Analysis of the Part I 

Southern Pine In-Grade 

Program Data 

James W. Evans

David E. Kretschmann

Cherilyn A. Hatfield

David W. Green

United States

Department of

Agriculture

Forest Service

Forest

Products

Laboratory

General

Technical

Report

FPL–GTR–221
April 2013

Evans, James W.; Kretschmann, David E.; Hatfield, Cherilyn A.; Green, 

David W. 2013. Analysis of the part I southern pine in-grade program data. 

General Technical Report FPL-GTR-221. Madison, WI: U.S. Department 

of Agriculture, Forest Service, Forest Products Laboratory. 11 p.

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Abstract

It has been suggested that within- and between-mill variability of samples may have changed since the original North 

American In-Grade Program and a new sampling method 

may be required. The cooperative research “In-Grade Program” was conducted in the late 1970s to the late 1980s to 

establish allowable properties (modulus of elasticity (MOE), 

allowable bending stress (Fb), allowable compressive stress 

parallel to grain (Fc), and allowable tensile stress parallel 

to grain (Ft)) for dimension lumber based on full-size testing of graded lumber. The In-Grade Program was divided 

into three major administrative parts, each with specific 

objectives. Part I estimated bending strength and stiffness 

of 2 by 8 No. 2 and 2 by 4 STUD grades of Douglas-fir and 

Southern Pine. Part II considered other grades, sizes, and 

methods of loading (such as tension and compression parallel to the grain) for Douglas-fir and Southern Pine. Part III 

considered other species. The purpose of this document is to 

explain how Part I of the In-Grade Program, which looked 

at regional and mill variability, was designed and to re-examine the analysis that was conducted in 1980 to determine 

sampling methods. The present report discusses Southern 

Pine data, and sampling design issues related to regions, 

mills, and pieces sampled in a mill are presented. Also, other 

techniques not applied in 1980 are used to reanalyze the test 

data. The random sampling of mills within region based on 

production was based on a balancing of the significance of 

regional, mill-to-mill, and within-mill variability. We feel 

that the decisions that were made in setting up the stratified cluster sampling methods to minimize variability in 

sampling for Part II and Part III were justified and necessary 

given the limited resources available to conduct Part II and 

Part III of the program. 

Keywords: sampling, In-Grade Testing, Southern Pine, 

Part I, variance component analysis

Contents

Executive Summary..........................................................1

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

Background on Initiation of the In-Grade Program in 

the United States...............................................................2

Part I of the In-Grade Program .........................................2

 Sampling Method for Part I ..........................................3

 Other Research Studies Conducted in Parallel with 

 Part I Work ....................................................................4

Analysis of In-Grade Program Part I Data........................4

 Review of Part I, 2 by 8 No. 2 Sampling and the 

 1980 Analysis................................................................4

 Alternatives to 1980 Analysis .......................................5

 Variance Component Analysis......................................6

Discussion and Conclusions .............................................8

 Application of the Results from Part I to Part II of the 

 In-Grade Program .........................................................9

 Conclusions from the Reanalysis of Past Data .............9

Summary of What Was Learned from Looking Back 

at Part I..............................................................................9

References.........................................................................9

Appendix—Quotes of Interest ........................................ 11
Analysis of the Part I Southern Pine 

In-Grade Program Data

James W. Evans, Ph. D., Research Mathematical Statistician

David E. Kretschmann, PE, Research General Engineer

Cherilyn A. Hatfield, Statistician

David W. Green, Ph. D. (retired)

Forest Products Laboratory, Madison, Wisconsin 

Executive Summary

Recently, concerns have been raised about the effect that 

changes in the lumber mill type (small log or large log 

mills) may have on deciding what stratified cluster sampling 

method to use for establishing a “global number.” A global 

number is one number that covers the entire growth range 

for Southern Pine dimension lumber for each allowable 

property. It has been suggested that within- and betweenmill variability of samples may have changed since the original North American In-Grade Program and a new sampling 

method may be required. This has led us to a re-examination 

of the methodology used to establish the sampling method 

that is currently used to gather data for the development of a 

global number for visually graded dimension lumber.

The cooperative research “In-Grade Program” was conducted in the late 1970s to the late 1980s to establish allowable properties (modulus of elasticity (MOE), allowable 

bending stress (Fb), allowable compressive stress parallel to 

grain (Fc), and allowable tensile stress parallel to grain (Ft)) 

for dimension lumber based on full-size testing of graded 

lumber. The In-Grade Program was divided into three major 

administrative parts, each with specific objectives. Part I 

estimated bending strength and stiffness of 2 by 8 No. 2 

and 2 by 4 STUD grades of Douglas-fir and Southern Pine. 

Part II considered other grades, sizes, and methods of loading (such as tension and compression parallel to the grain) 

for Douglas-fir and Southern Pine. Part III considered other 

species. This report documents how the information gathered in Part I of the In-Grade Program, which looked at regional and mill variability, was designed and how the statistical analysis that was conducted by James Haskell in 1980 

was used to determine sampling methods for Part II and Part 

III of the program. This report discusses Southern Pine data, 

and sampling design issues related to regions, mills, and 

pieces sampled in a mill are presented. Techniques not used 

by Haskell but commonly available at the time are also used 

to reanalyze the Southern Pine test data. 

