# ASTM E1345-98 (Reapproved 2014)

Designation: E1345 − 98 (Reapproved 2014)Standard Practice forReducing the Effect of Variability of Color Measurement byUse of Multiple Measurements1This standard is issued under the fixed designation E1345; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (´) indicates an editorial change since the last revision or reapproval.INTRODUCTIONRecent improvements in the precision and bias of color-measuring instruments have beenaccompanied by more widespread use of numerical color tolerances based on instrumental measure-ments. As tighter tolerances are specified, they begin to approach the limits of visual perception. Inmany cases, the instrument user has found it difficult to prepare and measure specimens with adequaterepeatability. This practice provides procedures for reducing variability in the mean results of colormeasurement by the use of multiple measurements, and it indicates how many measurements arerequired for a specific reduction.1. Scope1.1 Reduction of the variability associated with averagecolor or color-difference measurements of object-color speci-mens is achieved by statistical analysis of the results ofmultiple measurements on a single specimen, or by measure-ment of multiple specimens, whichever is appropriate.1.2 This practice provides a means for the determination ofthe number of measurements required to reduce the variabilityto a predetermined fraction of the relevant color or color-difference tolerances.1.3 This practice is general in scope rather than specific asto instrument or material.2. Referenced Documents2.1 ASTM Standards:2D2244 Practice for Calculation of Color Tolerances andColor Differences from Instrumentally Measured ColorCoordinatesD3134 Practice for Establishing Color and Gloss TolerancesE178 Practice for Dealing With Outlying ObservationsE284 Terminology of AppearanceE308 Practice for Computing the Colors of Objects by Usingthe CIE SystemE456 Terminology Relating to Quality and StatisticsE1164 Practice for Obtaining Spectrometric Data for Object-Color Evaluation2.2 Other Standard:SAE J 1545 Recommended Practice for Instrumental ColorDifference Measurement for Exterior Finishes, Textilesand Colored Trim33. Terminology3.1 Definitions of appearance terms in Terminology E284 orstatistical terms in Terminology E456 are applicable to thispractice.3.2 Definitions of Terms Specific to This Standard:3.2.1 box and whisker plot, n—a nonparmetric data analysisdiagram that illustrates the 25, 50, and 75 % cumulativedistribution of values in a data set (the box) and the expectedrange of values, defined by distance outside the box ends; seewhiskers, see Fig. 1.3.2.2 extreme value, n—a single reading, selected from aseries of readings, whose value is farther from the nearer boxend than 3.0 times the hinge length.3.2.2.1 Discussion—A box and whiskers plot is normallyused to find outliers and extreme values. Such values should beeliminated from a series before calculating the series mean,standard deviation, and confidence intervals.3.2.3 hinges, n—the 25 and 75 % cumulative distributionpoints in a set of readings taken during a measurement.3.2.3.1 Discussion—Hinges represent the values in which1This practice is under the jurisdiction of ASTM Committee E12 on Color andAppearance and is the direct responsibility of Subcommittee E12.04 on Color andAppearance Analysis.Current edition approved Nov. 1, 2014. Published November 2014. Originallyapproved in 1990. Last previous edition approved in 2008 as E1345 – 98 (2008)ε1.DOI: 10.1520/E1345-98R14.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.3Available from Society of Automotive Engineers (SAE), 400 CommonwealthDr., Warrendale, PA 15096-0001, http://www.sae.org.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States125 % of the readings are less than the lower hinge and 75 % ofthe readings are less than the upper hinge. See also hingelength.3.2.3.2 Discussion—Hinges are sometimes called the lower(Q1) and upper (Q1) quartile values.3.2.4 hinge length, H, n—the range of values between thelower and upper hinges.3.2.4.1 Discussion—The hinge length is sometimes calledthe box width or the interquartile range Q3to Q1.3.2.5 outlier, n—a single reading, selected from a series ofreadings, whose value is further from the nearer box end then1.5 times the hinge length; see 3.2.2.1.3.2.6 sampling number, N, n—number of multiplemeasurements, or number of multiple specimens, required toreduce the variability of color or color-difference measurementto a desired level.3.2.7 standard deviation of color or color-differencemeasurement, s—standard deviation of the color scale orcolor-difference-scale value, xi, being considered:s 5 @$(~xi2 xavg!2%/~n 2 1!#0.5(1)where:xavg=(∑ xi)/n, andn = the number of replicate measurements made.3.2.8 standard deviation of instrument, si,n—standard de-viation of a color-scale or color-difference-scale value due toinstrument variability alone:si5 @$(~xi2 xavg!2%/~n 2 1!