control groups at the five plantations (table 2). Coefficients of variation

(CV) expressing variation among replicate plots in treated and control groups seldom

exceeded 10 percent. The five fertilized plots at the Toledo South plantation varied

most in before-fertilization statistics.

Tree size—Although trees in all plantations were either 16 or 17 years from seed,

quadratic mean d.b.h. (QMD) was markedly larger at Toledo locations in central

Oregon than in the 1-year younger plantations at Bone Mountain in southern Oregon

(table 2). Height of the 40 largest diameter trees per acre (H40) clearly favored the

Toledo plantations, especially at Toledo South, where the modal 50-year site index for

the soil series was estimated at 143 feet compared to 126 feet and 127 feet at the two

other locations (table 1). H40 is similar to the sample height required by King (1966) to

estimate site index (Curtis 1983).

Tree numbers, basal area, and volume—All plantations were well stocked before

fertilization. Basal area showed less plot-to-plot variation within treatment groups than

did volume (table 2). This was expected, because basal area is derived from d.b.h.

measurement of all trees, whereas volume is further derived from a sample of tree

heights. The height sample in this study was unusually large, consisting of nearly all

trees at the prefertilization inventory, but reduced at remeasurement because a commercial thinning 4 years after fertilization removed every third row. Tree d.b.h., however, was measured before thinning occurred.

Only set E at Toledo North was concurrently thinned and fertilized. About 60 percent

of trees were retained, and this included at least two trees of each half-sib family on

each plot. Relative density (RD) averaged about 46 before thinning and 28 after thinning (table 2). The difference in QMD immediately after thinning (0.2 and 0.1 in for the

two thinned treatments) indicates that thinning removed slightly smaller-than-average

trees.

Data Summary

Statistical Analyses

Results

Stand Statistics Before

Fertilization

Thinning Intensity
6

Table 2—Mean live-stand statistics before fertilization, by location and treatment, per acre basis when pertinent

Before fertilization or thinningb After thinning

QMD H40 Stems BA Vol. RD QMD Stems BA Vol. RD

Location Set Tmt.a CV CV CV CV CV CV

In % Ft % No. % Ft 2 % Ft 3 % — % In No. Ft 2 Ft 3 —

Toledo North E C 6.3 5 43.6 4 521 4 114 6 1,709 9 45.2 5 — — — — —

F 6.7 3 44.2 1 529 1 127 5 1,978 5 49.2 4 — — — — —T 6.4 2 42.1 4 531 3 116 2 1,637 6 46.1 1 6.6 308 76 1,095 29.2

FT 6.3 1 44.4 1 533 2 115 1 1,749 1 45.8 1 6.4 298 68 1,051 26.6

F C 6.4 4 43.1 6 539 3 121 6 1,757 16 47.7 5 — — — — —

F 6.5 3 43.3 6 529 2 121 6 1,810 11 47.6 5 — — — — —

Toledo South A C 6.7 4 51.3 3 614 4 149 8 2,786 10 57.6 6 — — — — —

F 6.5 6 50.6 6 596 3 138 14 2,566 19 54.0 11 — — — — —

Bone Mountain A C 5.1 4 38.0 2 671 4 94 6 1,300 9 41.8 5 — — — — —

F 4.9 2 38.0 2 682 2 89 4 1,224 4 40.0 3 — — — — —

B C 5.4 2 39.2 4 676 2 108 7 1,548 9 44.7 12 — — — — —

F 5.0 4 37.0 6 673 1 93 10 1,245 13 41.3 8 — — — — —

a C = control, F = fertilized, T = thinned, FT = fertilized and thinned concurrently.b QMD = quadratic mean diameter; CV = (standard deviation ÷ mean) 100; H40 = mean height of largest 40 trees per acre (by d.b.h.); BA = basal area; Vol. = cubic

volume of total stem; RD (Curtis 1982) = BA/SQRT(QMD) 1⁄2.
7

Net change in QMD and mean height resulted from two components: arithmetic

changes resulting from tree losses and actual tree growth. Because mortality was

relatively slight between age 17 and 21 years in the plantations, change in QMD was

only slightly affected by the arithmetic effect of tree losses. Increase in QMD was accelerated by fertilization at most plantations (table 3). Analysis of mean height growth

was restricted to trees measured at both starting and ending measurement. Mean

height growth of these survivors on fertilized plots was similar to that on nonfertilized

plots (table 3).