The re-examination of the past analysis and reanalysis of the 

1980 data suggest that both the regions and the mills within 

regions were statistically significant in accounting for variation in lumber properties at the 0.05 level. Mill size based 

on production, which relates to mill type, was also a parameter investigated and accounted for in the Part I study. We 

also determined that a particular lot was highly significant 

in accounting for variation in MOE, suggesting that it would 

be beneficial to continue sampling by lots as opposed, say, 

to sampling more pieces from a single pack of lumber. The 

establishment of the sampling method that is currently used 

in determining global numbers for the major species groups 

in the North America took these statistical significances 

(for regions, mills, and lots) along with logistical and cost 

factors into account. The random sampling of mills within 

region based on production was based on a balancing of the 

significance of regional, mill-to-mill, and within-mill variability. We feel that the decisions that were made in setting 

up the stratified cluster sampling methods to minimize variability in sampling for Part II and Part III were justified and 

necessary given the limited resources available to conduct 

Part II and Part III of the program. 

Introduction

As a result of destructive testing of 2 by 4 No. 2 lumber in 

bending and tension parallel to grain (ASTM 2011c), the 

Southern Pine Inspection Bureau (SPIB) in 2011 proposed 

an interim drop in dimension lumber values (American Forest and Paper Association (AFPA) National Design Specifications (NDS)) for Southern Pine by approximately 30%. 

Large parts of the lumber industry are concerned about the 

disruption and economic effect that these changes would 

have and have challenged the sampling method used by 

SPIB to conduct their follow up bending, tension, and compression testing of three size 2 grades (ASTM 2011 a,b). 

Using procedures similar to those developed and used in the 

U.S. In-Grade Program (FPRS 1989), SPIB used a stratified sampling procedure. The growth region for Southern 

Pine was divided into 18 regions that were believed to be 

relatively homogeneous regions based on previous research. 

Specimens were sampled from each region in proportion to 

production for the region by randomly sampling mills in the 

region. In each mill, a limit of two lots was sampled with 

10 on-grade pieces taken sequentially from the lot. 

A recent challenge to this sampling methodology has raised 

the issues of whether it would be better to (1) randomly 
General Technical Report FPL–GTR–221

2

sample mills generally or to first stratify by regions or 

(2) (in reducing variation due to sampling) sample fewer 

mills with more specimens per mill. It is being advocated 

to repeat the preliminary work that was done in the U.S. InGrade Program that led to the adoption of the current sampling method. Before this preliminary work is repeated, the 

authors feel it is important to review the work done in Part 

I of the In-Grade Testing Program used to establish the current sampling methodology. 

This paper has four main parts. First, background will be 

provided on the reasons for initiating the In-Grade Program 

in the United States. Second, the preliminary work, including sampling method and analysis of data that led to the 

method used today, will be discussed. Third, alternatives to 

the original analysis commonly available at the time of the 

preliminary work will be explored. Fourth, an evaluation of 

the whole sampling method used will be presented. The intent is to provide useful guidance to anyone hoping to repeat 

a similar study.

Because this preliminary work (Haskell 1980) on sampling 

was never made widely available, it is desirable to recreate 

it and look at it under the present day concerns. This means 

reviewing the sampling method and analysis used, reassessing the conclusions drawn from the data, and looking 

at additional ways that could be used to analyze the preliminary data. This document contains a very thorough summary 

of the sampling portion of the unpublished Haskell report 

and a description of the proper interpretation of the results 

as it relates to current Southern Pine sampling. We have 

only evaluated the regional and mill size analysis sections 

of Haskell’s unpublished report thoroughly but have not 

investigated the analysis covered in the rest of the sections. 

We therefore do not address the analysis conducted or any 

errors or inconsistencies that may exist in that portion of the 

report.

The current challenge involves Southern Pine dimension 

lumber; therefore, only the Southern Pine data from the InGrade Program will be evaluated. Presently, other commercial species are being looked at to determine if the published 

design values are appropriate, as those species may be facing these same issues in the near future. 

Background on Initiation of the 

In-Grade Program in the United 

States

Prior to 1980, a concern arose that despite excellent in-service performance of wood-frame houses, some single pieces 

of full-size, visually graded structural may have strength 

values less than those published for use in design (Bodig 

1977; Madsen 1978; Galligan and Green 1980; Galligan 

and others 1980). However, tests of full-scale floor and wall 

components and of a full-scale house designed by current 

accepted methods, lumber grades, and design stresses 

indicated that houses were generally over-designed 

(Goodman and others 1974; Polensek and Atherton 1976; 

Tuomi and McCutcheon 1975), resulting in an anomaly that 

needed to be resolved if wood was to be used in the most 

efficient manner.

In 1977, a comprehensive research program was organized 

by the Forest Products Laboratory (FPL) to develop and 

implement light-frame construction research and to transfer 

the related technical information to designers and builders 

(Hans and others 1977). A by-product of this program was 

to look at material property research. 

In May 1977, a meeting of U.S. and Canadian rules-writing 

agencies was held. This meeting resulted in a request that 

a detailed plan be formulated for a more extensive study of 

the mechanical properties of lumber that related to design 

methods and use. Subsequent discussions with the U.S. Forest Service resulted in an offer by FPL to prepare an overview of research needs and to design a plan that could be 

considered for country-wide application.

In July 1977, representatives of four U.S. rules-writing 

agencies (Redwood Inspection Service (RIS), Southern Pine 

Inspection Bureau (SPIB), West Coast Lumber Inspection 

Bureau (WCLIB), and Western Wood Products Association 

(WWPA)), met to review a “Five-Year Testing Program” 

and a rough draft of a lumber sampling method, both prepared by FPL. The agencies agreed that the FPL sampling 

method had considerable merit but that some modifications 

were necessary in order to devise a workable schedule based 

on knowledge of mill production and similar considerations. 

