Chemical Variation of Soils in Missouri 

Associated with Selected Levels of the 

Soil Classificatim System 

By RONALD R. TIDBALL 

GEOCHEMICAL SURVEY OF MISSOURI 

GEOLOGICAL SURVEY PROFESSIONAL PAPER 954-B 

An examination of sampling efficiency in 

geochemical studies of standard soil 

classes in Missouri 

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1976 
UNITED STATES DEPARTMENT OF THE INTERIOR 

THOMAS S. KLEPPE, Secretary 

GEOLOGICAL SURVEY 

V. E. McKelvey, Director 

Library of Congress Cataloging in Publication Data 

Tidball, Ronald R. 

Chemical variation of soils in Missouri associated with levels of the soil classification system. 

(Geochemical survey of Missouri) (Geological Survey Professional Paper 954-B) 

Bibliography: p. 

Supt. of Docs. no.: I 19.16:954-B 

1. Soils-Missouri-Analysis. 2. Soils-Missouri-Classification. 3. Geochemistry-Missouri. 

I. Title: Chemical variation between and within selected levels of the soil classification system ... II. Series: Geochemical 

survey of Missouri. III. Series: United States Geological Survey Professional Paper 954-B. 

S599.M52T52 631.4'4'09778 75-619380 

For sale by the Superintendent of Documents, U.S. Government Printing Office 

Washington, D.C. 20402 

Stock Number 024-001-02797-6 
CONTENTS 

Page Page 

Abstract ........................................................................................ . Bl Results........................................................................................... B7 

Introduction ................................................................................ .. 1 Geochemical components of variability .. .... .. .. .. .. .. .. .. .. .. ...... . 7 

Acknowledgments ................................................................. . 2 Reliability of Suborder means computed from first-stage 

Review of literature ..................................................................... . 2 data..................................................................................... 8 

Materials sampled and methods .................................................. . 3 Second-stage sample designs .......... ....................................... 9 

Soil maps ............................................................................. .. 3 Geochemical summaries........................................................ 11 

Analytical procedures ........................................................... . 3 Discussion..................................................................................... 13 

Target and sampled populations ........................................ .. 4 Conclusions................................................................................... 14 

Statistical model ................................................................... . 6 References cited............................................................................. 14 

ILLUSTRATION 

Page 

FIGURE 1. Map showing soil sampling localities in Missouri .............................................................. ........ ................................................... B5 

TABLES 

Page 

TABLE 1. Analytical methods and lower limits of determination used in analyses for elements in Missouri soils ............ :......................... B4 

.2. Taxa of Missouri soils sampled in this study.................................................................................................................................. 4 

3. Nested analysis-of-variance design used for first-stage sampling program of Missouri soils........................................................ 7 

4. Logarithmic variance components for each element apportioned among the several levels of the analysis-of-variance design.. 8 

5. Comparison of the observed variance of the mean within Suborders with the maximum acceptable variance of the mean....... 9 

6. Comparison of average compositions of Missouri soil Suborder samples...................................................................................... 12 

III 

GEOCHEMICAL SURVEY OF MISSOURI 

CHEMICAL VARIATION OF SOILS IN MISSOURI 

ASSOCIATED WITH SELECTED LEVELS OF THE 

SOIL CLASSIFICATION SYSTEM 

By RoNALD R. TIDBALL 

ABSTRACT 

Natural variation in the total elemental composition of the plow 

zone (approximately 6 in. (15 em) in deptp) of soils in Missouri has 

been examined using a five-level hierarchical analysis-of-variance design. This study is an initial investigation of the chemical variation 

in the soils and can serve as a basis for planning future intensive 

sampling. The design includes three levels (Suborders, Subgroups, and 

Series) of the Soil Taxonomy developed by the National Cooperative 

Soil Survey and permits an objective evaluation of the geochemical 

properties of the taxonomic system. Components of geochemical variance for 31 elements were estimated for differences between soil Suborders, between soil Subgroups, and between soil Series. Significant 

differences in composition between Suborders were found for 23 elements, including the trace metals arsenic, barium, chromium, copper, 

gallium, lanthanum, lead, scandium, selenium, strontium, vanadium, 

ytterbium, and zinc. Such differences, however, account for no more 

than 45 and commonly less than 35 percent of the natural variation 

(excluding analytical effects) of any element. Maps based on the distribution of Suborders, therefore, would not be particularly useful in 

interpretation of geochemical characteristics. Variation between soil 

Series is, for the most part, much larger than variation within a given 

Series. Only cobalt, nickel, lead, and zirconium were found to have 

variation within Series larger than that between Series. Thus, maps 

based on the distribution of Series might serve as fairly good geochemical maps for most elements. 

INTRODUCTION 

This report is one in a series describing a variety of field 

studies undertaken as a part of a general survey of the 

geochemical environment in Missouri. The survey was 

undertaken in cooperation with medical scientists of the 

Environmental Health Surveillance Unit of the University of Missouri and all results have been published in 

a series of progress reports (U.S. Geological Survey, 

1972a-1973), which were compiled at 6-month intervals 

during the 4 years the work was under way. The work 

was performed partially in support of the Health Surveillance Units studies on the possible role of environmental geochemistry in health and disease. A preliminary 

description of the survey and its implications for epidemiologic research was published by Connor and others 

(1972), and a general statement of goals and methods was 

given by Miesch (1976). Preliminary results of the present 

study were reported by Tidball (1971) and this paper is 

a final report. 

The role of trace elements in health and disease has 

been of interest to medical researchers for a long time, 

but an increasing public awareness of trace-element 

hazards in the environment has focused attention on the 

need for data about the expected concentrations and 

ranges of many trace elements in ordinary environmental 

materials under natural conditions. Any attempt to describe the geochemistry of soils over a broad area must take 

into account the possible variations in trace-element concentrations at local scales. Developing such a description 

without generating an inordinately large analytical load 

(as might easily happen by sampling a very large landscape unit with a very small sampling interval) is a 

problem in sampling efficiency. 

The principles underlying sampling efficiency in traceelement investigations that were described by Miesch 

(1976) were in part formulated and tested in much of the 

Missouri work. Briefly, sampling efficiency is approached 

through the concept of sampling in more than one stage. 

That is, an initial or first stage of sampling, which is 

essentially exploratory, is undertaken to investigate the 

peculiarities of the particular kind of variation faced by 

the investigator. Later stages of sampling, if required, are 

then undertaken using a design specifically directed to 

delineation of the variation discovered during the first 

stage. Such a design should produce a stable or reproducible map of that variation. Discovery of natural variation 

lacking a regional component may make secondary sampling stages unnecessary. Likewise, failure to undertake 

the first stage subjects the investigator to the risk of either 

oversampling or undersampling when attempting to desBl 
B2 GEOCHEMICAL SURVEY OF MISSOURI 

cribe or map natural geochemical variation. Maps based 

on too few samples may be erroneous-that is, not reproducible; maps based on too many samples are financially 

wasteful-that is, inefficient. 

In order to minimize the sampling effort, similar soils 

should, where possible, be classed together in some. minimum number of larger groups rather than attempting to 

describe each of a large number of individual soils. The 

hierarchical taxonomy of the Soil Classification System 

(U.S. Soil Conservation Service, Soil Survey Staff, 1960; 

1967, 1968, in press) provides one method of grouping 

similar soils. The six levels of the hierarchy in descending 

sequence are as follows: Order, Suborder, Great Group, 

Subgroup, Family, and Series. This classification seems 

especially useful for the present purpose for several reasons: ( 1) if soil composition is uniform within taxonomic 

groups at any one level of the hierarchy, then estimates 

derived for a sample of one group (taxon) at that level 

may be extrapolated to the other groups (taxa) at the same 

level, thereby reducing the total number of samples required for description; (2) the geographic distribution of 

many soil taxons in the classification system is at least 

partially known; (3) some genetic inferences about the 

distribution of elements may be possible from the definition of the taxon being described; and (4) because the soil 

classification system provides a standard language for 

description of soils, communication with other interested 

researchers is facilitated. 

This report examines some properties of the geochemical variation in the classified soils of Missouri. At 

the time the study was initiated, about 275 (H. E. Grogger, 

oral commun., 1969) soil Series were recognized in Missouri, even though part of the State has yet to be mapped 

by modern standards. Because of this diversity of soil 

types, a first-stage, or exploratory, sampling program was 

undertaken to estimate some of the properties of the 

chemical variability in the soils of the State, in hopes of 

designing an efficient secondary sampling scheme for 

describing that variation. 

The soils at any taxonomic level are grouped by the 

distinctive attributes they have in common; accordingly 

the greatest number of general laws can then be deduced 

about the taxon. Each of the several attributes defining 

the taxon is ideally the cause, or at least the mark (referred 

to as a "marker" property), of numerous other properties. 

This commonality of attributes is called a natural taxonomy (Smith, 1963; Cline, 1963). The attributes which 

define a taxon are predominantly morphological, and 

only to a minor extent are chemical attributes included. 

We can, however, hypothesize that a taxon which is defined by certain fundamental marker attributes has a 

distinctive chemical composition and that the concentration of elements in the soils of the taxon is controlled 

by mechanisms related to those for morphologic properties. 

The objective of the study on which this report is based 

was to test the above hypothesis by answering two questions, as follows: 

1. Because the number of taxa increase downward in 

the hierarchical system, what level of the system 

yields the most information on geochemical 

variability for the least number of taxa? A level 

containing relatively few, but geochemically 

distinct, taxa constitutes an efficient soil classification system for definition of strata in stratified 

sampling designs. 

2. Having defined the most efficient level in the system, 

how many samples must be collected from each 

taxon at that level to reliably estimate the mean 

concentration of elements in each? 

ACKNOWLEDGMENTS 

The assistance of several staff personnel of the U.S. 

Soil Conservation Service throughout the State of Missouri in the selection of sampling locations is gratefully 

acknowledged. In particular, Mr. H. E. Grogger, State 

Soil Scientist (now retired), compiled the list of soil Series, 

current to May 1969, at the beginning of this study. The 

following U.S. Geological Survey chemists made the 

analyses for this study: Floyd Brown, Joseph Budinsky, 

G. T. Burrow, J. P. Cahill, I. C. Frost, Johnnie Gardner, 

Claude Huffman, Jr., Wayne Mountjoy, V. E. Shaw, D. 

G. Shipley, J. A. Thomas, and E. P. Welsch made the 

wet chemical analyses and atomic absorption analyses, 

M. W. Solt, and J. S. Wahlberg did the X-ray fluorescence 

analyses, and Harriet Neiman, the spectrographic analyses. Special acknowledgment is given to J. G. Boemgen, 

who gave much assistance in data processing. All statistical computations were performed on the U.S. Geological 

Survey's IBM 360/65 computer in Washington, D. C., 

using programs written or adapted by R. N. Eicher, G. 

I. Selner, Robert Terrazas, and George Van Trump. 

REVIEW OF LITERATURE 

Chemical variation in the soil may be described as a 

function of either geography (and thus increases as distances between sampling sites increase) or taxonomy (and 

thus increases as the degrees of differentiation between 

soil attributes increase). A review of the literature on the 

lateral variability of soil was given by Beckett and Webster 

(1971). The lateral variability of the soil is a function of 

the relative geographical homogeneity of the soil and will, 

in theory, define the size of the sampling interval needed 

for an accurate representation of the soil characteristics: 

that is, a homogeneous soil can be adequately represented 

by rather widely separated samples, whereas a heterogeneous soil requires a much shorter" sampling interval. 