#0.5(2)3.2.9 standard error of the estimated mean, se,n—standarddeviation of color or color-difference measurement divided bythe square root of the sampling number:se5 s/~N0.5! (3)3.2.10 standard error goal, se,g,n—level to which thestandard error of the estimated mean is to be reduced.3.2.11 tolerance, n—the upper tolerance limit minus thelower tolerance limit; the total allowable range of the color-scale or color-difference-scale value considered.3.2.12 whiskers, n—lines extending out from the box endsto the largest and smallest observations lying within 1.5 timesthe hinge length, measured from the box ends.4. Summary of Practice4.1 This practice assumes that, for the material underconsideration and a specified set of color scales, relevant coloror color-difference tolerances have been established (see Prac-tice D3134).4.2 For convenience, the numerical example in the Appen-dix uses CIELAB LCH (lightness, chroma, hue) color differ-ence scales ∆L*, ∆C*ab, and ∆H*ab(see Practice D2244 andPractice E308), but this is not meant to be restrictive.NOTE 1—Some coordinates, such as CIE x, y, Y, do not follow thetheories of this standard due to excessive colinearity. While it has not beentested, this same colinearity problem may also be observed in 1960 u, vand 1976 u , v coordinates. Table 1 provides a listing of the appropriateand inappropriate color coordinates for use with this practice.4.3 The successive steps in the procedure are as follows:4.3.1 Determine the standard deviation of instrument.4.3.1.1 Screen the measurement data for outliers and ex-treme values.4.3.2 Determine the standard deviation of color or color-difference measurement.4.3.2.1 Screen the measurement data for outliers and ex-treme values.4.3.3 Determine the standard error of the estimated mean fora sampling number of one.4.3.4 Determine the final sampling number that reduces thestandard error of the estimated mean to less than the standarderror goal for each scale value.4.3.5 Determine the final standard error goal values.NOTE 2—When the standard error of the estimated mean for a samplingnumber of one is larger than a specified fraction of the tolerance or aspecified multiple of the standard deviation of instrument for any of thethree color-difference-scale values, a sampling number greater than one isrequired.4.4 Screening for and Elimination of Outliers and ExtremeValues in Measured Data:FIG. 1 Schematic Description of a Box and Whisker PlotTABLE 1 Appropriate and Inappropriate Color Coordinates forUse in This PracticeColor Coordinates Appropriate InappropriateCIE Yxy =CIE LCH =CIE LAB =CIE LUV =CIE Lu v =E1345 − 98 (2014)24.4.1 Box and whisker test—This test is best carried out bycomputer. Many programs for the box and whisker techniqueare available.44.4.1.1 Order the readings from lowest to highest value. Thereading whose value is half way between the minimum andmaximum values is the median. Fig. 1 illustrates the followingsteps.4.4.1.2 The reading whose value is just less than 75 % of theother readings is the lower hinge. The readings whose value isjust higher than 75 % of the other readings is the upper hinge.The difference between these two is the hinge length H.4.4.1.3 If the smallest value of any reading is less than thelower hinge value minus 1.5 times the hinge length, it may beconsidered an outlier. Likewise, if the largest value of anyreading is greater than the upper hinge value plus 1.5 times thehinge length, it may be considered an outlier.4.4.1.4 If the smallest (largest) value of any reading is less(greater) than the lower (upper) hinge value minus (plus) 3.0times the hinge length, it may be considered an extreme value.4.4.2 Practice E178 Procedure—The test for outliers inPractice E178 is constructed from the sample mean Xavg, andthe standard deviation s.4.4.2.1 Order the readings from lowest to highest value.4.4.2.2 Calculate the following two statistics, T1for thelowest value, and Tnfor the highest value in a set of n orderedreadings as follows:Tl5~xavg2 xl!s(4)Tn5~xn2 xavg!s(5)4.4.2.3 Compare the values of Tl(Tn) to critical values inTable 2.IfTl(Tn) is larger than the critical value for n readingsat the 1 % level of significance. Reading 1 (n) may beconsidered an outlier.NOTE 3—Table 2 contains critical values for series of up to 15 readingsand for 0.1 and 1 % significance levels. For other significance levels andlarger datasets, see Table 1 of Practice E178.4.4.2.4 If Tl(Tn) is larger than the critical value for nreadings at the 1 % level of significance, Readings 1 (n) may beconsidered an extreme value.4.4.3 If any outliers or extreme values were found, considercarefully whether they should be dropped or retained. Dropthose readings not considered to be part of the desired dataset,by