Tree losses between age 17 and 21 years were similar on fertilized and nonfertilized

plots (table 3). No trees died on any plots at Bone Mountain, the area of lower site

quality.

Among the five plantations, unadjusted gross basal area growth on fertilized plots

ranged from 1.7 percent less to 13.1 percent greater than on nonfertilized plots (table

4). Without covariance adjustment, mean responses of 10 percent or more were statistically significant (P < 0.10). With covariance adjustment, both absolute and percentage

response were decreased at four of five plantations (table 4). This indicates that prefertilization stocking on fertilized plots at these four locations averaged more favorable

than those on control plots. After covariance analysis, mean adjusted responses of

about 9 percent or more were statistically significant. Basal area growth was more

frequently related to growth in the 3- to 6-year period before fertilization than to basal

area per acre at fertilization (table 4).

Observed (unadjusted) net volume growth on fertilized plots averaged statistically

significantly greater than that on nonfertilized plots only at two of the five plantations

(table 5). With covariance adjustment for differences in starting volume among fertilized

and nonfertilized plots, response was decreased at two of five plantations (table 5).

Covariance adjustment was especially strong at Bone Mountain, set B, where starting

volume averaged 24 percent greater on control plots than on fertilized plots (table 2).

Consequently, adjusted 4-year response was 50.9 cubic feet per year (14.9 percent)

compared to observed response of -6.8 cubic feet per year (-1.8 percent).

Although the number of residual trees in thinned plots at Toledo North (set E) averaged

about 60 percent of those in the nonthinned plots (table 2), observed net basal area

growth per acre on thinned plots was similar to that on nonthinned plots (table 3). Observed volume growth per acre, however, averaged less on thinned plots than on nonthinned. Reanalyses of the data as a 2 x 2 factorial instead of as separate thinned and

unthinned groups permitted statistical testing of these two groups. These tests showed

the following: (1) the thinning by fertilizing interaction was nonsignificant (table 6), so

that one could generalize separately about the general effects of thinning and of

fertilizing; (2) mean height growth for all measured trees that survived the 7-year period

was similar for thinned and nonthinned trees; (3) mean basal area growth per acre in

thinned plots was similar to that in nonthinned plots; but (4) annual volume growth of

thinned plots averaged 286 cubic feet per acre compared to 355 cubic feet per acre for

nonthinned plots (This shortfall of 68 ft3

/year [19 percent] is the expected consequence

of reduced basal area growing stock [40 percent] after thinning [Evert 1964: 813; Curtis

and Marshall 1986: 80]); and (5) N fertilization increased basal area growth by 9

percent in both thinned and nonthinned plots.

Change in Tree QMD and

Height After Fertilization

Tree Mortality After

Fertilization

Stand Basal Area Growth

and Response to N

Fertilization

Stand Volume Growth

and Response After

Fertilization

Effect of Concurrent

Thinning
8

Table 3—Observed mean annual change in the first 4 years (set E = 7 years) after fertilization, by location and treatment, per acrebasis when pertinent

Periodic net annual change b c

QMD HT Live stems BA Vol. Periodic annual mortality

Location Set Tmt a Yr CV CV CV CV CV Live stems BA Vol.

In % Ft % No. % Ft2 % Ft3 % No. Ft2 Ft3

Toledo North E-UT C 7 0.24 6 2.5 3 -2.1 72 9.2a 3 333b 5 1.6 0 0.10

F .24 6 2.6 5 -2.1 45 10.0a 6 376a 3 0 0.02 0

E-T T 7 .35 5 2.5 6 0 0 9.4b 3 282a 7 0 0 0

TxF .40 4 2.5 12 0 0 10.0a 4 291a 12 0 0 0

F C 4 .27 5 2.2 7 -0.4 156 11.1a 5 314a 11 .3 .02 .2

F .27 0 2.2 12 -0.9 196 10.9a 5 320a 11 .4 .03 .8

Toledo South A C 4 .24 12 2.9 10 -2.1 122 10.2b 6 441a 5 2.1 .30 6.0

F .27 12 2.9 4 -3.2 36 11.3a 8 439a 4 2.6 .40 7.4

Bone Mountain A C 4 .34 4 2.8 4 0 0 14.5b 2 381b 2 0 0 0

F .38 0 3.1 2 0 0 16.4a 1 418a 3 0 0 0

B C 4 .30 0 2.5 2 0 0 13.7b 2 371a 5 0 0 0

F .36 4 2.6 14 0 0 15.1a 2 365a 10 0 0 0

a C = control, F = fertilized, T = thinned, FT = fertilized and thinned concurrently.b HT = mean height of surviving, measured trees.c For each set, treatment means with differing letters are significantly different (P < 0.10).
9