In practice, the soil of a region is likely to have several 

geographic components of variance, each associated with 

increasing distance between sampling localities, and so 
CHEMICAL VARIATION OF SOILS B3 

both short and long sampling intervals would be necessary to describe all of the variance. Even a very small area 

may have a large lateral variation. For example, McKenzie 

(1955) intensively sampled a "uniform" soil within a 3-

by 8-foot (0.9- by 2.4-m) area and concluded that significant differences in copper, gallium, magnesium, manganese, molybdenum, and vanadium occurred between 

samples separated by a lateral distance of only 8.5 inches 

(21.5 em). The development of chemical maps for the 

major fertilizer nutrient elements over areas the size of 

a field or a farm was discussed by Vazhenin and others 

(1961). They found that concentrations of nutrient elements could be related not to taxonomic soil groups, but, 

rather, to previous history of land use. 

Thus, some workers have used designs that have 

examined variation as a function of distance, whereas 

others have approached the problem by using taxonomic 

or other differentiation factors rather than distance. 

Oertel ( 1959) discussed a method for estimation of the 

trace-element status of soils over an area of several thousand square miles. The objective was to express the traceelement status of an area by giving the range of expected 

concentrations for each soil group in the area. Yet, as 

Oertel (1959, p. 59) pointed out, "results must be expected" 

in which very different soil groups, taxonomically 

speaking, are chemically the same; and also, any one 

group may differ within itself from one geographic area 

to another. In other words, variance between taxonomic 

groups may be less than variance within groups. This is 

the circumstance that Petersen and Calvin (1965, p. 56) 

cautioned against: namely, that differences between 

groups cannot be estimated with any degree of reliability 

in the presence of excessive within-group variance. Any 

subtle differences between groups could be defined, therefore, only with a large number of samples; in fact, the 

number may be so large as to be totally impractical to 

collect and analyze. Variation between and within several 

mapping units (based on soil Series) in Ohio was estimated 

using a nested analysis-of-variance design similar to the 

one used in the study reported on here (Wilding and 

others, 1965). 

The first-stage sampling program used in the present 

study is based on a five-level nested analysis-of-variance 

design which incorporates both taxonomic and geographic components of variability. A detailed discussion 

of the mechanics and interpretation of the nested analysis 

of variance in geological applications is given by Olson 

and Potter (1954), Potter and Olson (1954), and Krumbein 

and Slack (1956). 

MATERIALS SAMPLED AND METHODS 

SOIL MAPS 

Since 1904, soil survey maps have been published for 

67 of the 114 Missouri counties (U.S. Soil Conservation 

Service, 1968); of these county maps, eight are based on 

the 1938 soil classification system (U.S. Department of 

Agriculture, 1938; revised by Riecken and Smith, 1949; 

Thorp and Smith, 1949). These eight counties are: Boone 

(Krusekopf and Scrivner, 1962), Daviess (Grogger, 1964), 

· Holt (Shrader and others, 1953), Jasper (Shrader and 

others, 1954), Linn (Shrader and others, 1945), Livingston 

(Rourke and others, 1956), Moniteau (Scrivner and Frieze, 

1964), and St. Charles (Shrader and Krusekopf, 1956). 

Six county soil surveys-for Worth (Brown, 1968), 

Pemiscot (Brown, 1971), Dent (Gilbert, 1971), Caldwell 

(Jeffrey, 1974), Barton (Hughes, 1974), and Lafayette 

(Jeffrey, 1975) Counties-have been published since the 

adoption in 1965 of the comprehensive system of soil 

classification (U.S. Soil Conservation Service, Soil Survey 

Staff, 1960, 1967, 1968, in press). Unpublished detailed 

soil surveys have either been completed or are in progress 

in 31 other counties and 3 ranger districts of the Mark 

Twain National Forest (J. H. Lee, Missouri State Soil 

Scientist, oral commun., 1975). Soil-association maps for 

counties not otherwise covered were published by the 

University of Missouri Agricultural Experiment Station, 

as follows: Blackwater and Lamine Townships, Cooper 

County (Scrivner and Baker, 1961); Mississippi delta area 

of southeast Missouri (Krusekopf, 1966); Howard County 

(Scrivner, 1961); and Taney County (Scrivner and Frieze, 

1953). Soil-association maps are in preparation by the 

experiment station staff for 19 counties and for the Missouri River flood plain from Kansas City to Jefferson City 

(C. L. Scrivner, oral commun., 1970). Statewide soilassociation maps present the broad picture (Missouri 

University Agricultural Experiment Station, 1931; 

Scrivner and others, 1966; U.S. Soil Conservation Service, 

in U.S. Geological Survey, 1970, p. 86). 

ANALYTICAL PROCEDURES 

The analytical procedures used in this study were described by Huffman and Dinnin (1976), Bartel and Millard 

(1976), Neiman (1976), and Wahlberg (1976). Table 1 

gives the procedures and the limits of determination for 

all of the elements commonly detected in the soil samples. 

A standard semiquantitative emission spectrographic 

procedure was used to scan for about 60 elements, but the 

concentration ranges for more than half of these elements 

are typically below the limit of determination for this 

method. Therefore, supplementary methods (listed in 

table 1) were used for some of the elements that were of 

particular interest and where the analytical methods were 

not highly expensive. The spectrographic data for elements with concentrations above the lower limits of determination are reported in six geometric classes per order 

of magnitude, which have approximate midpoints of 

0.00010, 0.00015, 0.00020, 0.00030, 0.00050, 0.00070, 

0.0010, ... , in each order of mat?nitude, up to 10.0 percent. 

Logarithmic transformation of data reported in such 

classes, as suggested by Bennett and Franklin ( 1954, p. 

91), is essential. 
B4 GEOCHEMICAL SURVEY OF MISSOURI 

TABLE I.-Analytical methods and lower limits of determination used 

in analyses for elements in Missouri soils 

Element 

AI .............. . As ............... . B ................ . 

Ba .............. . C (total) ..... . Ca .............. . 

Co .............. . Cr. .............. . 

Cu .............. . F ................ . 

Fe ............... . 

Ga .............. . 

Hg ............. . K ................ . 

La .............. . Mg ............. . Mn ............. . Na .............. . 

Ni .............. . P ................ . Pb .............. . 

& ............... . 

Se ............... . Si ............... . 

Sr ............... . Ti ............... . v ................ . Y ................ . 

Yb .............. . Zn .............. . 

Zr ............... . 

Analytical 

Method 

X-ray fluorescence ....................... . Di thiocarbamate-colorimetric ..... . Spectrographic ............................ . ... do ...................................... . Induction furnace ....................... . X-ray fluorescence ....................... . 

Spectrographic ............................ . ... do ...................................... . 

... do ...................................... . Selective ion electrode ................. . X-ray fluorescence ....................... . 

Spectrographic ............................ . 

Instrumental atomic absorption .. X-ray fluorescence ....................... . 

Spectrographic ............................ . Atomic absorption ...................... . Spectrographic ............................ . Atomic absorption ...................... . 

Spectrographic ............................ . X-ray fluorescence ....................... . Spectrographic ............................ . Spectrographic ............................ . X-ray fluorescence ....................... . ... do ...................................... . 

Spectrographic ............................ . . .. do ...................................... . ... do ...................................... . ... do ...................................... . ... do ..................................... .. Atomic absorption ...................... . 

Spectrographic ........................... .. 

Lower limit of 

determination 

(parts per million) 

10,000 

.2 

20 

1.5 

500 

1,000 

3 

1 

1 

10 

1,000 

5 

.01 

1,000 

30 

300 

1 

100 

5 

300 

10 

5 

10,000 

5 

2 

7 

.l 

10 

1 

10 

10 

TARGET AND SAMPLED POPULATIONS 

The soils of the State of Missouri cannot be regarded 

as a population in a statistical sense until the individuals 

are defined; the aggregate of these individuals may then 

be regarded as a population (Krumbein, 1960). The target 

population-or population of interest-is, therefore, 

defined as all of the potential samples of the uppermost 

horizon (Q-6 in. (0-15 em) in depth) of soil profiles 

throughout the State that had been mapped and classified 

by soil Series at the time of collection. A soil profile is 

defined as a vertical cross section of the sequence of soil 

horizons that extends downward from the ground surface 

to a variable depth, typically several feet, where the original properties of the parent material are more or less 

evident. The fact that the target population is specified 

as being "classified" implies that the soil individuals are 

defined in terms of taxonomic units. Although the coverage of Missouri soils by soil mapping is still incomplete, 

it is sufficiently extensive to consider the defined population as a reasonable representation of all soils in the State. 

The total variation in chemical composition of the soil 

population may be subdivided into variance components 

associated with each taxonomic level. Apportioning the 

variance in this manner permits a judgment of the relative efficiency of any taxonomically dependent design 

that might be used in a second-stage sampling program. 

The present study includes only three levels of the taxonomic system-Suborder, Subgroup, and Series-because of 

inadequate representation of some levels among Missouri 

soils. The source-of-variation designations for the more 

ideal complete design and for the abridged design used 

in this study are compared as follows: 

Complete design, 

source of variation 

Abridged design, 

source of variation 

Between Orders; within State 

Between Suborders; within Orders Between Orders and Suborders; 

within State 

Between Great Groups; within 

Suborders 

Between Subgroups; within Great 

Groups 

Between Great Groups and Subgroups; within Suborders 

Between Familes; within Subgroups 

Between Series; within Families Between Families and Series; 

within Subgroups 

Between Localities; within Series 

Between Samples; within LocaliBetween Localities; within Series 

Between Samples; within Localities ties 

Between Analyses; within Sam- Between Analyses; within Samples pies 

In the abridged design some levels are combined within 

the next lower level. The first three levels evaluate taxonomic variation, the next two levels evaluate local geographic variation, and the last level evaluates analytical 

variation. 

The sampled population is composed of the taxa of 

Missouri soils as shown in table 2. 

TABLE 2.-Taxa of Missouri soils sampled in this study 

[Leaders( ... ) indicate missing Series] 

Suborder Subgroup Series 

Aqualf ......... Aerie ochraqualf................. McCune, Dundee, 

Cal woods. 

Typic ochraqualf ............... Lightening, McGirk, 

Moniteau. 

Udal£ ... ... ..... Typic fragiudalf ................. Hobson, Loring, Viraton. 

Aquollic hapludalf..... ........ Liberal, Lineville, 

Mystic. 

Fluvent ........ Aquic udifluvent. ............... Collins, Dockery, 

Waubonsie. 

Typic udifluvent ................ Caruthersville, Elsah, . Nodaway. 

Ochrept ....... Fluventit dystrochrept ....... Beulah, Gladden, ... . Dystric fluventic eutro- Nebo, Ray, .... 

chrept ............................. . Aquept......... Aerie fluventic hapla- Commerce, Falaya, 

quept .............................. . Westerville. 

Vertic haplaquept ............. . Alboll .......... Argiaquic argialboll .......... . 

Alligator, Jacob, Sharkey. 

Arbela, Humestone, .... 

Typic argialboll ................ . Edina, .... , .... 

Aquoll......... Fluventic haplaquoll ....... .. Levasy, Myrick, Radley. 

Vertic haplaquoll .............. . Booker, Bosworth, 

McCroskie. 