A cooperative research agreement was reached between FPL 

and three of the agencies (SPIB, WCLIB, and WWPA).

This cooperative research agreement became known as the 

“In-Grade Program.” It was designed to be divided into 

three major administrative parts, each with specific objectives. Part I looked at bending strength and stiffness of 2 by 

8 No. 2 and 2 by 4 STUD grades of Douglas-fir and Southern Pine. Part II was to consider other grades, sizes, and 

methods of loading (such as tension and compression parallel to the grain) for Douglas-fir and Southern Pine. Part III 

was to consider other species. 

Part I of the In-Grade Program

Part I attempted to meet three major objectives:

1. Characterize the bending strength and stiffness of 2 by 8 

No. 2 and 2 by 4 STUD grades of Douglas-fir and Southern Pine lumber determined to be “on-grade” by agency 

quality supervisors.

2. Characterize the bending strength and stiffness of lumber 

“as-graded” by the mill grader.

3. Characterize wall and floor performance by modeling 

these light-frame components with the results of (1) 

and (2).
Analysis of the Part I Southern Pine In-Grade Program Data

3

A secondary objective was to provide information that 

would help in the design and analysis of the other parts of 

the In-Grade Program. Part I also looked at issues that included how we effectively and efficiently look at the population of material in a particular grade and size that is actually being produced at the time. This meant an emphasis on 

sampling material that reflected a “production” population 

and not a “forest” population. This means that conclusions 

from this research relate to the properties of the mill produced product, not the properties of the standing timber. 

Sampling Method for Part I

The first step in developing the sampling method of Part I 

was to compile a list of all the “potential” mills producing 

2 by 8 No. 2 or 2 by 4 STUD. These mills were then subdivided into 6 strata (regions) based on growth patterns and 

geographical boundaries as is shown in Figure 1 for the 

2 by 8 No. 2 Southern Pine data. In this way, the usual statistical philosophy of homogeneity of properties within a 

stratum (region) was approached. The result of this method 

was a stratified sampling method for mills. Note that in 

Part II the regions were further subdivided to produce 

18 regions (Fig. 2, Jones 1989).

The next important question that needed to be answered 

was “How to best sample material at each mill so that it 

represents properties of lumber furnished to the designer/

consumer?” It was decided to sample the material at mills 

either in lots (a stack of lumber bound together) from existing inventories or if no inventory was present, directly as it 

was produced by the mill. A lot became known as a sample 

from the mill. 

At a sampled mill, 10-piece serial lots were selected for testing. Serial lots meant that once the outer layers of a pack 

of lumber were removed, pieces of lumber were selected 

for a given layer in the order in which they were stacked 

until 10 pieces were obtained. The outermost two layers 

were excluded because of possible damage from banding 

the pieces together in the stack. Lots relate to the manner 

in which lumber is produced and distributed. Ten was the 

number of pieces chosen as “typical” for historical wall and 

floor assemblies. This serial selection method was used to 

approximate a “lot,” as what might be used by a carpenter in 

building a conventional wall or floor system. “After the first 

10 pieces were selected, the lumber was re-graded by an 

agency quality supervisor and, if the re-grade did not agree 

with the desired structural grade, additional pieces were 

taken to make a total of 10 ‘on-grade’ pieces available from 

each bundle” (Green 1983).

At a mill with an existing inventory, 10 pieces (a 10-piece 

lot) were taken in sequence from a pack. At a mill with no 

inventory, a 10-piece lot consisted of 10 successive pieces 

produced. Since observations from successive pieces from 

the sample mill were expected to have a higher correlation 

among themselves than randomly selected pieces, subsequent lots taken from the sample mill would each be taken 

from a separate bundle of lumber or after production of a 

number of intermediate specimens. If the mill inventory was 

large enough and there was a way to identify the production 

date, lots were to be sampled to span the production period. 

Statistically, this means we were now using a stratified cluster sampling method.

Part I work was broken into two phases called A and B. In 

some ways, Phase A was a trial for further work in Phase B 

and the two phases would be combined for the final analysis. Part I as a whole looked at several issues with either 

the 2 by 8 No. 2 data or the 2 by 4 STUD data or both. One 

issue explored was the comparison of “on-grade” samples 

and “as-graded” samples. Other issues considered included 

the effect of mill size on the 2 by 8 No. 2 data, the effect 

of mill type on the 2 by 4 STUD data, and the effect of 

Figure 1. Original six regions for Part I.

Figure 2. The current Southern Pine growth region 

boundaries.
General Technical Report FPL–GTR–221

4

kiln drying using a conventional schedule rather than the 

high-temperature schedule on both 2 by 8 No. 2 and 2 by 4 

STUD Southern Pine. All work except the kiln-drying study 

was done separately for Southern Pine and Douglas-fir data. 

For Southern Pine 2 by 4 STUD, the interaction of mill type 

and kiln type was also studied. The focus of this paper will 

be those items that influenced the method of sampling.

Other Research Studies Conducted 

in Parallel with Part I Work

A great deal of other research and work was done on issues 

that were needed in order to accomplish the In-Grade Program. A brief listing of some of this work includes major 

deviations from normal laboratory testing procedures such 

as (1) faster rate of loading, (2) random location of the load 

with respect to the length of the piece, (3) random placement of the “worst edge” with respect to the direction of 

loading, (4) shorter span-to-depth ratio and (5) non-equilibrium moisture contents at time of test. This and other work 

have been well documented in published sources and often 

incorporated into ASTM standards (Green and Evans 1988; 

FPRS 1989). 

