ASTM E1847-96(2013)

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation: E1847 − 96 (Reapproved 2013)
Standard Practice for
Statistical Analysis of Toxicity Tests Conducted Under
ASTM Guidelines
This standard is issued under the fixed designation E1847; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope 1.3 This standard does not purport to address all of the
safety concerns, if any, associated with its use. It is the
1.1 This practice covers guidance for the statistical analysis
responsibility of the user of this standard to establish appro-
of laboratory data on the toxicity of chemicals or mixtures of
priate safety and health practices and determine the applica-
chemicals to aquatic or terrestrial plants and animals. This
bility of regulatory limitations prior to use.
practice applies only to the analysis of the data, after the test
hasbeencompleted.Alldesignconcerns,suchasthestatement
2. Referenced Documents
of the null hypothesis and its alternative, the choice of alpha
2.1 ASTM Standards:
andbetarisks,theidentificationofexperimentalunits,possible
E178Practice for Dealing With Outlying Observations
pseudo replication, randomization techniques, and the execu-
E456Terminology Relating to Quality and Statistics
tion of the test are beyond the scope of this practice. This
E1241GuideforConductingEarlyLife-StageToxicityTests
practiceisnotatextbook,nordoesitreplaceconsultationwith
with Fishes
a statistician. It assumes that the investigator recognizes the
E1325Terminology Relating to Design of Experiments
structure of his experimental design, has identified the experi-
IEEE/ASTM SI 10 American National Standard for Use of
mental units that were used, and understands how the test was
theInternationalSystemofUnits(SI):TheModernMetric
conducted. Given this information, the proper statistical analy-
System
ses can be determined for the data.
1.1.1 Recognizing that statistics is a profession in which
3. Terminology
researchcontinuesinordertoimprovemethodsforperforming
the analysis of scientific data, the use of statistical methods 3.1 Definitions of Terms Specific to This Standard:
otherthanthosedescribedinthispracticeisacceptableaslong
3.1.1 The following terms are defined according to the
as they are properly documented and scientifically defensible. references noted:
Additional annexes may be developed in the future to reflect
3.1.2 analysis of variance (ANOVA)—a technique that sub-
comments and needs identified by users, such as more detailed
divides the total variation of a set of data into meaningful
discussion of probit and logistic regression models, or statisti-
component parts associated with specific sources of variation
cal methods for dose response and risk assessment.
forthepurposeoftestingsomehypothesisontheparametersof
the model or estimating variance components (1).
1.2 The sections of this guide appear as follows:
3.1.3 categorical data—variates that take on a limited
Title Section
number of distinct values (2).
Referenced Documents 2
3.1.4 censored data—some subjects have not experienced
Terminology 3
Significance and Use 4 the event of interest at the end of the study or time of analysis.
Statistical Methods 5
The exact survival times of these subjects are unknown (3).
Flow Chart 6
Flow Chart Comments 7
3.1.5 central limit theorem—whatever the shape of the
Keywords 8
frequency distribution of the original populations of X’s, the
References
frequency distribution of the mean, in repeated random
samples of size n tends to become normal as n increases (2).
This practice is under the jurisdiction of ASTM Committee E50 on Environ-
mental Assessment, Risk Management and Corrective Action and is the direct For referenced ASTM standards, visit the ASTM website, www.astm.org, or
responsibility of Subcommittee E50.47 on Biological Effects and Environmental contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Fate. Standards volume information, refer to the standard’s Document Summary page on
Current edition approved March 1, 2013. Published March 2013. Originally the ASTM website.
approvedin1996.Lastpreviouseditionapprovedin2008asE1847–96(2008).DOI: The boldface numbers given in parentheses refer to a list of references at the
10.1520/E1847-96R13. end of the text.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E1847 − 96 (2013)
3.1.6 central tendency measure—a statistic that measures 3.1.24 probit logit—when the response Y in binary, the
the central location of the sample observations (4). probit/logit equation is as follows:
3.1.7 concentration-response testing—the quantitative rela- p 5 Pr Y 50 5 C1 1 2 C F x'b (1)
~ ! ~ ! ~ !
tion between the amount of factor X and the magnitude of the
where:
effect it causes is determined by performing parallel sets of
b = vector of parameter estimates,
operationswithvariousknownamounts,ordoses,ofthefactor
F = cumulative distribution function (normal, logistic),
and measuring the result, that is called the response (5).
x = vector of independent variables,
3.1.8 continuous data—a variable that can assume a con-
p = probability of a response, and
tinuum of possible outcomes (4). C = natural (threshold) response rate.