Udall .......... . 

Udalt .......... . 

Aquic argiudoll .................. Lagonda, Grundy, Nevin. 

Aquic fluventic hapludoll .. Cooter, Gilliam Waldron. 

Ochreptic fragiudult ........ Nixa, .... , .... ' 

Typic paleudult ................. Baxter, Clarksville, 

Coulstone. 
CHEMICAL VARIATION OF SOILS B5 

At the top level of the first-stage design, all the Suborders (nine) that had full representation at the lower 

hierarchical levels were selected systematically. Random 

selections were made within each succeeding lower level 

as follows: two Subgroups within each Suborder, three 

Series within each Subgroup, two localities (areas 100 feet 

(30m) square) within each Series, and two samples within 

each locality. Also, duplicate analyses were performed on 

25 randomly selected samples; although variation due to 

the analytical procedures was estimated independently of 

the other variance components, it constitutes, in effect, 

a sixth level in the nested design. The geographic dis-

• 

• 

0 

tributions of the Series are available from both published 

and unpublished soil survey reports by the U.S. Soil Conservation Service, and the University of Missouri Agriculture Experiment Station. A random selection of 

sampling localities was achieved by having Soil Survey 

Staff personnel identify a number of widely scattered 

occurrences of each Series, then two localities (each representing a separate occurrence) for each Series were selected 

using a random number table. Randomly selected sampling localities are shown in figure 1. The soils on the 

major river flood plains have considerable morphologic 

diversity; accordingly, a disproportionate number of 

50 100 MILES 

0 50 100 KILOMETRES 

FIGUR.E I.-Soil sampling localities (dots) in Missouri. 
B6 GEOCHEMICAL SURVEY OF MISSOURI 

flood plain soil Series in relation to the total area of alluvium have been recognized and sampled. Sampling 

localities are, therefore, more concentrated along the 

Missouri River valley east of Kansas City and in the Mississippi River delta area of southeast Missouri. Areas without representation in the sample were excluded largely 

because of a lack of modern mapping. Two sampling 

localities are located in Kansas just across the border from 

Barton County, Missouri. 

The analysis-of-variance procedures (Anderson and 

Bancroft, 1952, p. 328) are sufficiently flexible that some 

missing data can be tolerated in lower levels of the design. 

Although omissions were not originally anticipated or 

intended, some vacancies in the sample design had to be 

accepted when certain soil Series could not be found in 

the field, and no alternate choices were available. These 

vacancies are indicated in table 2. 

Each soil sample consists of a channel composite of the 

surface horizon (approximately 6 in. (15 em) in depth). 

This horizon was selected on the premise that it exercises 

the greatest influence on plant growth and is the horizon 

most intimately involved in any phenomena at or near 

the ground surface. Most soil properties tend to exhibit 

their greatest variation in the surface horizon and the 

variation decreases with depth (Petersen and Calvin, 

1965, p. 56). 

STATISTICAL MODEL 

The statistical model used for this study is the standard 

model of the nested analysis of variance (Anderson and 

Bancroft, 1952, p. 327-330; Bennett and Franklin, 1954, 

p. 402-409), as follows: 

Xijklmn =p.+ai+/3ij +Yzjk +8ijkz+7lijklm+Eijklmn ' (I) 

where the subscripts are as follows: 

i refers to a Suborder 1 ~ i ~9, 

j refers to a Subgroup, 1~j~2, 

k refers to a Series, 1 S k S3, 

l refers to a Locality, 1 ~ l ~ 2, 

m refers to a Sample, 1 ~ m ~ 2, and 

n refers to an Analysis, 1 ~ n ~ 2. 

The term Xijklmn is a single analytical value for the mth 

Sample, within the lth Locality, representing the kth 

Series, and so forth. Equation I shows that Xijklmn is 

equal top., the grand mean for the entire soil population, 

plus the following deviations: ai is the difference between 

the grand mean p. and the mean for the ith Suborder; /3ij 

is the difference between the mean for the jth Subgroup 

and the mean for the ith Suborder; Yijk is the difference 

between the mean for the k th Series and the mean for the 

jth Subgroup; 8zjkl is the difference between the mean 

for the lth Locality and the mean for the kth Series;1Jijklm 

is the difference between the concentration of the element 

in the mth Sample and the mean for the lth Locality; and 

E ijklmn is the difference between the nth Analysis and 

the concentration in the mth Sample. The last term reflects the analytical precision. 

The analytical values for most minor elements have 

been transformed to the logarithmic form because the 

change in scale tends to improve the homogeneity of the 

variances, thus fulfilling one of the basic requirements 

for the analysis of variance. In addition the frequency distributions of geochemical data at trace concentrations are 

typically more nearly symmetrical on a logarithmic scale 

than on an arithmetic scale. The estimation of variance 

components in the analysis-of-variance method is not 

seriously affected by slight departures from normality, 

but tests for the significance of the differences among 

means may be more affected (Miesch, 1967a, p. Al4). 

All of the subscripted terms on the right side of equation 1 have means of zero; the purpose of the first-stage 

sampling program is to estimate the variance of each 

term. These components of variance have the property 

of being additive, giving: 

Ux 2 = Ua2+ uf32+ui+ u82+ ur,Z+ aE2 , (2) 

where ux 2 is the total variance within the sampled population of soils; all the tern1s on the right side of the equation 

represent the parts of the total variance apportioned to 

each level. 

The nested analysis-of-variance design, excluding the 

analytical (lowest) level is shown in table 3. The subscripted S2 terms are estimates of the population variance 

components, u 2• Note that each mean square is a progressive summation of weighted variance components from 

all lower levels; each component is multiplied by a coefficient that represents the number of samples that have 

contributed to that particular variance estimate. Fractional coefficients appear for Sa2 and S!l because of the 

unequal sizes of the classes in levels 2 ana 3; the fractional 

coefficients are considered "effective" sample sizes at 

these levels and are slightly less than they would be if 

the class sizes were equal. The analysis of variance is used 

both to test for significant differences between group 

means at each level by using the F-ratio and to estimate 

the variance components. 

The F -test for the equality of two variances (Snedecor 

and Cochran, 1967, p. 117) is used in the analysis-ofvariance design to test the hypothesis that the last variance 

component represented in each summation of the mean 

square (see table 3) equals zero. For example, consider the 

variance ratio of levels four and five, 

(3) 

where the hypothesis that ua2 (variance among localities) 

equals zero is being tested. As S 8

2 approaches zero, F 

approaches one. The judgment that calculated F is or is 

not significantly greater than one at a given probability 

is based on comparison with critical values from an Ftable for known degrees of freedom. If calculated F exceeds 

the critical F for a probability level of, say 0.05, then it 
CHEMICAL VARIATION OF SOILS B7 

TABLE 3.-Nested analysis-of-variance design used for first-stage sampling program of Missouri soils 

Degrees 

Level Source of varialion' of Mean·square estimates Variance component 

freedom 

Between Suborders .................. 8 MS1=S7]2+2S82+4Sy2+ 10.7Sp2+20.8Sa2 

S~= 

2 Between Subgroups: 

EMS1=S7]2+2S82+4Sy+ 10. 7S(i 

within Suborders ................. 9 MSz=Sif+2S82+4Sf+ 1 0.2S[f 

3 Between Series: 

within Subgroups ................ 29 MSs=5ry2+2S82+4Sf 

4 Between Localities; 

within Series ........................ 47 MS4~Sq +2S1)2 

5 Between Samples: 

within Localities 

Total ............................ . 

94 

187 

Population size 

Suborders in the State........... Na=9 

Subgroups per Suborder....... Ng=4.6 (average) 

Series per Subgroup.............. N 1 =7 (average) 

Localities and samples.......... N,;=N = oo 

Sample size 

na=9 

n

13=2 

n

1 =2.6 (average) 

n

8

=n71=2 

follows that the term S 8

2 is greater than zero for some 

reason other than chance, probably because u8

2 is greater 

than zero. Only one time out of 20 should the calculated 

F exceed the critical value ofF for the 0.05 level because 

of chance alone. A significant variation is present between the localities; that is, some or all localities within 

any Series differ from one another. 

The calculation for the estimates of variance components is shown in table 3. It is possible that on occasion 

the estimated mean square at some lower level is greater 

than at the next higher level. This results in a negative 

estimate of a variance component. A true variance component cannot be negative, but the probability of occurrence of negative estimates of the components is sometimes quite large (Leone and Nelson, 1966, p. 465). By 

convention, negative variance-component estimates are 

set equal to zero (Olson and Potter, 1954, p. 43) on the 

assumption that the real variance is either zero or very 

small, or that an unusual sampling event occurred 

(Krumbein and Slack, 1956, p. 757). The convention has 

been applied in this study with the understanding that 

the subject has been a matter of some debate (Neider, 1954; 

Thompson, 1962; Thompson and Moore, 1963;Anderson, 

1965; Leone and Nelson, 1966, p. 464). 

RESULTS 

GEOCHEMICAL COMPONENTS OF VARIABILITY 

The estimated logarithmic variance components associated with each level of the sample design for a number 

of elements commonly detected in Missouri soils are 

shown in table 4. The relative distribution of the total 

variance among the several levels is more readily seen 

when each variance component is expressed as a percentage. 

The percentage distribution of the variance components shows that the analytical procedure accounts for 

about 5 percent or less of the total variance for elements 

such as aluminum, calcium, iron, potassium, sodium, 

selenium, silicon, strontium, and zinc. In contrast, about 

80 percent of the total variance in mercury can be attributed to the analytical procedure. Determination of the 

distribution of mercury in these soils must clearly be 

based on a more precise analytical method. On the average, nearly two-thirds or more of the total elemental 

variance can be attributed to the taxonomic variation and 

the remaining third is associated about equally with geographic localities (within the Series) and analytical procedures. 

Most of the elements that exhibit significant variation 

between Suborders are also estimated to exhibit no variation between Subgroups. This feature has an important 

bearing on any future sampling designs based on soil 

taxonomy. For such elements, it would be wasteful to use 

any second-stage designs that employ Subgroups as a 

sampling unit. Moreover, because the Subgroup component of variance includes variations between Groups 

as well, it is clear that inclusion of either Groups or Subgroups in future designs for these particular elements 

would be inefficient. Taxonomic levels used in further 

sampling should be Suborders or Series. Because sampling 

of Suborders describes no more than about 45 percent of 

the total logarithmic variance for any element (notably 

aluminum), and describes a much smaller percentage for 

many of the elements studied, it seems reasonable torequire that taxonomically related designs must be based 

on soil Series. Sampling Series and describing differences 

between them would result in describing about 6Q-80 percent of the geochemical variance, but this method clearly 

could be costly, at least in Missouri, because of the large 

number of Series present. 

