ANALYSIS OF SOLID WASTE COMPOSITION
Statistical Technique to Determine
Sample Size
SW-19ts
Dennis E. Carruth and Albert J. Klee
U.S.. DEPARTMENT OF HEALTH, EDUCATION, AND WELFARE
Public Health Service
Consumer Protection and Environmental Health Service
Environmental Control Administration
Bureau of Solid Waste Management
1969
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Single copies of this publication will be distributed as supplies
permit. Request from the Bureau of Solid Waste Management, Envi-
ronmental Control Administration, 5555 Ridge Avenue, Cincinnati,
Ohio J»5213.
-------
ABSTRACT
This work analyzes data obtained after separating and weighing
solid waste and presents a statistical technique to determine the
minimum weight and number of samples needed to realistically and
reliably estimate the characteristics of a given quantity of solid
waste. Samples of solid waste of varying weights were taken and
separated into nine components; each component was weighed, and the
data were then statistically evaluated. It was determined that there
is no significant variance among sample weight groups. The study
recommends that 12, relatively small (200-lb) samples will validly
reflect the composition of a given supply of solid waste. (Author)
-------
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CONTENTS
PAGE
INTRODUCTION 1
Solid Waste Composition Criteria 2
Sample Criteria 4
DISCUSSION 7
Incineration Studies 7
Solid Waste Composition Classification 8
Method of Taking Samples 9
Effect of Sample Weight on Precision JQ
Statistical Technique to Determine Sample Size 17
Example 18
SUMMARY AND CONCLUSIONS 23
REFERENCES 25
TABLES
1 Weight, In Pounds, of Components Per Sample
and Per Weight Group 11
2 Percentage (by weight) of Components Per Sample
and Per Weight Group 13
3 Critical Statistics Obtained from Table 2 15
k Coefficients of Variation 16
5 Arcsin Transformation ig
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ANALYSIS OF SOLID WASTE COMPOSITION
Statistical Technique to Determine Sample Size
Dennis E. Carruth and Albert J. Klee*
INTRODUCTION
Whenever attempts are made to advance the frontiers of knowledge
and to acquire additional understanding of a phenomenon, operation,
or system, hypotheses must be formulated and tested. Certainly, the
data gathered in the course of such studies must contribute to estab-
lished objectives. Such a process of basic and applied research
(reporting -> description -> explanation)1 is universal to all creative
disciplines and research endeavors.
The Bureau of Solid Waste Management is not unique in this
respect nor is it a stranger to scientific research in attempting to
broaden the existing horizons of knowledge in solid waste management.
One objective is for Federal, State, county, and municipal governments,
industry, and other interested and concerned institutions and indivi-
duals to obtain increased knowledge and better understanding of solid
waste pract ices.
*Mr. Carruth is Staff Engineer, Division of Research and Development,
and Mr. Klee is Chief, Operational Analysis Branch, Division of Technical
Operations of the Bureau of Solid Waste Management, Environmental Control
Administration, Consumer Protection and Environmental Health Service,
Public Health Service, U.S. Department of Health, Education, and Wel-
fare.
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Solid waste is defined by the Solid Waste Disposal Act of 1965
as:
. . .garbage, refuse, and other discarded solid materials,
including solid waste materials resulting from indus-
trial, commercial, and agricultural operations, and from
community activities, but does not include solids or
dissolved material in domestic sewage or other signif-
icant pollutants in water resources, such as silt, dis-
solved or suspended solids in industrial waste water
effluents, dissolved materials in irrigation return flows
or other common water pollutants.2
To broaden the base of understanding in solid waste management,
the Bureau's Division of Technical Operations is charged with the re-
sponsibility to provide technical assistance, to develop basic technical
information on solid wastes and solid waste management practices, to
manage the State planning grant program, and to apply management
science to problems of solid waste handling and disposal. The commonly
recognized methods of disposal, which can prove satisfactory, include
sanitary landfilling, incinerating, and composting, as well as sal-
vage and reuse operations.
Solid Waste Composition Criteria
Through legislative action and increased public awareness, con-
siderable interest and activity have recently developed in the solid
waste field. Solid waste research, however, is primarily speculative
in nature and is currently more concerned with gathering data and
establishing hypotheses than with formulating broad generalizations
or conclusions.
