1、Designation: E 1847 96 (Reapproved 2008)Standard Practice forStatistical Analysis of Toxicity Tests Conducted UnderASTM Guidelines1This standard is issued under the fixed designation E 1847; the number immediately following the designation indicates the year oforiginal adoption or, in the case of re
2、vision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This practice covers guidance for the statistical analysisof laboratory data on the toxicity of c
3、hemicals or mixtures ofchemicals to aquatic or terrestrial plants and animals. Thispractice applies only to the analysis of the data, after the testhas been completed.All design concerns, such as the statementof the null hypothesis and its alternative, the choice of alphaand beta risks, the identifi
4、cation of experimental units, possiblepseudo replication, randomization techniques, and the execu-tion of the test are beyond the scope of this practice. Thispractice is not a textbook, nor does it replace consultation witha statistician. It assumes that the investigator recognizes thestructure of h
5、is experimental design, has identified the experi-mental units that were used, and understands how the test wasconducted. Given this information, the proper statistical analy-ses can be determined for the data.1.1.1 Recognizing that statistics is a profession in whichresearch continues in order to i
6、mprove methods for performingthe analysis of scientific data, the use of statistical methodsother than those described in this practice is acceptable as longas they are properly documented and scientifically defensible.Additional annexes may be developed in the future to reflectcomments and needs id
7、entified by users, such as more detaileddiscussion of probit and logistic regression models, or statisti-cal methods for dose response and risk assessment.1.2 The sections of this guide appear as follows:Title SectionReferenced Documents 2Terminology 3Significance and Use 4Statistical Methods 5Flow
8、Chart 6Flow Chart Comments 7Keywords 8References1.3 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of reg
9、ulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2E 178 Practice for Dealing With Outlying ObservationsE 456 Terminology Relating to Quality and StatisticsE 1241 Guide for Conducting Early Life-Stage ToxicityTests with FishesE 1325 Terminology Relating to Design of Experime
10、ntsIEEE/ASTM SI 10 American National Standard for Use ofthe International System of Units (SI): The Modern MetricSystem3. Terminology3.1 Definitions of Terms Specific to This StandardThefollowing terms are defined according to the references noted:3.1.1 analysis of variance (ANOVA)a technique that s
11、ub-divides the total variation of a set of data into meaningfulcomponent parts associated with specific sources of variationfor the purpose of testing some hypothesis on the parameters ofthe model or estimating variance components (1).33.1.2 categorical datavariates that take on a limitednumber of d
12、istinct values (2).3.1.3 censored datasome subjects have not experiencedthe event of interest at the end of the study or time of analysis.The exact survival times of these subjects are unknown (3).3.1.4 central limit theoremwhatever the shape of thefrequency distribution of the original populations
13、of Xs, thefrequency distribution of the mean, in repeated randomsamples of size n tends to become normal as n increases (2).3.1.5 central tendency measurea statistic that measuresthe central location of the sample observations (4).3.1.6 concentration-response testingthe quantitative rela-tion betwee
14、n the amount of factor X and the magnitude of the1This practice is under the jurisdiction of ASTM Committee E47 on BiologicalEffects and Environmental Fate and is the direct responsibility of SubcommitteeE47.06 on Technical Services and Support.Current edition approved Feb. 1, 2008. Published April
15、2008. Originallyapproved in 1996. Last previous edition approved in 2003 as E 184796(2003).2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Su
16、mmary page onthe ASTM website.3The boldface numbers given in parentheses refer to a list of references at theend of the text.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.effect it causes is determined by performing parallel sets o
17、foperations with various known amounts, or doses, of the factorand measuring the result, that is called the response (5).3.1.7 continuous dataa variable that can assume a con-tinuum of possible outcomes (4).3.1.8 controlan experiment in which the subjects aretreated as in a parallel experiment excep
18、t for omission of theprocedure or agent under test and that is used as a standard ofcomparison in judging experimental effects (6).3.1.9 dichotomous datavariates that have only 2 mutuallyexclusive outcomes, binary data, success or failure data (3).3.1.10 dispersion measurea statistic that measures t