The actual number of localities required within each 

Series and the optimum spacing of localities depend on 
B8 GEOCHEMICAL SURVEY OF MISSOURI 

TABLE 4.-Logarithmic variance components for each element apportioned among the several levels of the analysis-of-variance design 

[Numbers in parentheses express each variance component as a percentage of the total 

logarithmic variance. Significance of the 0.05 probability level for values in the Suborder, Subgroup, Series, and Locality columns is indicated by an asterisk (•). No test 

for significance was made for Sample and Analysis values] 

Element Suborder Subgroup Series Locality Sample Analysis 

(Sa2) (SfJ2) (Sy2) <Sa2> (STf2) (SE2) 

AI .................. 0.01794• 0.0 0.01517• 0.00~68· 0.00298 0.00081 (44) (0) (~7) (9) (7) (~) 

As .................. .00522• .0 .00925• .0064~· .00148 .00277 (21) (0) (~7) (26) (5) (ll) B ................... .0 .00226 .00764• .0 .005~9 .Oll04 (0) (9) (29) (0) (20) (42) Ba ................. .01428• .0 .01588• .00~20· .00456 .00556 (~~) (0) (~7) (7) (10) (I~) 

c ................... .0060~ .00615• .00~~~ .009~7· .000~6 .01750 (14) (14) (8) (22) (I) (41) Ca ................. .054~7· .0 .10151• .01558• .00276 .00500 (~0) (0) (57) (9) (I) (S) Co ................. .00674 .0 .01526• .01949• .00289 .00642 (I~) (0) (~0) (~8) (6) (13) Cr .................. .00951• .0 .01699• .00122 .00074 .00790 (26) (0) (47) (~) (2) (22) Cu ................. .0259~· .00989 .01484• .00890• .0 .01135 (~7) (14) (20) (I~) (0) (16) F ................... .02812• .00705 .01697• .00986• .00642 .02110 (~I) (8) (19) (ll) (7) (24) Fe .................. .00750• .00~68 .0087~· .00619• .00956 .00061 (21) (10) (24) (17) (26) (2) Ga ................. .028~1· .0 .0219~· .00~29 .01040 .00496 (41) (0) (~2) (5) (15) (7) Hg ................ .00702 .0 .01262• .0 .0 .08756 (7) (0) (12) (0) (0) (81) Kt .................. .08995• .0 .1451~· .0~652• .01298 .oom (~I) (0) (50) (13) (5) (I) La ................. .00729• .0 .01~~~· .00546• .00281 .01127 (18) (0) (~~) (14) (7) (28) Mg ................ .04942• .0 .04852• .Oll42• .0098~ .01~~ 

(~6) (0) (~6} (9) (7) (12) Mn ................ -~2 .0 .02847• .0~084• .00~97 .01401 (8) (0) (~4) (~7) (5) (16) Na 1 •••••••••••••••• .029~9· .0 .06481• .01051• .00051 .00182 (27) (0) (61) (10) (<I) (2) Ni ................. .00951 .00701• .00650 .01966• .011~7 .01086 (15) (II) (10) (30) (17) (17) P ................... .01435• .0 .00828• .01085• .0 .02284 (25) (0) (15) (19) (0) (41) Pb ................. .00193• .0 .00259 . 00331• .00403 .00404 (12) (0) (17) (21) (25) (25) & .................. .02466• .005~4 .01649• .00354• .01062 .00228 (39) (8) (26) (6) (17) (4) Se .................. .07265• .00377 .04240• .03246• .07610 .02470 (29) (I) (17) (13) (30) (10) Si 1 ••••••••••••••••• 6.109• .81605 4.8!4• 1.757• .45970 .78500 (41) (6) (33) (12) (3) (5) Sr .................. .03145• .0 .03374• .01302• .00596 .00462 (35) (0) (38) (15) (7) (5) Ti .................. .00210 .0 .01237• .00124 .00612 .00547 (8) (0) (45) (5) (22) (20) v ................... .02399• .00037 .01506• .011!3• .00566 .00598 (39) (<I) (24) (18) (9) (10) Y ................... .00202 .o .005!9• .00496• .00228 .00403 (II) (0) (28) (27) (12) (22) Yb ................. .00249• .0 .00435• .00374• .00186 .00248 (17) (0) (29) (25) (12) (17) Zn ................. .02374• .00374 .01304• .01329• .00520 .00042 (40) (6) (22) (22) (9) ( <.1) Zr .................. .00273 .00798 .01968• .01084• .00811 .00935 (5) (14) (34) (18) (14) (15) 

1

Variance components are arithmetic rather than logarithmic. 

the total variance within the Series as well as on the relative magnitudes of the variance between localities and between samples within localities. If the variance between 

localities is small enough to be ignored-as is the case 

for about one-third of the elements-then such elements 

could be described by sampling within any one randomly 

chosen locality in each Series. If the variance between 

localities is relatively large-as in the case of cobalt, manganese, nickel, or yttrium-then samples must be obtained 

from a number of localities within each Series. 

RELIABILITY OF SUBORDER MEANS COMPUTED FROM 

FIRST -STAGE DATA 

The previous section discussed in a general way _}he 

understanding to be gained about elemental variation 

from first-stage sampling. The components of variance 

can also be used to assess the reliability of any mean values 

that might be computed from the first-stage results, as 

well as to estimate the additional sampling necessary to 

insure a given reliability in such means. 

The following discussion will focus on the Suborders 

as the soil mapping unit of principal interest, rather than 

on lower taxonomic levels, for two reasons. First, the 

mapping units of Suborders cover a much larger area; 

hence, large areas can probably be described with a minimum sampling effort. Secondly, more reliable summary 

statistics for several elements may be calculated from the 

first-stage data because of the greater quantity of data per 

Suborder. 

The reliability of the estimate of a Suborder mean depends on the ratio of the variance between Suborders 

(ua2 from equation 2) to the total variance within Suborders (ug2+uy2+ u82+url+uE2). This is the variance ratio, V, 

used by Miesch (1976): 

Nv Sa2 

v Dv S,e2+S.y2+Sa2+Srl+SE2 (4) 

where the S2 terms are sample estimates of the respective 

population parameters, u2. The ratio, v, is a fundamental 

property of the soil and is dependent both on the inherent 

variation of the soil and on the analytical procedure used 

to estimate that variation. The larger v is, the smaller is 

the number, nr, of randomly selected specimens needed 

to make a reliable estimate of the mean of each Suborder . 

The terms v and nr are related to the F -statistic, as follows: 

F=l+nrv, (5) 

where nr is adjusted until F takes a value equal to or 

greater than the critical F-value for 1 and 2nr-2 degrees 

of freedom at a specified probability l~vel. Graphs from 

which nr may be read as a function of vat given probability levels are shown by Miesch (1976). 

After determining the value of nr, the error variance 

of the Suborder means, Er, may be calculated, as follows: 

s 2+.~-~+.~2+S 2+S 2 

Er= '/3 'I' ~l> YJ E • (6) 

nr 

This equation, which is based on a random sampling design, has the boundary condition that nr is the minimum 

number of samples required for distinguishing between 

two Suborder means, and, accordingly, Er becomes a 

maximum acceptable error variance. 

The observed error variance of the mean obtained from 

a nested design, E5 (s subscript denotes stratified), is calculated according to a rearranged version of the general 

equation of Cochran (1963, p. 268) as follows: 

sf32 Sy2 sa 2 

Es=(l-ff3)nf3 +(1-/(3/Y) n(3ny +(1-fpfyfa) nf3nYn8+ 

(7) S"72 Se2 

(l-fafyf8 17J) +(1-fafyf~ /"7/E) n n n n n fJ n(3 ny n8 n7] JJ o f3 y 8 7] E 
CHEMICAL VARIATION OF SOILS B9 

where the quantities in parentheses are finite population 

correction factors, and tp= ns!N/3, the sampling fraction 

at the Subgroup level, fy= ny!Ny, the sampling fraction 

at the Series level, and so forth. A correction factor is 

applied when more than 10 percent of the population is 

sampled (Cochran, 1963, p. 24). The values of 18, /"1, and 

/E in the present study are very small; therefore, these correction factors may be ignored and the final equation is 

as follows: 

Sp2 Sy2 Es=(l-fp~ + (1-fafy~ + f3 fJ '/3 y 

Sl +. $rf + SE2 (8) 

npnyn8 npnyn8 n.,., n

13 n1 n8 n.,.,n e 

The error variance, E1, represents a maximum acceptable value or "ceiling" under which the observed error 

variance, Es~ must fall, according to the inequality, as 

follows: 

Es S Er. (9) 

No further sampling is necessary if Es is equal to or less 

than E,. Otherwise, additional second-stage sampling 

is required; that is, then's in equation 8 must be increased 

so that the estimate of Es is decreased as required by expression 9. The several parameters discussed above, v, nr, 

Ey, andEs~ are shown in table 5 for each element. 

Assuming that the purpose of estimating means is to 

describe differences among Suborders, the first-stage data 

TABLE 5.-Comparison of the observed variance of the mean within 

Suborders with the maximum acceptable variance of the mean 

[v, observed variance ratio according to equation 4; n.,, required minimum number of 

randomly selected soil samples within each Suborder according to equation 5 for a 

95 percent probability level; Er. maximum acceptable value of the variance of the 

Suborder means according to equation 6; Es. observed vMiance of the mean within 

Suborders based on the first-stage data according to equation 8. Asterisk indicates that 

the inequality of expression 9 is fulfilled. Leaders ( ... ) indicate that no calculation 

could be made] 

Element v n, E, Es 

AI .......................... 0.79 6 0.00!177 0.00296• 

As .......................... .26 1!1 .0015!1 .00225 B ........................... 0 .00240 Ba ......................... .49 8 .00!165 .00!122• 

c ........................... .16 20 .00184 .00!161 Ca ......................... .44 9 .01!187 .01812 

Co ......................... .15 21 .00210 .0046!1 Cr .......................... .!15 10 .00268 .00!108 Cu ......................... .58 7 .0064!1 .006!12• 

F ........................... .46 8 .00768 .00649• 

Fe .......................... .26 I !I .00221 .00!152 Ga ......................... .70 6 .00676 .00447• 

Hg ........................ .07 40 .00244 .00414 KI .......................... .45 8 .02479 0276!1 La ......................... .22 15 .00219 .00!108 

Mg ........................ .57 7 .012!10 .0097ge 

Mn ........................ .08 !16 .00209 .00808 Na 1 •••••••••••••••••••••••• .!18 10 .00777 .0115!1 

Ni ......................... .17 19 .00292 .0057!1 P ........................... .!14 10 .00420 .0029!1• 

Pb ......................... .14 22 .00064 .OOIO!J 

& .......................... .64 7 .00547 .00507• Se .......................... .40 9 .01994 .01528• Sii ......................... .71 6 1.4!19 1.2168• 

Sr .......................... .55 7 .00819 .00709• Ti .......................... .08 !J6 .00066 .00254 v ........................... .6!1 7 .00546 .00402• Y ........................... .12 !18 .0004!1 .00152 Yb ......................... .20 16 .00078 .00121 Zn ......................... .67 6 .00595 .00470• 

Zr .......................... .05 55 .00102 .00709 

1Based on arithmetic data rather than logarithmic. 

are adequate to estimate Suborder means for 13 elements 

(as indicated by the asterisks in table 5). The value of n,. 

required to make adequate estimates for the remaining 

elements could be as high as 55 (for zirconium) per Suborder if all of the elements are to be described. However, 

such an element must necessarily be very important to 

warrant the excessive expense of sampling over and above 

the more modest requirements of the other elements. 

Therefore, in the interest of economy, it may be appropriate to limit n,1 to a more moderate value that would 

not so excessively oversample for most elements, and 

which would require sacrificing only a few possibly 

unimportant elements for which the sampling would be 

inadequate. The total sample loads for several values of ni 

in a random design including all of the 13 Suborders 

recognized in Missouri are as follows: 

Number of elements Total number 

'\- desCTibed of samples 

10 18 ISO 

15 20 195 

22 25 286 

37 26 481 

41 29 5S3 

55 so 715 

It is evident that a point of diminishing return occurs 

beyond n,. equal to about 22, for to add just one more 

element requires increasing n1 to 37-a considerable increase in cost for little additional information. 