-------
An important phase in data collection and survey design is
quantifying and qualifying solid waste materials generated from a
multitude of sources, including residential, commercial, industrial,
and institutional origins. Yet, our knowledge of the physical and
chemical composition of solid waste has remained undeveloped. Solid
waste is not only complex in its composition, but also extremely
variable because of such factors as geographical location, season
of the year, social and economic conditions, and methods and fre-
quency of collection.
For example, to design and operate a municipal incinerator and
to evaluate its efficiency in processing solid waste, the Btu (heat)
content of the fuel, i.e., solid waste, must be determined. Sanitary
landfill, as a disposal method, requires a knowledge of solid waste
composition to determine compaction properties, problems of leachates,
gaseous emissions, and so forth. Composting requires the separation
of glass, metals, rocks, and other nondegradable items from the
otherwise compostible material.
To learn more about the nature of solid waste, a reliable and
standard sampling procedure must be developed so that meaningful
samples of solid waste can be obtained for analysis and study. Studies
at Purdue University determined that analyzing a quarter-truckload
of solid waste produced satisfactory data.3 From this, the concept
of quartering a given supply of solid waste before appropriate anal-
ysis and separation was developed. Further, a statistical analysis
-------
gave the approximate number of sample households, in a homogeneous
area of a community, needed to estimate such quantities as pounds
per capita per day, pounds per household per day, cubic feet per
capita per day, and bulk density. When solid wastes generated from
a multitude of sources are analyzed, however, these concepts do
not seem to apply.
Sample Cr i teria
The preceding discussion indicates the need for quantifying
and classifying solid waste materials. It is, of course, practically
impossible and physically undesirable to separate, measure, weigh,
and analyze all of the solid waste deposited at a particular facility.
Therefore, should all the solid waste in a storage pit of an Incin-
erator be separated and analyzed, or what portion thereof? In de-
termining the physical composition of a truckload of solid waste,
should the entire truckload be sampled, or rather a smaller fraction?
What weight sample yields reasonable results and how many such sam-
ples are needed? Obtaining answers to these and similar questions
is troublesome, yet important.
Samples must be taken in sufficient weight and number to realis-
tically and reliably estimate the characteristics of a given quantity
of sol id waste.
In the planning of a sample survey, a stage is always
reached at which a decision must be made about the size
of the sample. The decision is important. Too large a
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sample implies a waste of resources, and too small a
sample diminishes the utility of the results. The de-
cision cannot always be made satisfactorily, for often
we do not possess enough information to be sure that
our choice of sample size is the best one.1*
Previous studies have not fully treated the problem of obtaining
adequate samples of solid waste for analysis, nor have practices been
developed to the extent of producing statistically comparable data.
The variable composition of solid waste from a given source should
be definable, however, and the following discussion, though specific
in scope, should offer a general technique by which to analyze solid
waste composition.
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DISCUSSION
Incineration Studies
These studies, which are projects of considerable depth and
scope, are undertaken by the Bureau's Division of Technical Operations
upon request of appropriate State, local, and private concerns. Data
are provided for comparative and operational purposes and, hopefully,
for future recommendations.
The study utilizes a systems approach whereby the total process
of incineration is observed, tested, and evaluated. Collection trucks
and vehicles are weighed to provide true weights of the quantity of
solid waste handled by the incinerator. Samples of solid waste mate-
rial from the storage pit are taken, separated, and weighed to provide
data on Btu content and composition of the input. Study of the in-
cineration process also yields information on mechanical function,
burning rate, burning temperature, pollution control systems, feed
flow, normal and unique situations and conditions, and operating
and control procedures. Samples of residue, gaseous and particulate
emissions, and liquid effluents are taken to quantify and qualify
the output of the systems and to ascertain the efficiency of the in-
cineration process. Physical plant and disposal facilities, as well
as economic and administrative support facilities, are also studied
and evaluated.
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Solid Waste Composition Classification
Determining the physical and quantitative composition of the
inputsolid wasteis a necessary step in studying the acceptability
of incineration as a disposal method. The composition of the solid
waste directly influences the Btu content of the waste, and deter-
mining the Btu content is necessary to evaluate the heat and com-
bustion properties of this feed material.