3.1.9 control—an experiment in which the subjects are The choice of the distribution function, F, (normal for the
treated as in a parallel experiment except for omission of the probit model, logistic for the logit model) determines the type
procedure or agent under test and that is used as a standard of of analysis (7).
comparison in judging experimental effects (6).
3.1.25 regression analysis—the process of estimating the
3.1.10 dichotomous data—variates that have only 2 mutu-
parameters of a model by optimizing the value of an objective
ally exclusive outcomes, binary data, success or failure data function(forexample,bythemethodofleastsquares)andthen
(3).
testing the resulting predictions for statistical significance
against an appropriate null hypothesis model (1).
3.1.11 dispersion measure—a statistic that measures the
closeness of the independent observations within groups, or
3.1.26 replication—the repetition of the set of all the treat-
relative to a sample’s central value (4).
ment combinations to be compared in an experiment. Each of
the repetitions is called a replicate (1).
3.1.12 distribution—a set of all the various values that
individual observations may have and the frequency of their
3.1.27 residual—Y minus Y −the difference between
obs pred
occurrence in the sample or population (1).
theobservedresponsevariablevalueandtheresponsevariable
value that is predicted by the model that is fit to the data (8).
3.1.13 duplication—the execution of a treatment at least
twice under similar conditions (1).
3.1.28 scedasticity—variance (5).
3.1.14 experimental unit—a portion of the experimental
3.1.29 significance level—the probability at which the null
space to which a treatment is applied or assigned in the
hypothesis is falsely rejected, that is, rejecting the null hypoth-
experiment (1).
esis when in fact it is true (4).
3.1.15 homogeneity—lack of significant differences among
3.1.30 transformation—the transformation of the observa-
mean squares of an analysis (2).
tions Xij into another scale for purposes of allowing the
standard analysis to be used as an adequate approximation (2).
3.1.16 hypothesis test—a decision rule (strategy, recipe)
which, on the basis of the sample observations, either accepts
3.1.31 treatment—acombinationofthelevelsofeachofthe
or rejects the null hypothesis (4).
factors assigned to an experimental unit (see Terminology
E456).
3.1.17 independence—having the property that the joint
probability(asofalleventsorsamples)orthejointprobability
3.1.32 variance—a measure of the squared dispersion of
densityfunction(asofrandomvariables)equalstheproductof
observed values or measurements expressed as a function of
the probabilities or probability density functions of separate
thesumofthesquareddeviationsfromthepopulationmeanor
occurrence (6).
sample average (see Terminology E456).
3.1.18 mean—ameasureofcentraltendencyorlocationthat
is the sum of the observations divided by the number of 4. Significance and Use
observations (1).
4.1 The use of statistical analysis will enable the investiga-
3.1.19 model—an equation that is intended to provide a
tor to make better, more informed decisions when using the
functionaldescriptionofthesourcesofinformationwhichmay
information derived from the analyses.
be obtained from an experiment (1).
4.1.1 The goals when performing statistical analyses, are to
3.1.20 nonparametric statistic—astatisticwhichhascertain summarize, display, quantify, and provide objective measures
desirable properties that hold under relatively mild assump-
forassessingtherelationshipsandanomaliesindata.Statistical
tions regarding the underlying populations (4). analyses also involve fitting a model to the data and making
inferencesfromthemodel.Thetypeofdatadictatesthetypeof
3.1.21 normality—having the characteristics of a normal
modeltobeused.Statisticalanalysisprovidesthemeanstotest
distribution (2).
differences between control and treatment groups (one form of
3.1.22 outlier—an outlying observation is one that appears
hypothesis testing), as well as the means to describe the
to deviate markedly from other members of the sample in
relationship between the level of treatment and the measured
which it occurs (see Practice E178).
responses (concentration effect curves), or to quantify the
3.1.23 parametric statistic—a statistic that estimates an degree of uncertainty in the end-point estimates derived from
unknown constant associated with a population (4). the data.