Table 4–Observed and adjusted, mean gross annual response in basal area growth after fertilization, nonthinned stands, peracre basisa

Observedb Adjustedc Adjustedd

Location Set Reps Response Response Regress. Response Regress.

Ft 2 % P Ft 2 % P P Ft 2 %P P

Toledo North E 3 0.80 8.7 0.11 1.31 14.6 0.11 0.33 0.96 10.5 0.20 0.71

F 6 -.19 -1.7 .59 -.21 -1.9 .53 .34 -.21 -1.9 .49 .07

Toledo South A 5 1.19 11.3 .07 e ee e .67 6.3 .25 .08

Bone Mountain A 3 1.90 13.1 .01 1.77 12.2 .01 .42 1.83 12.6 .01 .63

B 3 1.42 10.4 .01 1.20 8.7 .08 .58 1.26 9.2 .07 .68

a Response = PAI fertilized - PAI control; 7 years at set E, 4 years at other sets.b Analysis of variance; P = probability value.c Covariance analysis using prefertilization basal area as covariate.d Covariance analysis using prefertilization basal area growth as covariate (1982-89 or 7 years at Toledo North and South; 1983-89 or 6 years at Bone Mountain).e Covariance is inappropriate because the relation of growth-starting basal area differed between control and fertilized plots.
10

Table 5–Observed and adjusted, mean gross annual response in volume growth

after fertilization, nonthinned stands, per acre basis a

Observedb Adjustedc

Location Set Reps Response Response Regress.

Ft 3 % P Ft3 % PP

Toledo North E 3 42.9 12.9 0.02 31.0 9.1 .22 0.51

F 6 5.7 1.8 .79 -0.5 -0.2 .97 .01

Toledo South A 5 -1.1 -0.2 .92 4.2 .9 .7 .12

Bone Mountain A 3 37.2 9.8 .01 41.1 10.8 .03 .47

B 3 -6.8 -1.8 .79 50.9 14.9 .04 .01

a Response = PAI fertilized - PAI control; 7 years at set E, 4 years at other sets.

b Analysis of variance; P = probability value.

c Covariance analysis using prefertilization volume as covariate.

Table 6—Statistical significance of thinning, fertilizing, and their interaction at Toledo North, set E

Mean annual growtha

Factor d.f. Height %b Basal area % Volume %

Ft Ft2/acre Ft3/acre

P – value

Fertilizing (F) 1 1.000 — 0.018 — 0.075 —

Thinning (T): 1 1.000 — .695 — .001 —

F × T 1 .529 — .793 — .219 —

Error 8 — — — — — —

Residual mean square .031 — .182 — 482.100 —

Treatment means

Control 2.47 100 9.2 100 333 100

Fertilizing 2.53 102 10.0 109 376 113

Thinning 2.53 102 9.4 102 282 85

F + T 2.47 100 10.0 109 291 87

a For all trees 1.6 inch d.b.h. and larger.

b Percent relative to control = 100.
11

Except for thinned set E at Toledo North, a single-factor ANOVA in completely random design is appropriate for testing effects of fertilization in these five plantations.

According to ANOVA, observed mean basal area growth on fertilized plots differed

significantly from that on nonfertilized plots in three of the five plantations (table 4).

Observed responses ranged from 10.4 to 13.1 percent at those plantations.

We also used covariance analysis in an attempt to reduce or account for measurable

extraneous factors that contribute to variability in the dependent measures of interest,

for example, basal area or volume growth. In most field trials, either pretreatment

(starting) stand basal area or volume are readily available covariates to adjust for

initial difference between treated and nontreated plots. In our data sets, pretreatment

basal area growth also was available. We compared potential benefits of these two

covariates for isolating N fertilization effects on gross basal area growth (table 4). We

had three to six replicate plots per treatment in each set of half-sib families. Thus, we

could use covariance to compute treatment means adjusted for the effects of any random assignment of plots that favored one treatment over another.