Thus, as much as 44 percent of the variation of 25 elements in the soils of Missouri could be described by collecting 22 random samples from each of the 13 Suborders 

present in the State. 

SECOND-STAGE SAMPLE DESIGNS 

The development of an efficient second-stage sample 

design depends on a balance between field costs and the 

amount of information to be obtained. The principle cost 

factors to consider are ( 1) the analytical and sampling 

costs, which increase with the number of samples, (2) 

the travel time and distance between localities, and (3) 

the difficulty of fin4ing or identifying the mapping unit, 

especially if the area has never been mapped. These last 

two factors have major bearing on sampling costs. 

As a general principle, the larger the number of localities that have to be visited, the greater the cost for field 

work. The field costs within a nested design are less for 

an increase in the number of samples, n.,.,, than for an 

increase in the number of localities, na, because having 

once arrived at a site the cost of obtaining additional 

samples is small. Similarly, the cost of increasing n8 is 

less than that of increasing the number of Series, n1, because less time and travel are required for sampling a few 

small areas intensively than for collecting the same number of samples from more widely separated localities. 

Finally, on a per-unit basis, the costs of most types of 
BIO GEOCHEMICAL SURVEY OF MISSOURI 

chemical analysis are less than the field costs for the same 

samples. Thus, although a simple random-sample design 

always requires the smallest total number of samples, the 

increased amount of travel required results in a total cost 

greater than that for most nested designs. 

Equation 8 shows how the distribution of variance 

distribution of boron at the Suborder level. Rather, a map 

of Subgroups could be developed with provision for the 

large variance at both the Series level and analytical level. 

The first step is to calculate v using a modification of 

equation 4 as follows: 

components determines the levels at which second-stage Nv Sa2+S,e 2 0+.00226 

sampling should be carried out. As a first principle, a v Dv Sy2+Sa2+Sq2+Si .00764+0+.00539+.0ll04=.094 .(lO) 

larger number of samples should be collected at those A value of nr=32 is obtained from Miesch (1976, fig. 2) 

levels with large variance components, and a fewer corresponding to v. Then Er is calculated according to 

number at those levels with small variance components. a modification of equation 6: 

However, a second principle evident from equation 8 is 

that an increase in n/l is more effective in reducing Es than 

an increase of any of then's for levels within Subgroups. 

Similarly, an increase in ny is more effective than an 

increase of any of the n's for levels within Series. The 

procedure for adjusting n's to achieve a reduction in the 

estimate of the variance of the mean according to equation 

8 is just the opposite of the adjustment for minimizing 

field expenses. Therefore, the most efficient sample design 

requires a balance between information gained and cost. 

Some examples will illustrate how different distributions 

might be handled. 

If S(l is large compared to the remaining components 

within Suborders, then the Subgroup mapping units are 

considered to be homogeneous within themselves andrelatively distinct from each other. Equation 8 shows that 

an increase of nf3 will be the most effective means of reducing Es. Thus a nested design is appropriate, such as 

(nf3, ny, n

8, nTJ, nE)1 where nf3 has a large value, and ny, 

n

8, nTJ, and nE, are each equal to a small value, respectively. None of the elements in this study have such a distribution. 

If Si is much larger than the components within Series, 

then the Series mapping units are homogeneous within 

themselves and are distinct from one another. In this case, 

it would be inefficient to stratify the sampling by either 

Suborders or Subgroups unless the effect of the large variance at the Series level could be overcome. The elements 

boron, scandium, sodium, and titanium are examples of 

this case. 

The variance-component distribution of boron well 

illustrates how a second-stage sampling design is developed for a specific element because boron is a somewhat 

unusual case. The Suborder variance component is very 

small and the components at both the Series and analytical levels are large. 

Because the variance component at the Suborder level 

for boron is so small, it would be impractical to map the 

1

The notation describes a nested sampling design in which the value of n/3 is the 

number of Subgroups randomly selected within each Suborder, ny is the number of 

Series randomly selected within each Subgroup, n6

1 is the number of localities randomly 

selected within each Series, n 71 is the number of samples randomly selected within each 

locality, and ntis the number of independent analyses of each sample. 

(11) 

Substituting the appropriate n's in a revised version of 

equation 8, 

syz Sa 2 s,.,z Se 2 

E =(1-fy)-t-~-+ + '· (12) 

s ny nyn8 nyn8n7J nyn8 n7Jne 

minimizes Es to fulfill the inequality of 9. Thus, several 

nested sampling designs for mapping boron at the Subgroup level are as follows: 

Total number of Total number of. 

n"Yn6 n11nE Es analyses per localities per 

Subgroup Subgroup 

5 2 3 5 0.00069 150 10 

5 3 3 3 .00064 135 15 

5 2 3 3 .00074 90 10 

6 2 2 2 .00064 48 12 

In each case Es is less than the limit of Erequal to 0.00075, 

but some designs are more efficient than others. For example, the design 5, 3, 3, 3 results in an estimate of Es 

equal to 0.00064, based on a total of 135 analyses and travel 

to 15 (ny times na) localities within each Subgroup. The 

design 6, 2, 2, 2 gives the same estimate of E'S but specifies 

only 48 analyses and travel to 12 localities. Based on an 

average of five Subgroups per Suborder, the latter sample 

design indicates that the total number of samples needed 

to map the varying concentrations of boron between Subgroups is 1,560 (5 Subgroups times 13 Suborders times 

24 samples) collected from 780 localities and 3,120 analyses. We observed earlier that a sample design directed 

at the Subgroup level would be wasteful because of the 

very small variance at that level. Keeping this caution in 

mind, what is the consequence of sampling boron at the 

Subgroup level? We find that at this level we can expect 

to describe only about 9 percent of the total variation in 

boron (table 4). 

By a somewhat greater investment in sampling and 

analyses, about 38 percent of the variation in boron (table 

4) could be described by mapping concentrations at the 

Series level. Using a similar procedure with appropriate 

modifications of equations 10, 11, and 12 the value, v, for 

boron at the Series level equals 0.603, nr equals 7, and 

Er equals 0.00234. An efficient nested sampling design of 
CHEMICAL VARIATION OF SOILS Bll 

na, n'1, nf equal to 5, 2, 1 estimates Es as 0.00218. Collecting two samples at each of five localities within each 

of 275 Series within the State gives a total of 2, 750 samples 

and analyses. 

Several nested designs for second-stage sampling, which 

differ depending on the element, have been considered. 

It is impractical to have a separate sampling design for 

each element and it becomes necessary to select a single 

design which would serve best for the greatest number 

of elements. As noted previously, the point of diminishing 

returns occurs where n;equals 22; this sampling intensity 

will provide data adequate to describe 25 elements at the 

Suborder level. The elements carbon, cobalt, and lead require values of n(of 20, 21, and 22, respectively. Nested 

designs for second-stage sampling within Suborders for 

these elements are as follows (where the limiting values 

of Er for carbon, cobalt, and lead are 0.00184,0.00210, and 

0.00064, respectively): 

Element Total number Total number 

of analyses of localities 

per Subgroup per Subgroup 

C ................. : 5 1 3 2 0.00180 30 15 

3 3 4 1 .00174 36 36 

Co ................ 2 4 6 1 .00203 48 48 

3 3 4 1 .00202 36 36 

Pb ................ 2 4 4 1 .00060 32 32 

3 3 4 1 1 .00052 36 36 

The sample design 3, 3, 4, l, 1 is not necessarily the most 

efficient for any one of the three elements taken separately, 

but it is a design that would comfortably accommodate 

all of them without excessively oversampling any one. 

This design would also serve adequately for the remainder 

of the 25 elements, although the degree of oversampling 

will increase as the values of n 1 decrease for these elements. 

The total number of samples necessary to describe Suborders is 468 (36 times 13 Suborders). 

A sampling design for the case in which S y2 and S 8 2 are 

both large compared with all other components is illustrated by manganese. It is assumed that we wish to describe Suborders. Using equations 4, 6, and 8, the necessary 

calculations give values as follows: v equals 0.08, n1 equals 

37, E1 equals 0.00209. Several sampling designs are as 

follows: Total number of Total number of 

nf3 n,'Y nc5 n"' ne Es analyses per localities per 

Subgroup Subgroup 

1 7 10 1 0.00388 70 70 

1 7 20 l .00372 140 140 

1 7 30 1 .00342 210 210 

2 7 4 1 .00202 56 56 

3 4 3 2 .00199 72 36 

The variance component, S13 2, is equal to zero or is very 

small, and accordingly, in the first 3 designs, n/3 is set 

equal to one as a first approximation and ny is set equal 

to the maximum possible value of seven, which is the 

population size (see table 3 ). Although none of these first 

3 designs reduces Es sufficiently, they do illustrate the 

effect of increasing n8: namely, there is a large increase 

in the total number of analyses and localities but little 

reduction in Es. Alternatively, an increase in n13 from one 

to two has a dramatic effect on the overall efficiency by 

reducing Es to a value less than E1 using 75 percent fewer 

analyses. The efficiency is further improved by increasing 

'}3 to three and reducing travel requirements to 36localiues. Using the latter sample design, the distribution of 

manganese among Suborders could be described with 936 

(72 x 13) analyses of samples collected throughout the 

State from 468 (36xJ3) localities. However, only 8 percent 

of the total variation in manganese (table 4) would be 

accounted for. If a higher minimum percentage of 

variance is specified, say 40 percent, then more intensive 

sampling sufficient to the 275 Series is required. This 

could be done using a 5, 2, 1 nested design by collecting 

2,750 samples from 1,375 localities and analyzing each 

sample once. 

GEOCHEMICAL SUMMARIES 

Summary statistics based on the first-stage results are 

shown in table 6. The means are calculated using the 

maximum likelihood techniques of Cohen (1959, 1961) 

(compare with Miesch, 1967b) for those elements that are 

censored by the lower limit of determination. All of the 

means, except those for potassium, sodium, and silicon, 

are geometric. The variability- is measured by the geometric deviation, which is the antilogarithm of th~ standard deviation of the logarithms. The statistics for potassium, sodium, and silicon are expressed as the arithmetic 

mean and standard deviation. 

The elements are arranged in table 6 according to 

increasing value of the variance mean ratio, vm (Miesch, 

1976), as follows: 

s 2 Vm=_g_ 

Es 

where Es is computed for the data on hand. The value 

of vm serves as an index of the relative stability2 of the 

observed differences between the Suborder means. For 

small values of vm, the observed differences between the 

Suborder means are unstable. The estimate of the grand 

mean based on all of the data is a more reliable estimate 

for any given Suborder than is any individual estimate. 

As vm increases, the observed differences among the individual means tend to be ever more stable, and the superiority of the grand mean as an estimate of any Suborder 

mean diminishes. A value of Vim equal to 1.0 is approximately equivalent to the F-test criterion (equation 5) at 

the SO-percent probability level. 