After accounts of firsthand experiences and available literature
were analyzed and reviewed, solid wastes were classified into nine
categories. Each category is composed of materials similar in compo-
sition and Btu content; each category permits relatively direct com-
parisons with existing data; and each category is composed of materials
that can be effectively separated, when the human element and repro-
ducible methodology are considered.
The standard classification, based on nine mutually exclusive
components, is (1) food waste; (2) garden waste; (3) paper products;
(k) plastic, rubber, and leather; (5) textiles; (6) wood; (7) metals;
(8) glass and ceramics; (9) ash, rocks, and dirt (inerts).
The classification is adaptable to analyze waste received at any
disposal facility, although there are several significant differences
among various methods of solid waste handling (e.g., whether or not
"bulky" wastes, such as discarded refrigerators, are accepted).
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Method of Taking Samples
For 4 consecutive days, the study surveyed and collected data
from an incineration facility that primarily handled residential and
commercial solid wastes. A more thorough and complete study might
conceivably evaluate the composition of solid waste based upon
daily, weekly, monthly, seasonal, and yearly generation cycles.
Statistical analyses (in particular, Analysis of Variance) have
shown that often there are significant differences in composition
among solid waste samples taken on the same day and on different
days during the week. This additional source of variability is,
of course, unwanted in any experiment designed to compare precisions
of samples of different weights. Unfortunately, securing a sufficient
quantity of "homogeneous" material to perform such studies is impossi-
ble. Each truckload of material arriving at a disposal site represents
a different population of waste. Indeed, much the same occurs with
different grapple loads of waste taken from an incinerator pit even
though attempts are usually made to mix the material. Thus, to re-
duce such sources of variation, samples of different weights must be
taken at random times and days ("random block designs") or a system-
atic sampling plan ("partially random block designs") must be employed
to achieve the same results. In this study, the latter course was
followed so that samples of a particular weight class were partially
randomized with regard to time and day. Those effects inflate the
variances of the subsequent analyses, but they do not bias the varia-
tion of any weight class.
-------
Past experience indicates that four men can reasonably separate
and weigh approximately 2,000 Ib of solid waste material in an aver-
age 8-hr day. The decision whether to analyze one 2,000-lb sample
each day or whether analyzing smaller samples would be more reliable
was resolved by taking approximately equal numbers of samples in
three size ranges: Weight Group I, 1,400 to 1,700 Ib; Weight Group II,
700 to 900 Ib; and Weight Group III, 200 to 300 Ib. During the study,
a total of 11 such samples were taken three in the largest size range
and four each in the smaller ranges (Table 1).
The samples were taken with a front-end loader from the incoming
waste storage pile. Particular care was taken to obtain samples
similar to the bulk of the waste being delivered. To avoid biasing
the samples by actually handpicking the material to be classified,
however, each sample was removed in a single scoop from a point in
the pile that appeared to contain a relatively complete mixture of
the waste being delivered. Each sample scoop was subsequently placed
on a cleaned area of the dumping floor and immediately hand-separated
into the nine categories specified. The weight of each component was
then recorded.
Effect of Sample Weight on Precision
The study plan recognized the necessity of selecting samples of
solid waste of varying weights. The amount of time and manpower avail-
able, of course, limited the number of samples taken. Of primary
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importance, surely, is to determine the reliability and precision of
selecting a specified number of samples of a certain weight.
To evaluate the original data, the weights of each component were
converted to percentages of the total weight of the sample (Table 2).
By grouping the data according to sample weight ranges, comparisons
can be made among all samples, among samples within groups, and among
groups. Such analysis leads to the ultimate objective of determining
the optimum weight and number of samples to be taken. By presenting
the data in percentage form, the percentage of a given component can be
compared among samples and groups and among all components within a
given sample or group. It is the variances of these percentages, how-
ever, that determine the sample weight and number of samples needed to
adequately determine the composition of a given source of solid waste.
The data expressed as percentages follow a multinomial distribution.