Analysis of In-Grade Program 

Part I Data

As mentioned in the introduction, the Part I work of the InGrade Program has not been widely available. Some significant quotes from early reports of that time are reproduced 

in the Appendix. This paper is limited to Southern Pine data 

only and the sampling issues related to regions, mills, and 

pieces sampled in a mill (which also raises the question of 

lots in a mill). Part I on the 2 by 8 No. 2 data for Southern 

Pine that addresses the effort to look at the sampling issues 

will be examined first.

Review of Part I, 2 by 8 No. 2 Sampling 

and the 1980 Analysis 

Table 1 summarizes the sampling done in Part 1 for 2 by 8 

No. 2, which was stratified by regions and mill size (Green 

and others 1981). Mill size was defined, based on production, as small (<15 × 106 board feet), medium (15–40 

× 106 board feet), and large (>40 × 106 board feet). This 

method of sampling indicates that there was recognition of 

potential differences in mills by amount of production. It 

should be noted the number of mills, overall, for each size 

mill and the number of pieces within a mill were not constant throughout the design (Table 2). In all but one mill, a 

minimum of three 10-piece lots were taken. For a few mills, 

six 10-piece lots were taken. The initial analysis looked only 

at the effect of regions and mills within regions on modulus 

of elasticity (MOE), modulus of rupture (MOR), stiffness 

(EI), and moment potential (RZ). This analysis was done 

separately for both on-grade and as-graded samples. A nested analysis of variance (ANOVA) was performed to look at 

the effect of regions and mills nested in regions. If regions 

were statistically significantly different at the 0.05 level, 

a Duncan multiple-range test was performed to determine 

which regions were different from each other (Steel and 

Torrie 1960). 

When the data for Part I were used to conduct the same 

Duncan multiple-range test, they reproduced similar results 

as were reported in Haskell (1980). Tables 3 and 4 show the 

results for MOR and MOE, respectively. 

A brief discussion of how to interpret these results may be 

useful to some readers. Table 3 will be used to illustrate how 

Table 1. Sources of Southern Pine lumber

Type of lumber Region

2 by 8, No, 2, S-Dry 1 2 3 4 5 6 Total

Number of mills producing this lumber 50 82 100 128 143 47 550a

Number of mills sampled in Phase A 2 0 2 2 2 2 10

Number of mills sampled in Phase B 4 6 4 4 4 4 26

Number of mills sampled in Phase A & B 6 6 6 6 6 6 36

a

The 1981 report has 556 but the regional total based on our current data set adds to 550. 

Table 2. Distribution of Part I, 2 by 8 No. 2 

sample by mill size 

Region Small Medium Large Total Mills

1 30 59 60 6 

 30 30 239 

 30 

2 30 180 6 

 30 

 30 

 30 

 30 

 30 

3 59 30 60 239 6 

 30 30 30 

4 30 30 59 240 6 

 60 30 

 31 

5 31 30 60 241 6 

 60 60 30 

 31 

6 18 60 60 228 6 

 30 30 30 
Analysis of the Part I Southern Pine In-Grade Program Data

5

to interpret the results. GLM stands for general linear 

model. The first part of the output at the top provides a 

summary of the results of SAS ANOVA (SAS 2012). The 

first column of the table shows the sources of variability 

(regions, mills-within-a-region, and error, which is a combination in this case of lot variability within a mill in a region 

and piece variability within-a-region, mill, and lot). 

Column 2 gives degrees of freedom for each source of variability. The mean square error gives the variability of the 

source. Test is a visual display of the error term used to test 

each source of variability. Then comes the F-test and finally 

the significance level of the F-test. The table below the 

ANOVA gives a summary of the multiple comparison test 

used to see which regions are significantly different from 

each other. Regions connected with the same letter under 

the grouping column are not statistically different at the 

0.05 level. 

The results shown in Tables 3 and 4 indicate that both the 

regions and the mills within regions are statistically significant at the 0.05 level. The statement often quoted from 

Jones (1989) is the following: 

“This phase (Part I) of the U.S. program had a sampling 

strategy intended to evaluate the strength properties for the 

most typical species-grade-size for a given application, as 

well as the effect of mill size, regions, and peeler core mills. 

The results were used to design the rest of the program. Of 

particular importance was the conclusion that between-mill 

variation was not statistically significant considering withinmill variation.” 

This statement is poorly phrased and is not meant to suggest that the differences between mills were not observed 

to be significant. It is intended to emphasize, as described 

in Green and Evans (1988), that the variation in properties 

within a mill was at least as large as that between mills. The 

equivalent variation within a mill and between a mill also 

meant that fewer mills could be taken with more samples 

per mill (Green and Evans 1988).

Alternatives to 1980 Analysis

Other ways of looking at the data are now readily available 

and should be investigated. Duncan’s multiple range test has 

Table 3. GLM Procedure for on-grade MOR

Source DF Mean square Testa F-value Pr > F

Region 5 77064521.9 3.30 0.0170

Mill (region) 30 23320396.9 4.11 <0.0001

Error 1331 5676534.0 

 

Duncan grouping Meanb N Region 

A 6815.9 228 6 

A 6790.1 241 5 

B A 6558.6 239 3 

B A C 6083.7 239 1 

 B C 5770.0 240 4 

C 5314.9 180 2 a

Test shows the structure from ignoring an effect (start of arrow) to using an effect (point 

of and arrow) of the statistical test used in creating the significance results in the table. b

Means with the same letter in the Duncan grouping are not significantly different at the 

0.05 level. 