The analysis of variance shows that, at least between 

the two extreme Suborder means, 23 of the 31 elements 

studied, including all of the elements in table 6 with vm 

equal to or greater than 1.8, exhibit significant differences 

2A stable estimate is one that tends to be reproducible even if new samples are collected and 

analyzed. 
Bl2 GEOCHEMICAL SURVEY OF MISSOURI 

TABLE 6.-Comparison of average compositions of Missouri soil Suborder samples 

[Values are in pans per million, except as noted in percent. Relative stability of estimates is given according to ascending order of vm. The first number is the geometric mean, 

except where arithmetic mean noted, arranged in ascending order across the row. The second number is the geometric deviation, except where standard deviation noted. Suborder name appears below. The underscore designates groups of Suborders which are indistinguishable according to Duncan's multiple range test (Duncan, 1955). Asterisk (•) 

indicates elements that are significant according to F-test in analysis of variance (Snedecor and Cochran, 1967, p. 265}] 

Element 

B .......................... . 

Zr ......................... . 

Mn ....................... . 

Ti ......................... . 

¥ .......................... . 

Co ........................ . 

Ni ........................ . 

CI ......................... . 

Hg ....................... . 

Pb• ...................... . 

Yb• ...................... . 

Fe• 1 •••••••••••••••••••••• 

As• ...................... . 

La• ...................... . 

Na•I 2 .................. . 

ea• ~ .................... . 

cr• ....................... . 

K· I 2 •••••••••••••••••••• 

cu• ...................... . 

P ......................... . 

Ba• ....................... . 

Sr• ....................... . 

Se• ....................... . 

Sc· ························ 

p• ! ...................... . 

31 ~1.62 

Oo..:hrept 

220~1.86 

Aquoll 

520 ~1.78 

Flu vent 

0.31~ 1.51 

Flu~ent 

18~1.61 

Ochrept 

6.9.; 1.98 

Udult 

10 ~1.88 

Udult 

.87;1.81 

Ochrept 

.039~2.14 

Flu vent 

15 ~ 1.45 

Udult 

2.0 ~1.51 

Och.rept 

1.6~1.54 

Ochrept 

4.9~1.54 

Ochrept 

34~1.65 

Udult 

.19±.094 

Udult 

.12 ;us 

Udult 

38~1.60 

Udult 

.89 ±·.48 

Udult 

9.4~1.61 

Udult 

100~2.47 

Udu1t 

430;1.53 

Udult 

52~1.69 

Udult 

.11~2.96 

Ochrept 

4.1 ;1.75 

Udult 

.019~1.63 

Udu1t 

32~1.48 

Udult 

250~1.72 

Udoll 

610~2.49 

Udult 

0.33~ 1.84 

Ochrept 

20~1.60 

Udult 

7.6;1.46 

Ochrept 

14~1.64 

Ochrept 

.95~ 1.53 

Flu~ent 

.040~1.60 

Ochrept 

17~1.20 

Flu~ent 

2.1~1.38 

Udult 

1.9~1.30 

Flu~ent 

6.2r1.22 

Aq~ept 

44~1.46 

Flu~ent 

.45 ± .22 

Udalf 

.23;2.20 

Udalf 

41~1.93 

Ochrept 

1.2 ± .48 

Ochrept 

11~1.87 

Ochrept 

130;2.36 

Ochrept 

630~1.50 

Udal£ 

100~1.78 

Udal£ 

.19~2.36 

F1u~ent 

4.7~2.27 

Ochrept 

.029~1.60 

Udal£ 

35~ 1.55 

Udal£ 

270;1.84 

Ochrept 

640~1.62 

Udoll 

0.33 ~ 1.45 

Udult 

24~1.23 

Fluvent 

8.0 ;1.44 

AI boll 

1.3; 1.63 

Udalf 

.042~1.84 

Udult 

18;1.27 

Ochrept 

2.5 ~ 1.34 

Flu vent 

2.1; 1.53 

Udult 

6.5~1.21 

Flu vent 

45~1.76 

Ochrept 

.47± .30 

Ochrept 

.27~2.08 

Ochrept 

46~1.59 

Flu vent 

1.2± .33 

Udal£ 

16~1.44 

Flu vent 

200~1.66 

Udal£ 

720;1.49 

Ochrept 

100;.1.84 

Ochrept 

.20~2.33 

Udu1t 

6.6~1.53 

F1u~ent 

.031~ 1.62 

Ochrept 

Suborder means and deviations 

37 ~ 1.37 

Fluvent 

290~1.53 

Udult 

670~1.77 

A! boll 

0.40~1.36 

Udal£ 

8.8 ~1.35 

Fluvent 

15~1.84 

Fluvent 

1.3~1.80 

Udult 

.048~1.29 

AI boll 

20~1.24 

Aquept 

2.6~1.27 

Udal£ 

2.1~1.28 

Aqualf 

6.9 ;us 

Udal£ 

46~1.44 

Udalf 

.54± .20 

Aquoll 

.34~1.41 

Aqualf 

61; 1.35 

Udal£ 

1.5 ± .55 

Flu vent 

16~1.65 

Udal£ 

230~ 1.73 

Flu vent 

720 ;1.65 

Flu vent 

120~2.26 

Flu~ent 

7.6~1.48 

Udal£ 

.032 ;us 

Aqualf 

40~1.39 

Aquept 

29Q~l.62 

Aq~ept 

6so;us 

Aquoll 

0.40~1.37 

Udoll 

26~1.22 

AI boll 

8.8~1.32 

Aquept 

17~1.59 

Aq~lf 

1.3~1.45 

Aquept 

.050~2.09 

Aq~alf 

20~1.24 

Udoll 

2.8~1.30 

Udoll 

2.2.~1.86 

Udal£ 

7.2~1.53 

Udult 

56;us 

AI boll 

.63 ± .23 

Aquept 

.39~3.20 

Fluvent 

61~1.24 

Aq~lf 

1.5± .30 

Aqualf 

17 ~1.36 

Aq~alf 

250~1.58 

Aq~alf 

870.~1.35 

Aq~alf 

150~1.33 

Aqualf 

.40~1.53 

Aqualf 

8.6~1.24 

Aq~alf 

.032~1.24 

A! boll 

41 ~ 1.33 

Aquoll 

300~1.35 

A! boll 

700~ 1.77 

Aquept 

0.41; 1.35 

Aquoll 

27~ 1.21 

Aq~oll 

10~1.54 

Udoll 

18~1.42 

A! boll 

1.3~1.41 

Aq~alf 

.050~1.32 

Udoll 

20~1.32 

Udal£ 

2.8~ 1.17 

Aquoll 

2.3;1.17 

A! boll 

7.7~1.25 

A! boll 

57;1.24 

Aqualf 

.68± .20 

Aqualf 

.45~ 1.17 

AI boll 

66~1.14 

A! boll 

1.6± .27 

Aquept 

20~1.23 

A! boll 

260~1.24 

Alboll 

970;1.36 

Aquoll 

170~1.48 

Aq~ept 

.40;2.05 

Aquept 

11 ~ 1.28 

A1boll 

.036~1.35 

Aquept 

41~1.33 

Udoll 

360~ 1.73 

Flu vent 

830~1.42 

Ochrept 

0.43 ~1.31 

Aquept 

27 ~1.20 

Aqualf 

22~1.34 

Aquept 

1.6~1.23 

AI boll 

.058~1.53 

Aquoll 

21~1.40 

AI boll 

2.9 ~ 1.15 

Aquept 

2.5 ~1.38 

Aq~ept 

7.7~1.47 

Aqualf 

58~1.28 

Ud'oll 

.73 ± .41 

Fluvent 

.49 ~ 1.97 

Aq~ept 

67;1.29 

Udoll 

1.6±1.60 

A1boll 

26;1.53 

Aquept 

300~1.66 

Aquept 

980~1.33 

Aquept 

180 ~1.15 

A1boll 

.49~1.47 

Ud'oll 

11 ~1.36 

Aq~ept 

.043~1.58 

F1uvent 

43 ~1.34 

Aqualf 

400;1.61 

Udal£ 

880~2.26 

Udal£ 

0.48 ~ 1.16 

AI boll 

27~1.29 

Udoll 

12~1.86 

Udal£ 

1.7~1.42 

Aquoll 

22~1.30 

Aquoll 

2.9~1.20 

Aq~alf 

3.0~1.32 

Udoll 

9.o;t.32 

Udoll 

58 ~1.19 

Aquept 

.76 ± .89 

Udoll 

.12;1.52 

Udoll 

71~1.27 

Aquept 

1.8± .29 

Udoll 

28;1.54 

Udoll 

400~1.44 

Udoll 

1100~1.32 

A! boll 

200;1.28 

Udoll 

.51~1.71 

Aq~oll 

12;1.32 

Udoll 

.046~1.45 

Udoll 

44~1.26 

A1boll 

480~1.49 

Aq~lf 

970~1.59 

Aqua!£ 

0.49 ~1.32 

Aqua If 

28 ~1.18 

Aquept 

12;J..!J2 

Aquoll 

29~1.44 

Aq~oll 

1.9~1.31 

Udoll 

.077~2.28 

Aq~ept 

23~1.31 

Aq~alf 

3.o;I.oo 

AI boll 

3.6~ 1.37 

Aq~oll 

9.5;1.26 

Aquoll 

60~1.24 

Aquoll 

.78± .12 

A! boll 

.77~2.05 

Aq~oll 

1.9± .46 

Aquoll 

38;1.69 

Aquoll 

450;1.65 

Aquoll 

1100;1.22 

Udoll 

220~1.28 

Aq~oll 

.55 ~1.18 

A1boll 

.047~1.25 

Aq~oll 

Grand mean 

and deviation 

38~1.45 

310~1.75 

710;1.95 

9.6~1.68 

18;1.80 

1.3~1.61 

052;2.02 

2.3~1.55 

51~1.59 

.59± .33 

.46;2.65 

59~1.55 

1.5 ± .54 

19~1.84 

260;2.50 

810~1.62 

140~1.99 

.33~3.13 

8.6~1.78 

.035;1.69 

0 

0.39 

.78 

.83 

1.33 

1.46 

1.66 

1.67 

1.70 

1.87 

2.06 

2.13 

2.32 

2.37 

2.55 

3.00 

3.09 

3.26 

4.10 

4.33 

4.43 

4.44 

4.75 

4.86 

4.90 
CHEMICAL VARIATION OF SOILS Bl3 

TABLE 6.-Comparison of average compositions of Missouri soil Suborder samples-Continued 

Grand mean 

Element Suborder means and deviations and deviation vm 

Si• I 2 .................... 33 ±3.92 34±2.29 36±2.98 36 ±1.33 38±3.12 38±1.56 39f2.52 40±3.62 42±2.64 37±3.83 5.02 

Aquoll Udoll Aquept Alboll Udal£ Aqua!£ Flu vent Ochrept Udult 

.. Mg• ...................... .12~2.10 .16~1.84 .22~1.50 .29~1.49 .35~2.71 .37~1.41 .46;1.90 .58~1.70 .63~ 1.89 .33~1.31 5.05 

Udult Ochrept Udal£ Aqualf Fluvent Alboll Aquept Udoll Aq~ll 

Zn• ........................ 24~1.51 30~1.65 41~1.79 49;1.45 51~1.47 56~l.l5 64~1.36 69;1.46 90~1.46 51;1.75 5.05 

Udult Ochrept Udal£ Aqualf F1u~ent A! boll Aquept Udoll Aq~oll 

v• ......................... 45~1.55 49~1.90 53~1.72 61~1.51 75~1.31 89~1.27 93~1.50 uo;1.44 140;1.56 76;1.78 5.97 

Udult Ochrept Flu vent Udal£ Aq;.alf AI boll Aquept Udoll Aquoll 

AJ• '······················ 2.2~1.56 3.0~1.56 3.8~1.54 3.8~ 1.37 4.3~1.21 5.0~1.08 5.3~1.32 5.9~1.20 6.4~1.39 4.3;1.59 6.06 

Udult Ochrept Flu vent Udal£ Aqualf A1boll Aq~ept Udoll Aq~oll 

Ga• ....................... 5.6~1.76 8.4~1.90 9.0h67 10~1.54 13~1.25 15~1.09 15~1.49 17~1.24 21!1.54 12;1.83 6.33 

Udult F1u~ent Ocfu.ept Udal£ Aq;.alf 

1Values given in percent. 