Before attempting statistical analysis, however, it is important to
note that the individual percentages cannot, in general, be expected
to follow a normal distribution. A normal distribution is considered
a good approximation to the distribution of a percentage when the
percentage lies between 30 and 70 percent. Only the paper component
meets this criterion (Table 2); the other entries fall below the minimum
acceptable 30 percent.
The following is an excellent normalizing transformation, however.
Y = 2 arcsin /X
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where X is the original percentage value of a component expressed
as a decimal,
and Y is the transformed value of X.
After the data of Table 2 are similarly transformed and then the
sum of squares about the mean (SSM) is calculated for each component
within each weight group, the data in Table 3 are obtained.
A commonly used measurement of relative precision is the coeffi-
cient of variation, which is defined as the standard deviation (square
root of the variance) of a group of measurements divided by its mean.
The result is then usually multiplied by 100 to convert to percent.
CV = (/V~ / Y ) 100*
To facilitate visual examination, the coefficients of variation
are summarized separately (Table k) .
An examination of the coefficients of variation of the three groups
indicates no discernible pattern. For example, precision does not appear
to increase as the sample weight is increased. The food waste and gar-
den waste components have relatively high coefficients of variation but
that of the paper products component is low. Irregularly high coeffi-
cients include textiles in Group Ml and wood in Group II, whereas the
coefficients of variation of the inerts component vary erratically.
The Cochran C test5 may be employed to determine, in a rigorous
manner, (the Coefficient of Variation Table only provides insight)
whether the variances among sample weight groups can be pooled for a
-'See Table 3 for definition of terms.
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TABLE 4
COEFFICIENTS OF VARIATION
(EXPRESSED AT PERCENTAGES)
Components
Food waste
Garden waste
Paper products
Plastic, rubber, leather
Text i les
Wood
Metals
Glass and ceramics
Ash, rocks, dirt (inerts)
GROUP 1
31.2
1*8.9
0.5
15.4
19.5
14.5
13.8
10.9
37.8
GROUP 1 1
23-5
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6.6
27-0
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77.4
9-9
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189-3
GROUP 1 1 1
31.4
26.3
3.5
19-9
57.9
29.6
21 .0
13.7
7-5
16
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given component. The test compares the sum of a group of variances
with the largest member of the group. Results of the test indicate
that, at the 5 percent risk level, pooling of variances across groups
is indeed justified provided the "questionable deviates," represented
by the textile component in Group III and the wood component in Group
II, are removed.
Additional use of the Cochran C test indicates that pooling
variances among components is also justifiable. Thus, a single pooled
estimate of variance, which yields an estimated standard deviation,
s, for all transformed observations of 0.1413 at 72 degrees of freedom,*
is obtained from Table 3-
The conclusion to this portion of the analysis is that there is
no difference in precision among the three groups. Accordingly, a
"small" (20G-lb) sample is as adequate as a larger one. The desirabil-
ity of taking small samples, supported by the preceding statistical
analysis, is reinforced by the fact that they are much easier to handle.
Past experience has shown that separating "small" samples is simpler
and more accurate from a human standpoint than separating "large" ones.
Statistical Technique to Determine Sample Size
To determine the number of samples required for composition anal-
ysis, the following normal approximation is adequate.
*As percentages, there are only eight independent observations per
sample because the ninth component is predictable after the percent
values for the first eight have been determined. The transformed values,
however, are not subject to such predictability and thus yield nine in-
dependent observations per sample. All components from the samples in
the three groups are included in this estimate, as this best reflects
conditions to be found in practice during a 4-day sampling period.
17
-------
where z is the standard normal deviate for the confidence
level des i red,
s is the estimated standard deviation (transformed
bas is) ,
6 is the sensitivity (transformed basis), defined
below,
and n is the number of samples required.
At 90 percent confidence, z equals 1.6^5; s equals 0.1^13, as
just noted. The sensitivity, transformed basis, is determined as follows
transform X and either X + A or X - A by the previously mentioned arcsin
transformation (specific values shown in Table 5), where X is the ex-
pected percentage of the component in question and A is the desired
precision for the percentage to be estimated (see example for further
clarification of A). The choice of sign for X ± A is positive if X
is less than 0.50 and negative if X is greater than 0.50. Calculate
the sensitivity,
I i i I
6 = | 2 arcsin /X - 2 arcsin /X ± A j
and compute n (number of samples required) by the formula given.