Table 4. GLM Procedure for on-grade MOE

Source DF Mean square Testa F-value Pr > F

Region 5 5.16739 4.34 0.0044 

Mill (region) 30 1.19175 7.09 <0.0001 

Error 1,331 .16815 

 

Duncan grouping Meanb N Region 

A 1.8086 241 5 

B A 1.7162 239 3 

B A C 1.6766 228 6 

B C 1.5008 239 1 

 C 1.4632 240 4 

 C 1.4501 180 2 a

Test shows the structure from ignoring an effect (start of arrow) to using an effect 

(point of and arrow) of the statistical test used in creating the significance results in the

table.

b

Means with the same letter in the Duncan grouping are not significantly different at 

the 0.05 level.
General Technical Report FPL–GTR–221

6

largely been replaced with other multiple comparison tests 

that have better properties such as a lower number of false 

significant results and a better way of handling different 

sample sizes for the treatments being compared. The Tukey–

Kramer test, generally referred to as a Tukey test or Tukey 

hsd (honestly significant difference) test has been viewed by 

some statisticians as performing optimally or near optimally 

in a broad variety of circumstances (Steel and Torie 1960; 

Stoline 1981). So it will used in any further testing. Also, 

the lot variation within a mill in a region was combined with 

the piece-to-piece variation within a lot in a mill and region 

in the original analysis. In the interest of having a better 

understanding of the sources of variability, the nested lot 

variability will be added to the analysis. Finally, some other 

variables will be looked at in addition to the original MOR 

and MOE. 

Tables 5 and 6 show the analysis of MOR and MOE, respectively, using the Tukey test and separating the error variance 

into lot and piece variability. The results show a decrease in 

significant differences among regions as would be expected 

from a more conservative test. Looking at lots versus pieces 

within a lot shows lots were not significant for MOR, but 

highly significant for MOE. This result would imply that 

there might be a benefit to sampling from multiple lots for 

MOE, but not necessarily for MOR. Because it is not known 

which mills came from an existing inventory and how well 

spaced across time lots were for mills without inventory, it 

is hard to determine a reason for this. 

Another thing that can be done with the data that might 

prove beneficial is to adjust all specimens to a common 

moisture content. A standardized procedure for adjusting 

the properties of dimension lumber was not yet available 

in 1980 and was at the time a subject of ongoing research. 

Using present ASTM procedures, the MOR and MOE of all 

pieces were adjusted to 15% moisture content and labeled 

MOR15 and MOE15. For species that can be produced 

either green or dry, this could eliminate one source of 

variation. Tables 7 and 8 provide the results of looking at 

MOR15 and MOE15. For both MOR15 and MOE15, there 

is very little difference from the results for MOR and MOE. 

For MOR15, the regional effect is slightly less but still 

significant; and where region 2 results for MOR were significantly different from regions 6 and 5, for MOR15 region 

2 is different only from region 6. For MOE15, the regional 

effect is also slightly less but still significant; and where 

region 5 results for MOE were significantly different from 

regions 2 and 4, now for MOE15 region 5 is significantly 

different from regions 2, 4, and 1. 

Variance Component Analysis 

In addition to testing the mean regional results, the original 

1980 analysis looked at how much each source of variation contributed to the total variability of MOR and MOE 

through variance component analysis. The way this was 

done for the regional analysis in 1980 was to use the model 

that says each observation (Y) consists of an overall mean 

(μ) plus a regional effect (R) plus a mill within region effect 

(M) plus an error term (ε). Each effect is either fixed, random, or finite. Technically, region should be a fixed effect 

because the entire population of regions is sampled. Mills 

would be a finite effect because a subset of the finite number 

of mills in a region is sampled, and error is a random effect 

drawn from a population that is essentially infinite. Because 

only six mills were sampled from each region that has a 

very large number of mills that could be chosen, the finite 

population correction factor is essentially 1 as it would be 

for a random effect. So mills are often considered as a random effect. The original analysis chose to also label region 

as a random effect noting “It is recognized that this assumption is not strictly appropriate for the study. However, no 

statistical significance is attached to these estimates. They 

are only used to address the question of practical significance” (Haskell 1980).

Table 5. GLM procedure for on grade MOR

Source DF Mean square Testa F-value Pr > F

Region 5 77064521.9 3.30 0.0170

Mill (region) 30 23320396.9 3.71 <0.0001

Lot (region mill) 101 6289237.1 1.12 0.2078

Error 1,230 5626223.0 

 

Tukey grouping Meanb N Region 

A 6815.9 228 6 

A 6790.1 241 5 

B A 6558.6 239 3 

B A 6083.7 239 1 

B A 5770.0 240 4 

B 5314.9 180 a

Test shows the structure from ignoring an effect (start of arrow) to 

using an effect (point of and arrow) of the statistical test used in creating 

the significance results in the table.

b

Means with the same letter in the Tukey grouping are not significantly 

different at the 0.05 level. 