19、hecloseness of the independent observations within groups, orrelative to a samples central value (4).3.1.11 distributiona set of all the various values thatindividual observations may have and the frequency of theiroccurrence in the sample or population (1).3.1.12 duplicationthe execution of a treat
20、ment at leasttwice under similar conditions (1).3.1.13 experimental unita portion of the experimentalspace to which a treatment is applied or assigned in theexperiment (1).3.1.14 homogeneitylack of significant differences amongmean squares of an analysis (2).3.1.15 hypothesis testa decision rule (st
21、rategy, recipe)which, on the basis of the sample observations, either acceptsor rejects the null hypothesis (4).3.1.16 independencehaving the property that the jointprobability (as of all events or samples) or the joint probabilitydensity function (as of random variables) equals the product ofthe pr
22、obabilities or probability density functions of separateoccurrence (6).3.1.17 meana measure of central tendency or location thatis the sum of the observations divided by the number ofobservations (1).3.1.18 modelan equation that is intended to provide afunctional description of the sources of inform
23、ation which maybe obtained from an experiment (1).3.1.19 nonparametric statistica statistic which has certaindesirable properties that hold under relatively mild assump-tions regarding the underlying populations (4).3.1.20 normalityhaving the characteristics of a normaldistribution (2).3.1.21 outlie
24、ran outlying observation is one that appearsto deviate markedly from other members of the sample inwhich it occurs (see Practice E 178).3.1.22 parametric statistica statistic that estimates anunknown constant associated with a population (4).3.1.23 probit logitwhen the response Y in binary, theprobi
25、t/logit equation is as follows:p 5 PrY 5 0! 5 C 1 1 2 C! Fx*b! (1)where:b = vector of parameter estimates,F = cumulative distribution function (normal, logistic),x = vector of independent variables,p = probability of a response, andC = natural (threshold) response rate.The choice of the distribution
26、 function, F, (normal for theprobit model, logistic for the logit model) determines the typeof analysis (7).3.1.24 regression analysisthe process of estimating theparameters of a model by optimizing the value of an objectivefunction (for example, by the method of least squares) and thentesting the r
27、esulting predictions for statistical significanceagainst an appropriate null hypothesis model (1).3.1.25 replicationthe repetition of the set of all thetreatment combinations to be compared in an experiment. Eachof the repetitions is called a replicate (1).3.1.26 residualYobsminus Ypred the differen
28、ce betweenthe observed response variable value and the response variablevalue that is predicted by the model that is fit to the data (8).3.1.27 scedasticityvariance (5).3.1.28 significance levelthe probability at which the nullhypothesis is falsely rejected, that is, rejecting the null hypoth-esis w
29、hen in fact it is true (4).3.1.29 transformationthe transformation of the observa-tions Xij into another scale for purposes of allowing thestandard analysis to be used as an adequate approximation (2).3.1.30 treatmenta combination of the levels of each of thefactors assigned to an experimental unit
30、(see TerminologyE 456).3.1.31 variancea measure of the squared dispersion ofobserved values or measurements expressed as a function ofthe sum of the squared deviations from the population mean orsample average (see Terminology E 456).4. Significance and Use4.1 The use of statistical analysis will en
31、able the investiga-tor to make better, more informed decisions when using theinformation derived from the analyses.4.1.1 The goals when performing statistical analyses, are tosummarize, display, quantify, and provide objective measuresfor assessing the relationships and anomalies in data. Statistica
32、lanalyses also involve fitting a model to the data and makinginferences from the model. The type of data dictates the type ofmodel to be used. Statistical analysis provides the means to testdifferences between control and treatment groups (one form ofhypothesis testing), as well as the means to desc
33、ribe therelationship between the level of treatment and the measuredresponses (concentration effect curves), or to quantify thedegree of uncertainty in the end-point estimates derived fromthe data.4.1.2 The goals of this practice are to identify and describecommonly used statistical procedures for t
34、oxicity tests. Fig. 1,Section 6, following statistical methods (Section 5), presents aflow chart and some recommended analysis paths, with refer-ences. From this guideline, it is recommended that eachinvestigator develop a statistical analysis protocol specific tohis test results. The flow chart, al