Covariance analysis should not be used without preliminary plotting of observations.

For example, initial basal area stocking among the five fertilized plots at Toledo

South was most variable and averaged 7 percent less than nonfertilized plots (table 2).

Although this difference suggested benefits of covariance adjustment of observed treatment means, a plotting of growth related to basal-area stocking of the 10 plots suggested a different relation for the fertilized and control plots (fig. 5). Data from the five

nonfertilized plots fail to show a strong underlying relation between growth and initial

basal area. The apparent slope is horizontal or slightly positive. In contrast, corresponding data from fertilized plots suggest a strong negative slope either because (1)

response to fertilization at this site is extremely variable or (2) response depends on the

amount of starting basal area; that is, strong response at relatively low stocking levels

and weak or no response at greater basal area stocking. Although one cannot infer

which of the two explanations is likely, we concluded from this scattergram that covariance adjustment of observed means of control and fertilized growth would be invalid.

Statistical testing supported this concern by showing that slopes of fertilized and control

regressions differed (P = 0.08). This real difference in regression slopes invalidated use

of covariance to fit a common linear regression to quantify the 10 observations (fig. 5),

and then to adjust the two treatment means along this regression line to a common

starting basal area. The inherent assumption of parallel slopes was more readily assumed at Toledo North, set F (fig. 6), and Bone Mountain, sets A and B (fig. 7).

One- vs. two-tail testing—If one assumed that conventional dosages of N, as applied

in this study, could only increase growth, and not decrease it, then one-tailed testing is

warranted. One-tailed testing increases the likelihood of statistical significance because

critical t- and F-values are lower. Although we observed a small, so-called “negative

response” in basal area growth to 200 lb N/acre at Toledo North, set F (based on six

replications of each treatment), this negative response was statistically nonsignificant

in both ANOVA and covariance tests (P = 0.49 to 0.59; table 4). Hence, this “negative

response” likely was due to chance and was interpreted as “no effect” of fertilization.

Although this interpretation warranted our using one-tail testing, we remained with

conventional two-tail tests.

Discussion

Statistical Tests
12

Figure 5—Toledo South, set A: mean periodic annual basal area growth and prefertilization basal

area, by treatment, per acre basis.

Figure 6—Toledo North, set F: mean periodic annual basal area growth and prefertilization basal

area, by treatment, per acre basis.
13

Figure 7—Bone Mountain, sets A and B: mean periodic annual basal area growth and prefertilization

basal area, by treatment, per acre basis.
14

Alpha level—We assigned statistical significance to differences among treatments,

when P < 0.10. In most scientific journals, however, alpha is conventionally set at

< 0.05 for statistical significance testing. An alpha of 0.05 corresponds to a 0.95 probability of a correct statistical conclusion when the null hypothesis (no effect) is true. This

conservative alpha provides high protection against committing a type 1 error (inferring

a difference among treatment means when in fact there is none), but has tradeoffs that

should be understood and reconsidered by those conducting field trials. As expressed

by Lipsey (1990: 39):

For example, a promising treatment might be investigated to determine if it has

beneficial effects in some problem area. In such applied research the implications

of errors of inference may be quite different from those in basic research. To “discover” that an applied treatment is effective when, in fact, it is not, does indeed

mislead practitioners just as the analogous case misleads theoreticians. Practitioners, however, are often in situations where they must act as effectively as

they can irrespective of the state of their formal knowledge, and it is not unusual

for them to use treatments and techniques of plausible but unproven efficacy.

Moreover, demonstrably effective treatments for many practical problems are not

easy to come by and candidates should not be too easily dismissed. Accepting a

relatively high probability of Type 1 error in applied treatment effectiveness

research amounts to giving a treatment the benefit of the doubt about whether

statistically modest effects represent treatment efficacy or merely sampling error.

A high probability of Type II error [inferring no difference among treatments means

when in fact there is], however, presents a rather different circumstance. In that

case the research is likely to yield null results for a genuinely effective treatment.

Not surprisingly, such results are often taken to indicate that the treatment does

not work. In a context where effective treatment is needed and not readily available, a Type II error can represent a great practical loss–an effective treatment is

falsely discredited. In applied treatment effectiveness research it may often be

desirable to keep the likelihood of such error low even at the expense of accepting an increased probability of Type I error.