Table 6. GLM Procedure for on-grade MOE

Source DF Mean square Testa F-value Pr > F

Region 5 5.16739 4.34 0.0044

Mill (region) 30 1.19175 4.07 <0.0001

Lot (region mill) 101 .29274 1.85 <0.0001

Error 1,230 .15792 

 

Tukey grouping Meanb N Region 

A 1.8086 241 5 

B A 1.7162 239 3 

B A 1.6766 228 6 

B A 1.5008 239 1 

B 1.4632 240 4 

B 1.4501 180 2 a

Test shows the structure from ignoring an effect (start of arrow) to using 

an effect (point of and arrow) of the statistical test used in creating the 

significance results in the table.

b

Means with the same letter in the Tukey grouping are not significantly 

different at the 0.05 level.
Analysis of the Part I Southern Pine In-Grade Program Data

7

Using the ANOVA for each MOR and MOE, expected mean 

squares can be calculated for the data. These are given in Tables 9 and 10. From these, the actual mean squares for each 

factor can be used to estimate the size of each component of 

variation. The resulting variance component estimates are 

shown below the respective ANOVA tables. One way to estimate variance components is as follows: note that the error 

mean square is the estimate of the error term (ε), which can 

then be used to estimate the mill within region (M) variance 

component, etc. When finished, these estimates can be used 

to estimate the variability of an individual observation and 

decide how best to allocate the sampling. 

Another interesting feature to point out is found in the expected mean squares. If you look at the regions and millswithin-region effects, it can be seen that the number in front 

of the variance of mill-within-region term is different. This 

is due to the slight unbalanced sample sizes taken in the 

study. In the study, six regions and six mills in a region were 

chosen. However some mills had three lots and some had 

six lots. In addition, an occasional lot only had nine pieces. 

This means the test using mill-within-regions to test regional effects is only approximate. However, the difference from 

being an exact test is not very much and should not make 

any practical difference in any conclusions. 

In trying to reproduce the analysis that was used in Haskell 

(1980), we must note that the exact analysis is not given in 

detail in the paper. Haskell states that he used SAS to estimate variance components. The first step is to calculate 

the expected mean squares. If SAS was used as shown in 

Tables 9 and 10 in a way to estimate the expected mean 

squares that take into account the slight unbalance in the 

sample sizes, the results are as shown. However, the difficulty of calculating expected mean squares led many researchers to use a balanced design for calculations that approximated the unbalanced design. Because the paper does 

not actually show the expected mean squares, we are using 

Table 7. GLM Procedure for on-grade MOR15

Source DF Mean square Testa F-value Pr > F

Region 5 60627810.7 2.92 0.0289 

Mill (region) 30 20745198.4 3.49 <0.0001 

Lot (region mill) 101 5950500 1.09 0.2682 

Error 1,230 5473811 

 

Tukey Grouping Meanb N Region 

 A 6667.4 228 6 

B A 6605.0 241 5 

B A 6322.5 239 3 

B A 5872.6 239 1 

B A 5710.8 240 4 

B 5325.6 180 2 a

Test shows the structure from ignoring an effect (start of arrow) to using an 

effect (point and arrow) of the statistical test used in creating the significance 

results in the table.

b

Means with the same letter in the Tukey grouping are not significantly 

different at the 0.05 level. 

Table 8. GLM Procedure for on-grade MOE15

Source DF Mean square Testa F-value Pr > F

Region 5 4.295939 4.02 0.0065

Mill (region) 30 1.068413 4.18 <0.0001

Lot (region mill) 101 .255489 1.70 <0.0001

Error 1,230 .150143     

        

Tukey Grouping Meanb N Region

A 1.7692 241 5   

B A 1.6665 239 3   

B A 1.6422 228 6   

B    1.4607 239 1   

B    1.4540 240 4   

B    1.4516 180 2    a

Test shows the structure from ignoring an effect (start of arrow) to using an effect (point 

and arrow) of the statistical test used in creating the significance results in the table. b

Means with the same letter in the Tukey grouping are not significantly different at the 0.05 

level.
General Technical Report FPL–GTR–221

8

the unbalanced design. The actual design is so close to balanced, the results should be very similar either way. 

In either case, the estimates of the variance components 

would proceed in a similar fashion. The estimate of the 

variance (error) is the error mean square in column 3. Thus, 

from Table 9, the variance (error) equals 5676534. The estimate of the mill(region) variance component comes from 

the mean square of 23320397 equal to the variance of the 

error of 5676534 plus 37.098 time variance (mill(region)). 

Similarly, the variance (region) can be estimated. This method of estimating variance components was still common at 

the time of the Haskell report. Now many new and better 

procedures are available. 

Having the variance component estimates can help design 

more efficient studies. For example, consider the MOE results in Table 10. If the study had six regions, six mills in 

a region, and 30 pieces within a mill in a region, the mean 

MOE would have the following variance:

 

 

Using the variance component estimates above as estimates 

of these variances

 

Note that if the study design had six regions, nine mills 

per region, and 20 pieces per mill in a region, the variance 

would have been less (0.00348). If the study had 12 regions, 

three mills, and 30 pieces per mill in a region, the variance 

would have also been considerably less (0.00233). The within mill variation is much larger than the mill within a region 

variation and the regional variation, but that does not mean 

that the latter two are not important and thus need to be incorporated in the design to get the best estimate for the same 

number of specimens tested. It is a balancing act of cost and 

accuracy to determine the best sampling method. 

Discussion and Conclusions

Any sampling method must be constructed using a balancing process to account for the various significant sources of 

variability. In the case of the In-Grade Program, those sources of variability were identified as being region, between 

mill-within-a-region, and pieces within-a-mill as influenced 

by lots. In the original analysis of 1980, the conclusion 

of the regional analysis stated, “Even though the variance 

component for regions is small, the effect is significant and 

unstable between dependent variables. The use of regions 

should be maintained for planning to guarantee representative sampling and because other grades and sizes may display different effects” (Haskell 1980). The reanalysis of the 

1980 data also shows this. Between-mill variability was also 

observed to be a significant source of variability. Finally, 

the piece variability within a mill was identified as being the 

largest source of variability.