35、ong with the rest of thisguideline, may provide both useful direction, and service as aquality assurance tool, to help ensure that important steps in theanalysis are not overlooked.E 1847 96 (2008)25. Statistical Methods5.1 Exploratory Data AnalysisThe first step in any dataanalysis is to look at th
36、e data and become familiar with theircontent, structure, and any anomalies that might be present.5.1.1 Plots:5.1.1.1 Histograms are unidimensional plots that show thedistributional shapes in the data and the frequencies of indi-vidual values. These diagrams allow the investigator to checkfor unusual
37、 observations and also visually check the validity ofsome assumptions that are necessary for several statisticalanalyses that may be used (9).5.1.1.2 Scatter plots of two or more variables demonstratethe relationships among the variables, so that correlations canbe observed and interactions can be s
38、tudied. These plots arevery useful when looking for concentration effect relationships(9).5.1.1.3 Normality and box plots are additional plots thatgive distributional information, quantiles and pictures of thedata, either as a whole or by treatment group (9).5.1.2 OutliersOn occasion, some data poin
39、ts in the histo-gram, scatter plot, or box plot, appear to be quite different fromthe majority of points. These data, known as outliers, can betested to determine if they are truly different from the distri-bution of the experimental data (10). The Z or t scores areusually used for testing, with a c
40、onfidence level chosen by theinvestigator. If they are different and can be attributed to anerror in the execution of the study (violation of protocol, dataentry error, and so forth), then they can be removed from theanalyses. However, if there is no legitimate reason to removethem, then they must b
41、e kept in the analyses. It is recom-mended that the analyses can be conducted on two data sets,the complete one and one with the outliers removed. In thisway, the outliers influence on the analyses can be studied.5.1.3 Non-Detected Data:5.1.3.1 Data that fall below a chemical analysis thresholdlevel
42、 of detection, in an analytical technique used to measure avalue, are called non-detected. Values that occur above thedetection limit but are below the limit of quantitation, arecalled non-estimable. Occasionally, the two terms are usedinterchangeably. Essentially, these data are results for which n
43、oreliable number can be determined.5.1.3.2 In analyzing a data set containing one or morenon-detects, several methods can be used. If the amount ofnon-detects is below approximately 25 % of the entire data set,then the non-detects can be replaced by one half the detectionlimit (or quantitation limit
44、, whichever is appropriate) andFIG. 1 Flow Chart for Practice for Statistical AnalysisE 1847 96 (2008)3FIG. 1 Flow Chart for Practice for Statistical Analysis (continued)FIG. 1 Flow Chart for Practice for Statistical Analysis (continued)E 1847 96 (2008)4analysis proceeds (11). One half the detection
45、 or quantitationlimit is often used to prevent undue bias from entering theanalysis. In some cases, the full detection limit may be moreappropriate for the analyses, or substituting values derivedfrom a distribution function fit to the non-detected range, thatis appropriate given the distribution of
46、 the detected values.Zero is not usually used as a substitute because of the bias itintroduces to the analyses, and potential underestimation of thestatistics involved. However, zero may be the most appropriatevalue in certain situations, as determined by best professionaljudgment. One example is th
47、e analysis of control samples, thatare known with a very high degree of confidence to be free ofthe chemical being analyzed, that is, zero concentration. Ifthere are more than approximately 25 % non-detects in the dataset, then the proportions of non-detects to the total sample sizefor each group ar
48、e analyzed on a present/absent basis, and theanalysis is done on the proportions. If there are more thanapproximately 50 % non-detects in the data set, the proportionscan be analyzed as above, or the data can be partitioned intodetects and non-detects. The detects group is then analyzed byitself, to
49、 reveal the information it holds.5.1.4 Descriptive StatisticsThe next step is to summarizethe information contained in the data, by means of descriptivestatistics. First and foremost is the sample size or number ofobservations in the test, broken out by treatment groups,experimental units, or blocks, whatever is appropriate for thetest being analyzed. Other most common ones are measures ofcentral tendency and of dispersion within the data. Centraltendency measures are the mean, median (also known as the50th percentile), mode, and trimmed m