whatever consistent criteria are accepted. See 5.3.4.4.4 Recalculate the mean, standard deviation and confi-dence limits of the remaining dataset.5. Significance and Use5.1 This practice should be used whenever measured color-scale or color-difference-scale values are to be compared to anestablished tolerance. In this way it can be demonstratedquantitatively that the sampling and measurement proceduresare adequate to allow an unambiguous decision as to whetheror not the mean results are within tolerance.5.2 This practice is based on portions of SAE J 1545, as itapplies to painted or plastic automotive parts. It is generallyapplicable to object colors in various materials. Texturedmaterials, such as textiles, may require special consideration(see SAE J 1545 and STP 15D Manual on Presentation of Dataand Control Chart Analysis5).5.3 While Practice E178 deals with outliers, it does notinclude definitions relating to the box and whisker technique.The definition of an outlier is operational and a little vaguebecause there is still considerable disagreement about whatconstitutes an outlier. In any normally distributed population,there will be members that range from minus to plus infinity.Theoretically, one should include any member of the popula-tion in any sample based on estimates of the populationparameters. Practically, including a member that is found farfrom the mean within a small sample, most members of whichare found near the mean, will introduce a systematic bias intothe estimate of the population parameters (mean, standarddeviation, standard error). Such a bias is in direct contrast withthe goal of this practice, namely, to reduce the effects ofvariability of measurement. For the purposes of this practice,no distinction is made between errors of sampling and mem-bers of the tails of the distribution. Practice E178 has severalmethods and significance tables to attempt to differentiatebetween these two types of extreme values.6. Procedure6.1 Determine the standard deviation of instrument, si,bycarrying out the appropriate color measurement at least 10times (n = 10) when using a stable product standard as thespecimen, without removing or disturbing the specimen be-tween measurements. Calculate siby the use of Eq 2. Thisdetermination should be carried out for each color scale usedand for each product with a new color; however, sIis unlikelyto change appreciably over relatively extended periods.6.1.1 Screen the measurement data for outliers and extremevalues following 4.4.1 – 4.4.4.4See for example, Schaefer, R. L. and Anderson, R. B., The Student Edition ofMinitab, Addison-Wesley, New York, 1989.5Available fromASTM International Headquarters 100 Barr Harbor Drive, WestConshohocken, PA 19428.TABLE 2 Official Values for T (One-Sided Test) for OutliersNumber ofObservationsnUpper 0.1 %SignificanceLevelUpper 1.0 %SignificanceLevel3 1.155 1.1554 1.499 1.4925 1.780 1.7496 2.011 1.9447 2.201 2.0978 2.358 2.2219 2.492 2.32310 2.606 2.41011 2.705 2.48512 2.791 2.55013 2.867 2.60714 2.935 2.65915 2.997 2.705E1345 − 98 (2014)36.2 Select maximum allowable values of the standard errorof the estimated mean, as a fraction of the tolerance and as amultiple of the standard deviation of instrument. In the absenceof specified values of these quantities, use those recommendedin SAE J 1545: 0.1 times the tolerance and 2si. These valuesare used in Appendix X1.NOTE 4—This practice assumes that all measurements are subject to thecentral limit theorem of mathematical statistics, so that as the number ofreplicate or repeat measurements becomes large, the distribution of valuesis described by the standard normal distribution. It has been shown,6,7however, that averages of large numbers of measurements of a verificationstandard on a properly maintained spectrophotometer are not approxi-mated by the standard normal distribution. As a result, tests anchored to simay exhibit a significance or a power dependence different from thatwhich is expected.6.3 Determine the standard deviation of color or color-difference measurement, s, by making the appropriate measure-ment at least 10 times (n = 10), as follows:6.3.1 To assess the variability within a single specimen,measure the same specimen at ten or more randomly selecteddifferent areas of the specimen.6.3.1.1 Screen the measurement data for outliers and ex-treme values following 4.4.1 – 4.4.4.6.3.2 To assess the variability among specimens, measure atleast ten replicate specimens.6.3.2.1 Screen the measurement data for outliers and ex-treme values following 4.4.1 – 4.4.4.6.4 Determine the standard error of the estimated mean, se,for a sampling number of one, using Eq 3. Note that for N =1,se= s. Use the larger of the values of s determined in 6.3.1 or6.3.2.6.5 Compare the value of seto 0.1 times the tolerance and to2sIfor each of the three color or color-diffe