Example. Suppose one wishes to estimate the percentage of metals
in raw solid waste to within two (2) percentage units with a confi-
dence of 90 percent. Metals are expected to be found at a concentration
of approximately 9 percent. The first step is to convert the average
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TABLE 5
ARCS IN TRANSFORMATION
Y = 2 arcsin /X
X
.001
.002
.003
.004
.005
.006
.007
.008
.009
.010
.011
.012
.013
.014
.015
.016
.017
.018
.019
.020
.021
.022
.023
.024
.025
.026
.027
.028
.029
.030
.031
.032
.033
.034
.035
.036
.037
.038
.039
.040
Y
.0633
.0895
.1096
.1266
.1415
.1551
.1675
.1791
.1900
.2003
.2101
.2195
.2285
.2372
.2456
.2537
.2615
.2691
.2766
.2838
.2909
.2978
.3045
.3111
.3176
.3239
.3301
.3363
.3423
.3482
.3540
.3597
.3654
.3709
.3764
.3818
.3871
.3924
.3976
.4027
X
.041
.042
.043
.044
.045
.046
.047
.048
.049
.050
.06
.07
.08
M
.10
-n
.12
.13
.14
.15
.16
.17
.18
.19
.20
.21
.22
.23
.24
.25
.26
.27
.28
.29
.30
31
32
.33
.34
.35
Y
.4078
.4128
.4178
.4227
.4275
.4323
.4371
.4418
.4464
.4510
.4949
.5355
.5735
*'«
.6435
**|6!
.7075
.7377
.7670
.7954
.8230
.8500
.8763
.9021
.9273
.9521
.9764
.0004
.0239
.0472
.0701
.0928
.1152
.1374
.1593
.1810
.2025
.2239
.2451
.2661
X
.36
.37
.38
.39
.40
.41
.42
.43
.44
.45
.46
.47
.48
.49
.50
.51
.52
.53
.54
.55
.56
.57
.58
.59
.60
.61
.62
.63
.64
.65
.66
.67
.68
.69
.70
.71
.72
.73
.74
.75
Y
1 .2870
.3078
1.3284
1.3490
1.3694
1.3898
1 .4101
1.4303
.4505
1.4706
1 .4907
1.5108
1.5308
1.5508
1.5708
1.5908
.6108
.6308
.6509
.6710
.6911
.7113
.7315
1.7518
1.7722
1.7926
1 .8132
1.8338
.8546
.8755
.8965
.9177
.9391
.9606
.9823
2.0042
2.0264
2.0488
2.0715
2.0944
X
.76
.77
.78
.79
.80
.81
.82
.83
.84
.85
.86
.87
.88
.89
.90
.91
.92
.93
.94
.95
.951
.952
.953
.954
.955
.956
.957
.958
.959
.960
.961
.962
-963
.964
.965
.966
.967
.968
.969
.970
Y
2.1177
2.1412
2.1652
2.1895
2.2143
2.2395
2.2653
2.2916
2.3186
2.3462
2.3746
2.4039
2.4341
2.4655
2.4981
2.5322
2.5681
2.6062
2.6467
2.6906
2.6952
2.6998
2.7045
2.7093
2.7141
2.7189
2.7238
2.7288
2.7338
2.7389
2.7440
2.7492
2.7545
2.7598
2.7652
2.7707
2.7762
2.7819
2.7876
2.7934
X
971
.972
.973
974
.975
.976
.977
.978
.979
.980
.981
.982
.983
.984
.985
.986
.987
.988
.989
.990
.991
.992
.993
.994
.995
.996
.997
.998
.999
Y
2.7993
2.8053
2.8115
2.8177
2.8240
2.8305
2.8371
2.8438
2.8507
2.8578
2.8650
2.8725
2.8801
2.8879
2.8960
2.9044
2.9131
2.9221
2.9315
2.9413
2.9516
2.9625
2.9741
2.9865
3.0001
3.0150
3.0320
3.0521
3.0783
19
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percentage and the acceptable precision to decimals, i.e., 0.09 and
0.02, respectively. The corresponding values of Y (the transformed
quantities) obtained from Table 5 (X equals 0.09 and X + A equals 0.11,
since X is less than 0.50) are 0.6094 and 0.6761. Thus, & = 0.0667,
and
(0.1413) ..