The larger the effect produced by treatment on a dependent variable, the more likely

that statistical significance will be attained and the greater the statistical power (Lipsey

1990). The “effect size” relates effect (difference between the treatment means) and

the common variance in the treatment and control distributions. This common variance

is the “residual mean square” (RMS) of the error term in ANOVA or covariance tests.

For computing ES, this RMS is expressed as standard deviation (variance1/2). Symbolically, ES = (mean of treatment 1 – mean of treatment 2) / .

Factors that affect either the numerator (effect) or the denominator (variance) can alter

“effect size.” In theory, covariance analyses can affect both “effect” (by generating adjusted means of growth, hence adjusted mean response by difference) and “variance”

(by reducing the RMS or unaccounted variation).

In these plantations, ES in observed basal area response to fertilization ranged from

-0.32 to 7.88 (table 7). Effect sizes of 3.28 or larger in adjusted basal area response

were statistically significant (P < 0.10; table 7). This usually corresponded to 9 percent

or greater increases in basal area growth (table 5). Effect sizes were much larger at the

Bone Mountain plantations than at the two Toledo locations because both observed

and adjusted responses were larger and the variation in response (residual mean

square) was consistently smaller (table 7). With larger ES, fewer replications are required to detect significant differences among treatments (reject a “no effect” hypothesis) from statistical testing (table 8).

Effect Size (ES)

RMS
15

Table 7—Effect size of observed and adjusted response in gross 4-year mean annual basal area growth (PAI) after fertilization,

nonthinned stands, per acre basis a b

Observedc Adjustedd Adjustede

Location Set Reps Yr Response RMS ES Response RMS ES Response RMS ES

– – – – – – – – – – – – – – – – – – – – – – – – – Ft2 – – – – – – – – – – – – – – – – – – – – – – – –

Toledo North E 3 7 0.80 0.230 1.67 1.31 0.212 2.85 0.96 0.291 1.78

F 6 4 -.19 .344 -.32 -.21 .343 -.36 -.21 .261 -.41

Toledo South A 5 4 1.19* .789 1.34 f ff .67 .569 .89

Bone Mountain A 3 4 1.90* .058 7.88 1.77* .060 7.22 1.83* .070 6.91

B 3 4 1.42* .113 4.23 1.20* .134 3.28 1.27* .142 3.37

a Effect size (ES) = response/square root of the residual mean square (RMS).b Response = PAI fertilized - PAI control; 7 years at set E, 4 years at other sets; * = significant at P < 0.10.c Analysis of variance; P = probability value.d Covariance analysis using prefertilization basal area as covariate; this equaled postthinning basal area/acre at set E.e Covariance analysis using prefertilization basal area growth as covariate (1982-89 or 7 years at Toledo North and South; 1983-89 or 6 years at Bone Mountain).f Covariance inappropriate because the relation of growth-starting basal area differed between control and fertilized plots.
16

Install adequate replication—Increased replication is a common recommendation for

improving experimental design. Estimating adequate sample size, however, requires

several decisions (table 8): (1) What risk of type 1 error (alpha) and type 2 error (beta)

is acceptable? Lowering risk of either error type increases the required sample size.

(2) What is the expected magnitude of response to treatment and of the experimental

error that reflects variation among the replicates of each treatment? Large response

and small experimental error result in large ES, which markedly reduces the estimated number of needed replications (table 8). (3) What magnitude of effect (that is,

response) has practical meaning? There is no point in increasing replication to enable

detection of differences that are trivial in magnitude.

With only two replications per treatment, as is common in many field trials, it is less

likely that randomization will provide a balanced or comparable mix of above- and

below-average plots for each treatment. As demonstrated at Toledo South, even five

replications did not provide balanced allocation. To demonstrate the potential effects of

only two replications on direction and possible magnitude of observed responses, we

deliberately mismatched two fertilized and two control plots in each set. This matching

was based on initial basal area (BA) stocking at fertilization. In match 1, we compared

periodic annual increment (PAI) of the two best stocked, fertilized plots and the two

poorest stocked, nonfertilized plots. In theory, this matching should maximize response

(the average difference in PAI between fertilized and control). Conversely in match 2,

we computed response as the difference in PAI of the two most poorly stocked fertilized plots and of the two best stocked control plots. In theory, match 2 should minimize response.