E1847 − 96 (2013)
4.1.2 The goals of this practice are to identify and describe 5.1.1.2 Scatter plots of two or more variables demonstrate
commonly used statistical procedures for toxicity tests. Fig. 1, the relationships among the variables, so that correlations can
Section 6, following statistical methods (Section 5), presents a be observed and interactions can be studied. These plots are
flow chart and some recommended analysis paths, with refer- veryusefulwhenlookingforconcentrationeffectrelationships
ences. From this guideline, it is recommended that each (9).
investigator develop a statistical analysis protocol specific to
5.1.1.3 Normality and box plots are additional plots that
his test results. The flow chart, along with the rest of this
give distributional information, quantiles and pictures of the
guideline, may provide both useful direction, and service as a
data, either as a whole or by treatment group (9).
qualityassurancetool,tohelpensurethatimportantstepsinthe
5.1.2 Outliers—On occasion, some data points in the
analysis are not overlooked.
histogram, scatter plot, or box plot, appear to be quite different
from the majority of points.These data, known as outliers, can
5. Statistical Methods
be tested to determine if they are truly different from the
5.1 Exploratory Data Analysis—The first step in any data
distributionoftheexperimentaldata (10).The Zor tscoresare
analysis is to look at the data and become familiar with their usually used for testing, with a confidence level chosen by the
content, structure, and any anomalies that might be present. investigator. If they are different and can be attributed to an
5.1.1 Plots: error in the execution of the study (violation of protocol, data
5.1.1.1 Histograms are unidimensional plots that show the entry error, and so forth), then they can be removed from the
distributional shapes in the data and the frequencies of indi- analyses. However, if there is no legitimate reason to remove
vidual values. These diagrams allow the investigator to check them, then they must be kept in the analyses. It is recom-
forunusualobservationsandalsovisuallycheckthevalidityof mended that the analyses can be conducted on two data sets,
some assumptions that are necessary for several statistical the complete one and one with the outliers removed. In this
analyses that may be used (9). way, the outliers’ influence on the analyses can be studied.
FIG. 1 Flow Chart for Practice for Statistical Analysis
E1847 − 96 (2013)
FIG. 1 Flow Chart for Practice for Statistical Analysis (continued)
FIG. 1 Flow Chart for Practice for Statistical Analysis (continued)
E1847 − 96 (2013)
FIG. 1 Flow Chart for Practice for Statistical Analysis (continued)
5.1.3 Non-Detected Data: for each group are analyzed on a present/absent basis, and the
5.1.3.1 Data that fall below a chemical analysis threshold analysis is done on the proportions. If there are more than
levelofdetection,inananalyticaltechniqueusedtomeasurea
approximately50%non-detectsinthedataset,theproportions
value, are called non-detected. Values that occur above the can be analyzed as above, or the data can be partitioned into
detection limit but are below the limit of quantitation, are
detects and non-detects. The detects group is then analyzed by
called non-estimable. Occasionally, the two terms are used
itself, to reveal the information it holds.
interchangeably.Essentially,thesedataareresultsforwhichno
5.1.4 Descriptive Statistics—The next step is to summarize
reliable number can be determined.
the information contained in the data, by means of descriptive
5.1.3.2 In analyzing a data set containing one or more
statistics. First and foremost is the sample size or number of
non-detects, several methods can be used. If the amount of
observations in the test, broken out by treatment groups,
non-detectsisbelowapproximately25%oftheentiredataset,
experimental units, or blocks, whatever is appropriate for the
then the non-detects can be replaced by one half the detection
test being analyzed. Other most common ones are measures of
limit (or quantitation limit, whichever is appropriate) and
central tendency and of dispersion within the data. Central
analysis proceeds (11). One half the detection or quantitation
tendency measures are the mean, median (also known as the
limit is often used to prevent undue bias from entering the
50th percentile), mode, and trimmed mean (also called Win-
analysis. In some cases, the full detection limit may be more
sorized mean). Dispersion measures are range, standard
appropriate for the analyses, or substituting values derived
deviation, variance, and quantiles (percentiles, interquartile
from a distrib
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