2Arithmetic mean and standard deviation given. 

at the 0.05 probability level. The first-stage sample data 

are judged, by the criterion of expression 9, to be adequate 

for describing the differences between Suborder means for 

13 elements. (See table 5.) These are the same 13 elements 

that appear in table 6 with Vm equal to or greater than 

4.0. The considerable overlap between the groups for 

most of the elements suggests that the only individual 

Suborders that can be demonstrated to be significantly 

different are those at the opposite ends of the range. For 

elements such as boron and zirconium none of the means 

are significantly different, and, accordingly, the Duncan 

test shows that the Suborders are essentially the same with 

respect to these elements. 

The grand mean concentrations of most trace elements 

in soils, as reported in table 6, are about equal to or 

slightly higher than the means reported by Shacklette and 

others (1971) for U.S. soils located east of the 97th meridian. In Missouri soils the mean concentrations of major 

elements such as aluminum, calcium, iron, magnesium, 

phosphorus, potassium, sodium, and titanium are 1.25 

to 2 times higher than in the soils of the eastern United 

States. This may be due in part to the fact that Missouri 

is covered to a large extent by loess and glacial material, 

which tend to be relatively more enriched in a number 

of elements than are the more highly weathered parent 

materials of the southeastern United States. The grand 

means in table 6 are nearly equal to corresponding means 

based on 1,140 soil samples collected extensively throughout Missouri in a later study (U.S. Geol. Survey, 1972e, p. 

41-55; 1972f, p. 19-57; 1973, p. 16-25). 

DISCUSSION 

The soil classification scheme is a useful tool for reducing a great complexity of information about soils 

down to several more manageable levels of generalization 

(Smith, 1963, p. 7). The classification scheme emphasizes 

Alboll Aquept Udoll Aq;.oll 

relationships between the soils and their environmental 

settings. The taxa are defined, especially at the higher 

levels, so as to group soils of similar genesis (Smith, 1963, 

p. 8); however, the criteria used for definition are not the 

factors of soil formation (climate, topography, parent 

material, and organisms, each operating through time) 

(Jenny, 1941) that prevail, but rather the soil characteristics that result from any combination or intensity of these 

formational factors. Thus, chemical composition of the 

soil is a characteristic that could be reflected in the taxa, 

although currently it is not. Moreover, translation of 

knowledge of the geographic distribution of soils onto 

maps is a practical necessity for both the sampler and 

those who will interpret the sampling results for environmental studies. The geographic distribution of soils 

serves as a bridge between our knowledge about the chemical composition of soils and the physical environment 

of the Missouri landscape. Unfortunately, coverage of the 

State by detailed mapping according to modern concepts 

is incomplete. 

Although we would hope that a relatively large part 

of the total variance would occur at the higher taxonomic 

levels so that the soils could be more easily sampled and 

described, the results show that the largest part of the 

variation occurs at the lower levels. This is perhaps not 

so surprising if we consider first that the variance is related to distance between sampling localities, in that 

samples dose together tend to ·be more similar than those 

farther apart. The soil Series as a mapping unit has a 

minimum area of five acres; thus the distance between 

Series mapping units is more than that between localities within a Series but less than the distance between more 

regional mapping units such as Suborders. A second consideration is that, inasmuch as the taxa at the higher levels 

of the classification system are defined by their most 

general properties and the taxa at successively lower levels 
Bl4 GEOCHEMICAL SURVEY OF MISSOURI 

are defined by ever more detailed properties, quite a diversity of Series may be permitted within a Suborder. The 

variance component, Si, , is characteristically large, and 

sampling only a few of the Series at random within each 

Suborder (as is implied by concentrating the sampling 

at the Suborder level) may fail to describe the Suborder 

adequately. Thus, while a sample of the higher taxa improves the level of generalization, it may describe only 

a small percentage of the total mappable variance. 

The alternative is to sample at the Series level, which 

means that every Series would have to be sampled. The 

results show that up to about 85 percent of the variance 

for some elements can be described by sampling all of the 

soil Series. However, Smith (1963, p. 7) observed that the 

broad view of soils (for example, on a Statewide scale) 

cannot be grasped at the Series level because there are too 

many categories. If Series were used to map the distribution of elements in the soils of a large region, the very 

number of detailed mapping units could overwhelm any 

reasonable effort to define general principles; but a more 

immediate drawback is that the sampling effort required 

is quite impractical. 

What is the consequence of describing only a small part 

of the total variance? It provides only a lim~ted ability 

to understand or to predict what mechanisms or factors 

are controlling the distribution of elements in the Suborders. In other words, the mechanisms that control the 

"marker" properties of the Suborders are apparently only 

distantly related to the mechanisms that control the distribution of elements. The only remedy to this situation is 

to search for alternative classifications based on a small 

number of chemically distinct classes. 

Twenty-three elements show significant differences between Suborder means (table 6). With the exception of 

silicon, the highest concentrations of these elements are 

generally found in the Suborders of the Mollisols (Alboll, 

Aquoll, and Udall). The Mollisols have developed in the 

temperate climatic conditions of the central Great Plains, 

have thick, nearly black surface horizons, and are high 

in exchangeable bases, such as calcium, magnesium, 

potassium, and sodium. The Aquolls in particular have 

the highest concentrations of all Suborders. These are the 

seasonally wet members of the Mollisols that typically 

occur on alluvium in the Missouri River valley (U.S. 

Geological Survey, 1970, p. 86). 

Conversely, the Udults(aSuborderofthe Ultisols), with 

the Ochrepts (a Suborder of the Inceptisols), and the 

Fluvents (a Suborder of the Entisols), generally contain 

the lowest concentrations of these elements. The Udults 

are older soils than the Aquolls, with more intensely weathered profiles, and probably developed under a warmer, 

more humid climate. The Udults of Missouri are a northern extent of the Ultisols, which cover most of the southeastern United States. The Ultisols are depleted in bases 

and organic matter, have a thick accumulation of clay 

with a minimum of weatherable minerals, and are developed on sedimentary parent materials of Pleistocene 

or Holocene age. Most of the soils having low elemental 

concentrations tend to be more base-rich-implying less 

leaching-than the Udults; although in the case of the 

Ochrepts, considerable variation in base saturation is permitted by the definition. The amount of organic matter 

in the Ochrepts and Fluvents also is higher than in the 

Udults, but as a whole these soils contain considerably 

less organic matter than the Mollisols. 

CONCLUSIONS 

Examination using analysis-of-variance techniques of 

the geochemical properties of the soils classified by the 

Soil Taxonomy of the National Cooperative Soil Survey 

suggests the following. 

1. Although significant differences are found between 

the Suborders for many of the elements examined, these 

differences account for only a limited percentage of the 

total variation in elemental abundances among the soils 

of the State. The differences for 13 of the elements are 

adequately described by the results of the first-stage 

sampling; the differences for 9 additional elements could 

be described by implementation of the recommended 

second-stage sampling. Such multistage sampling is 

necessary because the list of taxonomic criteria by which 

the Suborders are defined does not include chemical composition. 

2. Geochemical differences between soil Groups and 

Subgroups within the same Suborder are negligibly small 

for most elements studied. 

3. A large percentage of the total variation in the soils 

of the State could be described by sampling each soil 

Series, but the number of Series in the State and the chemical variation within each Series would result in a very 

large sampling and analytical load. 

4. Geographic variation within soil Series is, on the 

average, about half of that observed between Series. 

5. The estimates of the grand mean for each of the elements do not differ significantly from estimates based on 

a much more extensive sample of Missouri soils. 

6. The concentrations of numerous elements are two 

or more times greater in Suborders of the Mollisols than 

in Suborders of the Ultisols. 

7. An alternate classification scheme based on a small 

number of chemically distinct classes would be helpful 

in minimizing the second-stage sampling required to 

produce geochemical maps. 

REFERENCES CITED 

Anderson, R. L., 1965, Negative variance estimates-Answer to query 

9: Technometrics, v. 7, no. 1, p. 75-76. 

Anderson, R. L., and Bancroft, T. A., 1952, Statistical theory in research: New York, McGraw-Hill, 399 p. 

Bartel, A. J., and Millard, H. T., Jr., 1976, Analysis of rocks and soils 

for iodine by radio-isctope dilution-neutron activation, in Miesch, 
CHEMICAL VARIATION OF SOILS Bl5 

A. T., Geochemical survey of Missouri-Methods of sampling, 

laboratory analysis, and statistical reduction of data: U.S. Geol. 

Survey Prof. Paper 954-A, p. Al5-Al7. 

Beckett, P. H. T., and Webster, R., 1971, Soil variability-A review: 

Soils and Fertilizers, v. 34, no. l, p. l-15. 

Bennett, C. A., and Franklin, N. L., 1954, Statistical analysis in chemistry and the chemical industry: New York, John Wiley, 724 p. 

Brown, B. L., 1968, Soil survey of Worth County, Missouri: U.S. Soil 

C'.onserv. Service Soil Survey [Rept.], 50 p. 

___ 1971, Soil survey of Pemiscot County, Missouri: U.S. Soil 

Conserv. Service Soil Survey [Rept.], 99 p. 

Cline, M. G., 1963, Logic of the new system of soil classification: 

Soil Science, v. 96, no. l, p. 17-22. 

Cochran, W. G., 1963, Sampling techniques [2d ed.]: New York, John 

Wiley, 413 p. 

Cohen, A. C., Jr., 1959, Simplified estimators for the normal distribution when samples are singly censored or truncated: Technometrics, v. l, no. 3, p. 217-237. 

___ 1961, Tables for maximum likelihood estimates-Singly truncated and singly censored samples: Technometrics, v. 3, no. 4, 

p. 535-541. 

Connor, J. J., Feder, G. L., Erdman, J. A., and Tidball, R. R., 1972, 

Environmental geochemistry in Missouri-A multidisciplinary 

study: lnternat. Geol. Cong., 24th, Montreal 1972, Symposium 

1-Earth sciences and the quality of life, p. 7-14. 

Duncan, D. B., 1955, Multiple range and multiple F tests: Biometrics, 

v. 11, no. l, p. l-42. 

Gilbert, F. L., 1971, Soil survey of Dent County, Missouri: U.S. Soil 

Conserv. Service Soil Survey (Rept.], 141 p. 

Grogger, H. E., 1964, Soil survey of Daviess County, Missouri: U.S. 

Soil Conserv. Service Soil Survey [Rept.], ser. 1959, no. 34, 39 p. 