Results of our purposeful mismatching of fertilized and nonfertilized plots were as expected (table 9). When best stocked plots are assigned arbitrarily or randomly to fertilized treatments (match 1), measured response is inflated. Conversely, response is

deflated or negative when best stocked plots are assigned to control treatments. Responses computed from matches 1 and 2 clearly differed from those observed from

all replicate plots by 30 percent to 32-fold (table 9).

Select uniform conditions—Locating field trials in uniform stand and site conditions is

an effective way to reduce experimental error. We initially assumed that plots in these

genetic-test plantations would be especially uniform because each plot was planted

with the same 30 half-sib families, and the planting area was nearly level and smooth.

Moreover, the entire plantation was fenced to exclude large animals, and was sprayed

or mowed to control vegetative competition. Despite this intensive culture, the three to

Table 8—Table for determining sample size for analysis of variance (fixed-effects

model) when alpha = 0.10

Power (1 - beta)

0.70 0.90

Treatments tested ES = 1.0 ES = 3.0 ES = 1.0 ES = 3.0

Number – – – – – – – – – – – Sample size (no.) – – – – – – – – – – – –

2 11 3 18 3

4 15 3 25 4

Sources: Adopted from Bratcher and others (1970) and Lipsey (1990).

Ways to Increase

Sensitivity of Field Trials
17

six replications of each imposed treatment (fertilized or control) differed in growing

stock (basal area per acre) at age 16 or 17 years from seed. Within the two treatment groups at each plantation, coefficients of variation ranged from 1 to 14 percent

(table 2), which is similar to that for 31 nonthinned fertilizer trials in mostly naturally

regenerated stands in the Oregon Coast Range (fig. 8). Each of these 31 trials had six

to eight plots that were subsequently allocated to three or four treatments. Two comments about figure 8 are pertinent: (1) among-plot variation in stand basal area appears to decline with stand age, and (2) the two trials with unusually large CV of about

28 percent are the only trials with eight plots. This could illustrate the difficulty of locating sufficient area of uniform stand and site conditions to accommodate more than a

few plots.

Use blocking or covariance—When faced with heterogeneity among experimental

plots or subjects, one can use two other techniques to improve sensitivity of field trials.

These are “blocking” and covariance. “Blocking” clusters or stratifies plots of similar

stocking into subgroups, then assigns treatment within each subgroup or block. This

also ensures that all treatments sample the range of stocking within the test site. We

did not block our available plots because these plantations initially appeared to be

exceptionally uniform.

Table 9—Observed and theoretical responses in mean annual gross growth after

fertilization in nonthinned plantations, per acre basis

Mean annual response

Location Set Reps Basal area Volume

Ft 2 Relative Ft3 Relative

Toledo North E 3 0.80 100 42.9* 100

2a 1.15 144 55.7 130

2b .30 38 28.2 66

F 6 -.19 100 5.7 100

2 a .93 489 74.7 1,334

2 b -1.32 -695 -68.8 -1,228

Toledo South A 5 1.19* 100 -1.1 100

2 a 2.53 213 27.0 2,454

2 b -.38 -32 -35.7 -3,245

Bone Mountain A 3 1.90* 100 37.2* 100

2 a 2.12 112 47.3 127

2 b 1.67 88 27.2 73

B 3 1.42* 100 -6.8 100

2 a 1.74 122 19.3 280

2 b 1.18 83 -35.6 516

* Statistically significant (P < 0.10); see table 4. a Best (by starting basal area) two fertilized plots matched to worst two control plots.

b Worst (by starting basal area) two fertilized plots matched to best two control plots.
18

Covariance uses the linear correlation between the dependent variable (growth) and

the covariate (for example, starting basal area or calibration growth) to compute an adjusted mean growth for each treatment, then a mean response. We demonstrated effects of that technique (table 4). Covariance did not consistently reduce experimental

error (RMS) or increase ES in this data set (table 7). We would expect covariance to be

more effective where among-plot variations were greater than in these test plantations.

To improve detection of response to fertilizers, the following should be attempted:

• Install trials in uniformly stocked and structured stands, or group plots in blocks of

similar within-block stocking and structure.