Table 9. Variance components estimation procedure for MOR

Source DF Mean square Expected mean square

Region 5 77064522 variance(error) + 42.238 variance (mill(region)) + 227.42 variance(region)

Mill(region) 30 23320397 variance(error) + 37.098 variance (mill(region))

Error 1,331 5676534 variance(error)

Variance component Estimate

Variance (region) 225578.5

Variance (mill(region)) 475596.2

Variance (error) 5676534.0

Table 10. Variance components estimation procedure for MOE

Source DF Mean square Expected mean square

Region 5 5.16739 variance(error) + 42.238 variance (mill(region)) + 227.42 variance(region)

Mill(region) 30 1.19175 variance(error) + 37.098 variance (mill(region))

Error 1,331 0.16815 variance(error)

Variance component Estimate

Variance (region) 0.01686

Variance (mill(region)) 0.02759

Variance (error) 0.16815
Analysis of the Part I Southern Pine In-Grade Program Data

9

Application of the Results from Part I 

to Part II of the In-Grade Program

By the time that Part II of the In-Grade Program was started, 

in addition to the statistical significance of regions, another 

reason for maintaining regions had been recognized as valuable. In Part II other grade–size combinations were to be 

tested. It was planned to go to a mill and collect two lots for 

each of the grade–size combinations chosen for the Part II 

studies. Invariably, as was discovered in Part I, at the time of 

the visit, some mills did not have much in the way of inventory on hand or may not have been producing the particular 

grade-size combinations needed to collect a sample. 

Two elements of the sampling method in Part I greatly reduced the effort and cost of the sampling in Part I and the 

design of Part II. 

First, if a mill had been the primary unit of sampling and 

the region was ignored, a sampled mill that did not have 

all the material needed would have required another mill to 

be randomly selected. That might mean having to travel to 

any other mill in the population to try to obtain the rest of 

the missing sample. This could require more than one additional mill to be sampled. Sampling by regions and mills in 

a region limited the potential cost and time it might take to 

acquire the sample.

Second, the assumption that the regions divided the total 

growth region into homogeneous regions also played an important part into further reducing costs. If the region is homogeneous, any mill in the region would have material from 

the same population. That meant if a mill chosen randomly 

in a region and when sampled only had 2 by 4 and 2 by 10 

for the select structural specimens, any mill in a homogeneous region could provide 2 by 8 specimens. This concept 

was so important to the cost of the Program that agencies 

subdivided the original six regions into sub-regions based 

on other studies (such as the density survey studies done 

in the 1960s: U.S. Forest Service 1965a, b) and on expert 

analysis by people from the grading agencies that had a long 

history of interacting with mills in a proposed sub-regions. 

Issues like elevation, soil quality and type, climate factors, 

and many other criteria were available to the experts that 

decided on 18 regions for Southern Pine as shown in Figure 2. When actual sampling in Part II occurred, two of the 

original regions (15, 16) had no mills that could be sampled 

and thus only 16 regions were used. 

The assumption of homogeneity of a region was accepted 

by a broader group that reviewed the sampling method. 

Regions were accepted as a primary sampling unit because 

their variability, when compared to the mill within region 

variability, was significant. 

The division of the regions into smaller geographic areas 

was based on the issues discussed above. It was felt that the 

multiple regions would enhance the homogeneity within a 

region. This assumption allowed sampling regions in proportion to production in order to facilitate a simpler estimation of population parameters.

Conclusions from the Reanalysis of 

Past Data

In the re-examination and re-analysis of the 1980 data, both 

the regions and the mills within regions are statistically significant at the 0.05 level. This information was available and 

used as part of the background decision making for setting 

up Part II of the In-Grade Program. It was also determined 

that a lot was highly significant for MOE, suggesting that it 

would be beneficial to continue sampling by lots.

Summary of What Was Learned 

from Looking Back at Part I

The development of the current sampling and testing methodology that is used to determine global numbers for major 

species groups involved a series of tradeoffs between capturing the significant sources of variability and what was 

practical to accomplish. At the time that the decisions were 

being made for sampling, it was known that regions and 

between-mill variation were a significant part of the overall 

variation that would describe a global number. The reexamination and reanalysis of the 1980 data suggest that both 

the regions and the mills within regions were statistically 

significant in accounting for variation at the 0.05 level. The 

establishment of the sampling method that is currently used 

in determining global numbers for the major species groups 

in the North America took this finding into account. The 

current random sampling of mills within a region in proportion to production was based on a balancing of the significant regional, mill-to-mill and within-mill piece variability. 

It was also affirmed that the lot variability for MOE was 

highly significant. The use of region in the sampling method 

had the added benefit of controlling costs for sampling and 

testing. Thus, the decision to continue with the random 

sampling of mills in proportion to production by region was 

justified and necessary to keep costs at a reasonable level to 

conduct the extensive sampling envisioned for Part II. 

References

American Forest & Paper Association and American Wood 

Council, National Design Specification for Wood Construction. [current edition] Washington, D.C.: American Forest & 

Paper Association.

ASTM. 2011. Annual Book of Standards, Vol. 04.10. West 

Conshohocken, PA.: American Society for Testing and Materials. 

a. ASTM D1990–07. Standard methods for establishing 

allowable properties for visually-graded dimension lumber from In-Grade tests of full-size specimens.
General Technical Report FPL–GTR–221

10

b. ASTM D2915–10. Standard method for evaluating 

properties for stress grades of structural lumber. 

c. ASTM D4761–05. Standard methods for mechanical 

properties of lumber and wood-base structural materials.

