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1、INTERNATIONAL STANDARD INTERNATIONAL ORGANIZATION FOR STANDARDIZATION ORGANISATION INTERNATIONALE DE NORMALISATION MEXAYHAPO)JHAR OPrAHLlSAklR IlO CTAHAPTM3AkWl Ferroalloys - Experimental methods for checking the bias of sampling and sample preparation Ferro-alliages - M on either 10 gross samples o
2、r 10 sub-samples). 3.5 Selection of methods of data analysis When individual increments taken by Method A and by Method B are correctly paired, the method of analysis for paired data shall be applied. When pairing of individual increments taken by Method A and by Method 6 is not conducted, the metho
3、d of analysis for unpaired data shall be applied. When the number of experiments is the same, the method of analysis for paired data is higher in sensitivity, in a statistical sense, than that for unpaired data in detecting the significance of difference. In order to apply the method of paired data
4、analysis, it is necessary to design and perform the experiment so that pairing of increments, one from Method A and the other from Method B, is assured technically. The method of analysis for unpaired data is based on the con- dition that the number of measurements of Method A and of Method B are th
5、e same. Care should be taken to obtain the same number of increments for both of the methods. NOTE - The prescribed methods for statistical analysis of experimen- tal data may also be applied to the case of checking the difference in the results obtained from different samples of one consignment tak
6、en at different places, for example, a loading point and a discharging point (see clause 6). 4 Experimental methods 4.1 Examples of experiment The reference methods (Method A) are different and vary ac- cording to the intended purposes, and it is therefore difficult to establish rigid rules. Example
7、s of reference methods are given below. The methods to be checked (Method B) are given in relation to the respective reference methods. 1 Copyright International Organization for Standardization Provided by IHS under license with ISO Licensee=NASA Technical Standards 1/9972545001 Not for Resale, 04/
8、21/2007 10:22:46 MDTNo reproduction or networking permitted without license from IHS -,-,- IS0 7347 : 1997 (El Example 1: Bias due to mass increment Method A: A reference sample is a composite of in- crements of larger mass than the mass specified for routine sampling. Method B : A sample is a compo
9、site of increments of equal or smaller masses than those specified for routine sampling which is considered to introduce no bias into the sample. NOTE - Segregation of quality of ferroalloys is normally observed along the vertical direction of crushed ingots. Care should therefore be taken in taking
10、 the increments of reference samples. Example 2: Sampling of ferroalloys in bulk Method A: A reference sample is a composite of in- crements taken from new surfaces of the ferroalloy exposed during loading or unloading a consignment. Method B: A sample is a composite of increments taken from stockpi
11、les. Example 3: Sampling of ferroalloys packed in containers Method A : A reference sample is a composite of the entire quantity of packed units of the ferroalloy taken as the in- crements. Method B: A sample is a composite of increments taken from several points selected at random within packed uni
12、ts of the ferroalloy. . Example 4: Drilled sample Method A: A reference sample is a composite of in- crements taken by drilling from the top surface through to the bottom surface of ferroalloy lumps having vertical crushed surfaces. Method B : A sample is a composite of increments taken by drilling
13、in random order from several points on ferroalloy lumps of which the top and bottom surfaces are not clear. Example 5: Ladle sampling Method A: A reference sample is a composite of in- crements of specified mass and specified number taken from a consignment constituted by the tapped lot method. Meth
14、od B : A sample is a composite of ladle samples taken from a corresponding consignment. Example 6: Mechanical sample dividing apparatus Method A: A reference sample is the rest of a sample ob- tained after the divided sample has been taken. Method B: A sample is a divided sample obtained by a routin
15、e method. 4.2 Sampling 4.2.1 Two gross samples shall be taken from the same con- signment under study or the same part of the consignment: one of the two is by Method A and the other by Method B. The gross sample taken by Method A is designated as gross sample A and the one taken by Method B as gros
16、s sample B. NOTE - For the purposes of checking the difference in the results ob- tained from different samples of one consignment (see note in 3.51, either of the two samples is regarded as gross sample A and the other as gross sample B. 4.2.2 Each pair of increments for constituting the gross samp
17、les A and B shall be taken from the same point of a ferroalloy consignment. 4.2.3 When pairing of increments is not intended, gross sample A shall be the one obtained by Method A and gross sample B the one obtained by Method B. 4.3 Preparation of samples 4.3.1 For the cases of examples 1 through 5 i
18、n 4.1, when checking the bias of sampling, the two gross samples A and B shall be processed separately by the same method for the preparation of the respective test samples A and B. 4.3.2 For the case of example 6, when checking the bias of sample preparation, two different test samples A and B shal
19、l be prepared separately from the same gross sample or from the same sub-sample. 4.4 Determination and recording The quality characteristic shall be determined on the test samples A and B by the same method. The results of chemical determination shall be recorded in a data log such as those shown as
20、 examples in tables 1 and 2. Table 1 is applicable to the case of paired increments and table 2 to unpaired increments. 2 Copyright International Organization for Standardization Provided by IHS under license with ISO Licensee=NASA Technical Standards 1/9972545001 Not for Resale, 04/21/2007 10:22:46
21、 MDTNo reproduction or networking permitted without license from IHS -,-,- IS0 7347 : 1987 (E) Table 1 - Example of a data log of a t-test of paired data. (For explanation of the symbols, see annex A.) Designation of experiment : Type and grade of ferroalloy : (for example, ferrochromium A) Identifi