']k
or n is approximately equal to 12 samples.
By performing a similar computation for each of the nine compo-
nents and by using the expected percentages based upon the averages
of the Group III samples, the following number of samples required
for each component are obtained (assuming 90 percent confidence and
a reasonable error of no more than 2 percent).
Component Number of samples size
1 . Food waste 9
2. Garden waste 6
3. Paper products 20
^. Plastic, rubber, leather 8
5. Text! les 10
6. Wood 10
7. Metals 11
8. Glass and ceramics 11
9. Ash, rocks, dirt (inerts) 12
If all components are considered equally important to the total
analysis and if a conservative approach is taken, a maximum number of
20 samples is needed to analyze the composition of solid waste. With
the exception of the paper component, however, 12 samples should prove
20
-------
adequate." Further, within the confines and limitations of the study,
the preceding analysis suggests that 12 of the smaller (200-lb) sam-
ples will yield valid and reliable results for composition evaluation.
"This conclusion is, of course, based upon an assumption that at
90 percent confidence, reasonable error should be limited to no more
than 2 percentage units. If this criterion were relaxed, the necessary
sample size would be reduced accordingly.
21
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-------
SUMMARY AND CONCLUSIONS
Important to the study of problems associated with solid waste
management is the definition, analysis, and evaluation of the generated
waste. Such materials entering a solid waste management stream, re-
quire storage, collection, handling and processing, and ultimate dis-
posal or salvage and reuse. Developing a reliable and standard sam-
pling procedure to determine the composition of solid waste materials
generated from any of a multitude of sources is of primary importance.
It is undesirable and impracticable to separate, measure, weigh,
and analyze all the solid waste generated at specified sources or
disposed of at particular facilities. Thus, to balance the resources
available with the need for accurate results, appropriate statistical
analysis holds promise of yielding information regarding optimum weights
and number of samples to be taken. By initiating a planned sample sur-
vey, the composition of solid waste can be determined and evaluated
within acceptable statistical limits.
To draw conclusions and to make recommendations based upon the
preceding analysis, the study analyzed one incinerator operation and,
more specifically, its solid waste composition for a 't-day period of
time. A more thorough and complete analysis would also consider monthly,
seasonal, yearly, and cyclical variations. Note also that solid waste
must be properly mixed to yield adequate samples from a given supply
23
-------
of waste materials; and further, that if the criteria to classify solid
waste differ from those applied in selecting the nine categories used
in this analysis, the results may be influenced significantly.
With these facts in mind, the study of this incinerator indicates
that there is no significant variance among sample weight groups. Con-
sequently, smaller (200-lb) samples will yield valid results in deter-
mining the composition of a given supply of solid waste. Data from
later studies, which are presently being evaluated and analyzed, appear
to confirm and verify the results of this analysis. Indeed, it may
be found that samples somewhat smaller than 200 Ib will provide accep-
table results.
It is encouraging to note that, upon the basis of this study,
smaller samples than previously thought adequate hold promise of pro-
viding reasonable and reliable information concerning the composition
of solid waste.
-------
REFERENCES
1. Brown, R. R. Explanation in social science. Chicago, Aldine
Publishing Company, 1963- 198 p.
2. The Solid Waste Disposal Act; Title II of Public Law 89-272,
89th Cong. S.306, October 20, 1965. Washington, U.S.
Government Printing Office, 1966. [5 p.]
3. Bell, J. M. Development of methods of sampling and analyzing
municipal refuse 1957~1962. Unpublished paper. Purdue
University Library. 20 p.
k. Cochran, W. G. Sampling techniques. 2d ed. New York, John
Wiley and Sons, Inc., 196^t. p. 71.
5. Winer, B. J. Statistical principles in experimental design.
New York, McGraw-Hill Book Company Inc., 1962. p. 9^-95.
25
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