Huffman, Claude, Jr., and Dinnin, J. 1., 1976, Analysis of rocks and 

soils by atomic absorption and other methods, in Miesch, A. T., 

Geochemical survey of Missouri-Methods of sampling, laboratory analysis, and statistical reduction of data: U.S. Geol. Survey 

Prof. Paper 954-A, p. Al2-Al4. 

Hughes, H. E., 1974, Soil survey of Barton County, Missouri: U.S. 

Soil Conserv. Service Soil Survey (Rept.], 76 p. 

Jeffrey, A. H., 1974, Soil survey of Caldwell County, Missouri: U.S. 

Soil Conserv. Service Soil Survey [Rept.], 56 p. 

___ 1975, Soil survey of Lafayette County, Missouri: U.S. Soil 

Conserv. Service Soil Survey [Rept.], 67 p. 

Jenny, Hans, 1941, Factors of soil formation, a system of quantitative 

pedology: New York, McGraw-Hill, 281 p. 

Krumbein, W. C., 1960, The "geological population" as a framework 

for analyzing numerical data in geology: Liverpool and Manchester Geol. Jour., v. 2, pt. 3, p. 341-368. 

Krumbein, W. C., and Slack, H. A., 1956, Statistical analysis of lowlevel radioactivity of Pennsylvanian black fissile shale in Illinois: 

Geol. Soc. America Bull., v. 67, p. 739-761. 

Krusekopf, H. H., 1966, Delta soils of southeast Missouri: Missouri 

Univ. Agr. Expt. Sta. Bull. 854, 38 p. 

Krusekopf, H. H., and Scrivner, C. L., 1962, Soil !Iurvey of Boone 

County, Missouri: U.S. Soil Conserv. Service Soil Survey [Rept.], 

ser. 1951, no. 12, 39 p. 

Leone, F. C., and Nelson, L. S., 1966, Sampling distributions of variance components-[Pt.] I, Empirical studies of balanced nested 

designs: Technometrics, v. 8, no. 3, p. 457-468. 

McKenzie, R. M., 1955, Sampling variations in the concentrations of 

elements in soils: Australian Jour. Agr. Research, v. 6, p. 699-706. 

Miesch, A. T., 1967a, Theory of error in geochemical data: U.S. Geol. 

Survey Prof. Paper 574-A, 17 p. 

___ l967b, Methods of computation for estimating geochemical 

abundance: U.S. Geol. Survey Prof. Paper 574-B, 15 p. 

___ 1976, Geochemical survey of Missouri-Methods of sampling, 

laboratory analysis, and statistical reduction of data, with sections 

on Laboratory methods, by Barnett, P. R., Bartel, A. J., Dinnin, 

]. 1., Feder, G. L., Harms, T. F., Huffman, Claude, Jr., Janzer, 

V. J., Millard, H. T., Jr., Neiman, H. G., Skougstad, M. W., and 

Wahlberg,]. S.: U.S. Geol. Survey Prof. Paper 954-A, 39 p. 

Missouri University Agricultural Experiment Station, 1931, Reconnaisance survey soil map of Missouri: Columbia, University of 

Missouri, l sheet. 

Neiman, H. G., 1976, Analysis of rocks, soils, and plant ashes by 

emission spectroscopy, in Miesch, A. T., Geochemical survey of 

Missouri-Methods of sampling, laboratory analysis, and statistical reduction of data: U.S. Geol. Survey Prof. Paper 954-'-A, p. 

Al4-Al5. 

Neider, J. A., 1954, The interpretation of negative components of 

variance: Biometrika, v. 41, p. 544-548. 

Oertel, A. C., 1959, Estimation of the trace-element status of large 

areas of soil: Australian Jour. Agr. Research, v. 10, p. 58-70. 

Olson, J. S., and Potter, P. E., 1954, Statistical methods, (Pt. l] of 

Variance components of cross-bedding direction in some basal 

Pennsylvanian sandstones of the eastern interior basin: Jour. 

Geology, v. 62, p. 26-49. 

Petersen, R. G., and Calvin, L. D., 1965, Sampling, in Black, C. A., 

Evans, D. D., Ensminger, L. E., White, J. S., and Clark, F. E., 

eds., Methods of soil analysis-Pt. I, Physical and mineralogical 

properties including statistics of measurement and sampling: 

Am. Soc. Agronomy, Agronomy Mon. 9, p. 54-72. 

Potter, P. E., and Olson, J. S., 1954, Geological application, (Pt. 2] 

of Variance components of cross-bedding direction in some basal 

Pennsylvanian sandstones of the eastern interior basin: Jour. 

Geology, v. 62, p. 50-73. 

Riecken, F. F., and Smith, G. D., 1949, Lower categories of soil classification-Family, series, type, and phase: Soil Science, v. 67, p. 

107-115. 

Rourke, J. D., Shrader, W. D., and Atkinson, C. H., 1956, Soil survey 

of Livingston County, Missouri: U.S. Soil Conserv. Sel'Vice Soil 

Survey (Rept.], ser. 1950, no. I, 54 p. 

Scrivner, C. L., 1961, Soils of Howard County, Missouri: Missouri 

Univ. Agr. Expt. Sta. Bull. 749, 20 p. 

Scrivner, C. L., and Baker, J. C., 1961, Soils of Blackwater and Lamine 

Townships, Cooper County, Missouri: Missouri Univ. Agr. Expt. 

Sta. Bull. 772, 20 p. 

Scrivner, C. L., Baker, J. C., and Miller, B. J., 1966, Soils of MissouriA guide to their identification and interpretation: Missouri Univ. 

Extension Div. Circ. 823, 48 p. 

Scrivner, C. L., and Frieze, J. A., 1953, Soils of Taney County, Missouri: 

Missouri Univ. Agr. Expt. Sta. Prog. Rept. 24, 6 p. 

___ 1964, Soil survey of Moniteau County, Missouri: U.S. Soil 

Conserv. Service Soil Survey [Rept.], ser. 1953, no. 11, 42 p. 

Shacklette, H. T., Hamilton, J. C., Boerngen, J. G., and Bowles, J. 

M., 1971, Elemental composition of surficial materials in the conterminous United States: U.S. Geol. Survey Prof. Paper 574-D, 

71 p. 

Shrader, W. D., and Krusekopf, H. H., 1956, Soil survey of St. Charles 

County, Missouri: U.S. Soil Conserv. Service Soil Survey [Rept.], 

ser. 1939, no. 28, 49 p. 

Shrader, W. D., Springer, M. E., and Hall, N. S., 1953, Soil survey 

of Holt County, Missouri: U.S. Soil Conserv. Service Soil Survey 

(Rept.], ser. 1939, no. 21, 61 p. 

Shrader, W. D., Springer, M. E., Hall, N. S., DeYoung, William, and 

Jordan, H. V., 1945, Soil survey (reconnaissance) of Linn County, 

Missouri: U.S. Bur. Plant Industry Soils, and Agr. Eng. (Soil 

Conserv. Service] Soil Survey [Rept.], ser. 1938, no. 7, 28 p. 

Shrader, W. D., Springer, M. E., Hamby, Robert, Pettijohn, W. J., 

and Miller, J. T., 1954, Soil survey of Jasper County, Missouri: 
Bl6 GEOCHEMICAL SURVEY OF MISSOURI 

U.S. Soil Conserv. Service Soil Survey [Rept.], ser. 1942, no. 5, 

67 p. 

Smith, G. D., 1963, Objectives and basic assumptions of the new soil 

classification system; Soil Science, v. 96, no. 1, p. 6-16. 

Snedecor, G. W., and Cochran, W. G., 1967, Statistical methods [6th 

ed.]: Ames, Iowa State Univ. Press, 593 p. 

Thompson, W. A., Jr., 1962, The problem of negative estimates of 

variance components: Annals of Math. Statistics, v. 33, p. 273-289. 

Thompson, W. A., Jr., and Moore, J. R., 1963, Non-negative estimates 

of variance components: Technomeuics, v. 5, no. 4, p. 441-449. 

Thorp, James, and Smith, G. D., 1949, Higher categories of soil 

classification-Order, suborder, and great soil groups: Soil Science, 

v. 67, p. 117-126. 

Tidball, R. R., 1971, Geochemical variation in Missouri soils, in 

Hemphill, D. D., ed., Trace substances in environmental healthIV [4th Ann. Con£. Proc.]: Columbia, Missouri Univ., p. 15-25. 

U.S. Department of Agriculture, 1938, Soils and men: U.S. Dept. 

Agriculture, Yearbook of Agriculture 1938, 1232 p. 

U.S. Geological Survey, 1970, National Atlas of the United States of 

America: Washington, D. C., 417 p. 

---l972a, Geochemical survey of Missouri-Plans and progress for 

first six-month period (July-December, 1969): U.S. Geol. Survey 

Open-file Rept., 49 p. 

---l972b, Geochemical survey of Missouri-Plans and progress for 

second six-month period (January-June, 1970): U.S. Geol. Survey 

Open-file Rept., 60 p. 

---1972c, Geochemical survey of Missouri-Plans and progress for 

third six-month period (July-December, 1970): U.S. Geol. Survey 

Open-file Rept., 33 p. 

--1972d, Geochemical survey of Missouri-Plans and progress for 

fourth six-month period (January-June, 1971): U.S. Geol. Survey 

Open-file Rept., 63 p. 

___ l972e, Geochemical survey of Missouri-Plans and progress for 

fifth six-month period (July-December, 1971): U.S. Geol. Survey 

Open-file Rept., 145 p. 

___ l972f, Geochemical survey of Missouri-Plans and progress for 

sixth six-month period (January"-June, 1972): U.S. Geol. Survey 

Open-file Rept., 86 p. 

___ 1973, Geochemical survey of Missouri-Plans and progress for 

seventh six-month period (July-December, 1972): U.S. Geol. Survey Open-file Rept., 59 p. 

U.S. Soil Conservation Service, 1968, List of published soil surveys: 

Washington, D.C., U.S. Govt. Printing Office, 47 p. 

U.S. Soil Conservation Service, Soil Survey Staff, 1960, Soil classification, a comprehensive system (7th Approximation): Washington, 

U.S. Govt. Printing Office, 265 p. 

___ 1967, Supplement to soil classification system (7th approximation): Washington, U.S. Govt. Printing Office, 207 p. 

___ 1968, Supplement to soil classification system (7th approximation), histosols: Washington, U.S. Govt. Printing Office, 22 p. 

___5oil taxonomy of the National Cooperative Soil Survey: 

Washington, U.S. Govt. Printing Office, (in press). 

Vazhenin, I. G., Muzychkin, Ye. T., Prokhorova, Z. A., and Aleshina, 

T. N., 1961, Method of compiling large-scale soil agricultural 

chemical maps for fertilizer application: Soviet Soil Science 1961, 

no. 4, p. 363-374. 

Wahlberg, J. S., 1976, Analysis of rocks and soils by X-ray fluorescence, in Miesch, A. T., Geochemical survey of MissouriMethods of sampling, laboratory analysis, and statistical reduction 

of data: U.S. Geol. Survey Prof. Paper 954-A. p. A11-Al2. 

Wilding, L. P., Jones, R. B., and Schafer, G. M., 1965, Variation of 

soil morphological properties within Miami, Celina, and Crosby 

mapping units in west-cenual Ohio: Soil Sci. Soc. America Proc., 

v. 29, p. 711-717. 

~U.S. GOVERNMENT PRINTING OFFICE: 1976-677-340/69