Bodig, J. 1977. Bending properties of Douglas-fir-Larch 

and Hem-Fir dimension lumber. Special report No. 6888. 

Department of Forestry and Wood Science. Colorado State 

University, Fort Collins, CO. 59 p.

FPRS. 1989. Proceedings of the Workshop on In-Grade 

Testing of Structural Lumber, Madison, WI, April 25–26, 

1988, Proceedings 47363, Forest Products Research Society: Madison, WI.

Galligan, W.L., and D.W. Green. 1980. Development of 

standardized concepts for assignment and assessment of the 

mechanical properties of lumber—a continuing challenge 

for the 80’s. Forest Products Journal. 30(9):39–46. 

Galligan, W.L., D.W. Green, D.S. Gromala, J.H. Haskell. 

1980. Evaluation of lumber properties in the United States 

and their application to structural research. Forest Products 

Journal. 30(10):45–50.

Goodman, J.R., M.E. Criswell, J. Bodig. 1974. A rational 

analysis of wood joist floor systems. Final Report; National 

Science Foundation Grant GK-30853. Colorado State University, Fort Collins, CO.

Green, D., W.L.A. Marin, J.W. Evans. 1981. Flexural properties of 2 × 8, No. 2 and 2 × 4 stud grades of Douglas-fir 

Southern Pine dimension lumber. Un-numbered Buff Colored Report. USDA Forest Service, Forest Products Laboratory, Madison, WI. 171 p.

Green, D. W. 1983. In-grade testing impetus for change in 

the utilization of structural lumber. In: Proceedings, from 

stump thru mill: recent advances in spruce-fir utilization 

technology. Publication No. 83-13. Bethesda, MD: Society 

of American Foresters.

Green, D.W. and J.W. Evans. 1988. Evaluating lumber properties: practical concerns and theoretical restraints. Invited 

keynote address for the Wood Properties session. International Conference on Timber Engineering. American Society 

of Civil Engineers, Seattle, WA. Sept. 19–22, 1988. 

Hans, G.E., W.L. Galligan, W.L. Lehmann, H.M. Montrey, 

R.C. Moody. 1977. Five-year action plan for light-frame 

construction research. U.S. Department of Agriculture, Forest Service, Forest Products Laboratory, Madison, WI. 

Haskell, J.H. 1980. Interim Statistical Report Part I. “For 

Official Use Only not for publication.” USDA Forest Products Laboratory, Madison, WI. Internal Report, June 1980.

Jones, E. 1989. Sampling procedures used in the in-grade 

lumber testing program. In: Proceedings of workshop sponsored by In-grade Testing Committee and Forest Products 

Society. Proceedings 47363. Madison, WI: Forest Products 

Society.

Madsen, B. 1978. In-grade testing: Problem analysis. Forest 

Products Journal. 28(4):42-50.

Polensek, A., and Atherton G.H. 1975. Compression, bending strength, and stiffness of walls with utility grade studs. 

Forest Products Journal. 26(11):17–25.

SAS. 2012. Statistical Analysis System. Cary, NC: SAS Institute Inc. 

Stoline, Michael R. 1981. The status of multiple comparisons: simultaneous estimation of all pairwise comparisons 

in one-way ANOVA designs. The American Statistician 

(American Statistical Association). 35(3): 134–141. 

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procedures of statistics. New York: McGraw-Hill Book Co. 

481 p. 

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1965 status report. Research Paper FPL-RP-26. Madison, 

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Laboratory. 
Analysis of the Part I Southern Pine In-Grade Program Data

11

Appendix—Quotes of Interest

Quote from Haskell (1980)

Region Analysis Conclusion

“Even though the variance component for regions is small, 

the effect is significant and unstable between dependent 

variables. The use of regions should be maintained for plan-

ning to guarantee representative sampling and because other 

grades and sizes may display different effects.”

Mill Size Analysis Conclusion

“From a practical view point mill size was not an important 

factor in 2 × 8’s of No. 2 grade. Pieces within a mill was 

once again the dominant source of lumber property varia-

tion. This statement does not imply that weighting design 

values estimates by mill volume can be ignored.”

Mill Type Analysis Discussion and Conclusion

“Variance component estimates for mill type in the case of 

on-grade Southern Pine 2 x 4’s are greater than those for 

mills within mill type. This fact is contrary to the main effects discussed earlier. Thus, of the main effects studied in 

this report, mill type would appear to be a major factor of 

importance for future sampling considerations. Note, how-

ever, the variance component for pieces within mills is still 

much larger than the other components.”

Quote from Green and Evans (1988)

“In the initial phase of Part I of the In-Grade program, the 

committee conducted a limited amount of testing to evaluate 

our procedures and to get an estimate of property variability. 

From this initial study the committee could detect no drastic 

mechanical property variations across geographic growth 

regions for the major volume species groups. Further, the 

variation in properties within a mill was at least as large as 

that between mills. This meant that we could divide the spe-

cies growth regions into broad subregions to assure a repre-

sentative sample. The equivalent variation within a mill and 

between a mill also meant that we could sample fewer mills 

with a larger sample per mill. These assumptions saved us 

a considerable amount of time and money in collecting our 

sample because we did not have to collect as many samples 

from as many mills. However, it also restricted our ability to 

precisely identify any low-strength pockets in our data. Had 

the committee’s objective been to determine the existence 

of low pockets, or if the between-mill variation had been 

much larger than the within-mill variation, we would have 

sampled more mills and taken fewer samples per mill.”