• Install at least three replications to enable covariance analysis and adjustment of

observed means.

• Recognize that a large number of replications of each treatment is necessary to

detect the small response to N fertilization that is characteristic of above-average

site quality stands of coast Douglas-fir. This characteristically small response

(<10 percent) may or may not have practical meaning. There is no point in increasing replication or sensitivity to enable detection of differences that are trivial in a

practical sense.

1. Coefficients of variation in tree and stand attributes before fertilization were about

5 percent in trees per acre, 15 percent in basal area, and 20 percent in cubic

volume, despite the fact that all trees in each plantation (1) originated from the

same half-sib families, (2) were planted at precise tree-to-tree spacing, and (3)

received intensive protection from large animals and weed competition.

Figure 8—Coefficients of variation in stand basal area within 31 fertilizer trials sampled by six or

eight plots each. Adapted from Miller and others (1991, see footnote 1).

Conclusions
19

2. Random assignment of three to six plots per treatment did not assure balanced or

comparable plots for fertilized and nonfertilized treatments. Covariance adjustment

of observed growth (for initial differences in basal area or volume stocking between

fertilized and control plots) changed magnitude and, in some plantations, direction

of observed (unadjusted) response.

3. Covariance analysis did not consistently reduce experimental error (residual mean

square) or increase effect size.

4. Without covariance adjustments, effect sizes ranged from -0.32 to 7.88 for responses in gross basal area growth per acre. Effect sizes of 1.34 and larger were

statistically significant.

5. Detection of response to fertilization of Douglas-fir stands on above-average site

quality requires careful planning and execution. Expected response to 200 lb N/acre

is small and experimental error (unaccounted sources of variation) is usually large.

We thank the following cooperators: Georgia-Pacific Corporation (tree data and

professional assistance); University of Washington, Regional Forest Nutrition Research

Project (professional and technical assistance); Olympic National Forest and Siskiyou

National Forest (partial funding); Unocal Chemical Company (urea fertilizer); U.S.

Department of the Interior, Bureau of Land Management (field assistance); and Eunice

Ham, formerly at the Forestry Sciences Laboratory, Olympia, WA (data management).

1 inch (in) = 2.54 centimeters

1 foot (ft) = 0.3048 meter

1 square foot (ft2

) = 0.0929 square meter

1 cubic foot (ft3) = 0.028 cubic meter

1 acre = 0.4047 hectare

1 square foot per acre = 0.2296 square meter per hectare

1 cubic foot per acre = 0.06993 cubic meter per hectare

1 pound (lb) = 453.592 grams

1 gallon (gal) = 3.785 liters

Bratcher, T.L.; Moran, M.A.; Zimmer, W.J. 1970. Tables of sample sizes in the

analysis of variance. Journal of Quality Technology. 2: 156-164. [As cited in Lipsey

(1990).]

Bruce, D.; DeMars, D.J. 1974. Volume equations for second-growth Douglas-fir. Res.

Note PNW-239. Portland, OR: U.S. Department of Agriculture, Forest Service,

Pacific Northwest Forest and Range Experiment Station. 5 p.

Curtis, R.O. 1982. A simple index of stand density for Douglas-fir. Forest Science.

28(1): 92-94.

Curtis, R.O. 1983. Procedures for establishing and maintaining permanent plots for

silvicultural and yield research. Gen. Tech. Rep. PNW-155. Portland, OR: U.S.

Department of Agriculture, Forest Service, Pacific Northwest Research Station. 56 p.

Acknowledgments

Metric Equivalents

Literature Cited
20

Curtis, R.O.; Marshall, D.D. 1986. Levels-of-growing-stock cooperative study in

Douglas-fir: Report No. 8–The LOGS study: twenty-year results. Res. Pap. PNW356. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest

Research Station. 113 p.

Evert, F. 1964. Components of stand volume and its increment. Journal of Forestry.

62: 810-813.

King, J.E. 1966. Site index curves for Douglas-fir in the Pacific Northwest.

Weyerhaeuser For. Pap. 8. Centralia, WA: Weyerhaeuser Company.

Lipsey, M.W. 1990. Design sensitivity: statistical power for experimental research.

Newberry Park, CA: Sage Publications, Inc.

SAS Institute. 1988. SAS/STAT user’s guide 6.03 ed. Cary, NC.
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