22、cation of consignment (or gross sample) : Date of experiment: Quality characteristic Increment for example, % (m/m) Crl No. xBi xAi di = XBi - XAi d; 1 2 k Sum I I I Calculation for t-test on one consignment : 2 = (plus or minus) v, = t, = t I; 0,025) = Statement on the result of the t-test : NOTE -
23、 The experimental conclusion is derived from the overall result obtained after the repetition of experiments on at least ten consignments (or parts of the consignments) of the same type of ferroalloy. Table 2 - Example of a data log of a t-test of unpaired data (For explanation of the symbols, see a
24、nnexes B and C.) Designation of experiment : Type and grade of ferroalloy: (for example, ferrochromium A) Identification of consignment (or gross sample) : Date of experiment: Quality characteristic Consign- Grade of for example, % kfzlm) Crl ment ferro- No. alloy Gross sample B Gross sample A xBi x
25、Bi x 0,025) = Statement on the result of the t-test : 3 Copyright International Organization for Standardization Provided by IHS under license with ISO Licensee=NASA Technical Standards 1/9972545001 Not for Resale, 04/21/2007 10:22:46 MDTNo reproduction or networking permitted without license from I
26、HS -,-,- ISO7347:1967(E) 5 Data analysis 5.1 Test for significance of difference The test for significance of difference between two experimen- tal results, in other words, the deviation of the results of Method B from the results of reference Method A, shall be car- ried out by a statistical method
27、 called the t-test. For unpaired data, prior to conducting the t-test, the F-test for equality of the two variances of both of the methods shall be carried out. The analysis of data according to the note in 3.5 shall be made by the procedure given in 5.3. 5.2 Paired data 5.2.1 Calculate the observed
28、 value of t, denoted by t,. The method of calculation is given in annex A. 5.2.2 Compare the absolute value of to obtained by iment with the t(; 0,025) point obtained from table annex A) : exper- 3 (see When 1 t, 1 t(; 0,025), then dis significant. NOTE - See clause 6 for the conclusions that may be
29、 drawn from the outcome of these tests. 5.3 Unpaired data 5.3.1 The equality of the variance of the results of Method A and the variance of the results of Method B shall be tested by a statistical method called the F-test referred to as the variance ratio test. The method of calculation is given in
30、annex 6. 5.3.2 Compare the observed F, value obtained by experiment with the F(; 0.05) point obtained from table 3 (see annex B). When F, F(; 0,051, then the test is failed. 5.3.3 If the F-test is passed, apply the t-test. If the F-test is failed, reject the experimental re.sults, and, if necessary,
31、 carry out a further experiment. 5.3.4 The method of calculation for the t-test for significance of difference is given in annex C. 5.3.5 Compare the absolute value of t, obtained by exper- iment with the t(; 0,025) point obtained from table 3 (see annex A). When 1 t, I t (; 0,025), then ,d is signi
32、ficant. NOTE - See clause 6 for the conclusions that may be drawn from the outcome of these tests. 6 Review of experimental results In the event that the difference between the results obtained from Method B and Method A is insignificant by the t-test, then Method B may be adopted as a routine metho
33、d, provided that an agreement is reached between the interested parties, where such is required. The following conditions shall also be taken into account: a) The absence of bias means that the value obtained from routine operations does not depart from the true value or reference value in this meth
34、od with a statistically significant difference. b) If, even though the difference is statistically significant, it is regarded as being negligible from a practical standpoint, Method B may be adopted as a routine method, provided that the interested parties agree, where this is required. c) When the
35、 difference is statistically insignificant but is regarded as being so large as to be significant from a practi- cal standpoint by the interested parties, a further exper- iment shall be carried out. Copyright International Organization for Standardization Provided by IHS under license with ISO Lice
36、nsee=NASA Technical Standards 1/9972545001 Not for Resale, 04/21/2007 10:22:46 MDTNo reproduction or networking permitted without license from IHS -,-,- IS0 7347 : 1987 (E) Annex A Method of calculation of the t-test for paired data (This annex forms an integral part of the Standard.) A.1 Calculate
37、the difference between paired measurements : dj = XB - XAi i= 1,2,.,k . . . (I) di is the ith difference or deviation Of xaj from XAi; xai is the ith measurement of sample B obtained by method B to be controlled; xAi is the ith measurement of sample A obtained by the reference method A; k is the num
38、ber of pairs of measurements. A.2 Calculate the mean value of differences to one decimal place more than that used in the measurements themselves : k is the number of degrees of freedom - in this method =k-1. A.4 Calculate the observed value of t, denoted by t, by rounding off to the third decimal p
39、lace: ;i t, = . . . (4) . . (2) A.5 Obtain the statistic t point at a 2,5 % level of significance for qt degrees of freedom, denoted by it; 0,025). from table 3. d is the mean value of k differences. Table 3 - Point of t(t); 0,025) (two-sided) fP 9 10 11 12 13 14 t 2,262 2,228 2,201 2,179 2,160 2,14
40、6 15 16 17 18 19 20 t 2,131 2,120 2,110 2,101 2,693 2,686 5 Copyright International Organization for Standardization Provided by IHS under license with ISO Licensee=NASA Technical Standards 1/9972545001 Not for Resale, 04/21/2007 10:22:46 MDTNo reproduction or networking permitted without license fr
41、om IHS -,-,- IS0 7347 : 1987 (E) Annex B Method of calculation of the F-test for uripaired data (This annex forms an integral part of the Standard.) B.l For the sake of simplicity, transform the crude measurements to integers : XAi = (XAi - Cl)h i= 1,2,.,n 1 (5) x,j = (XBj - c2)h i= 1,2,.,n where Xn
42、i, Xei are the respective ith transformed measurements of sample A and of sample B; x Cl1 CP are the respective subtracting constants arbitrarily selected separately for the transformation; h is the multiplying constant arbitrarily selected for the transformation; n is the number of measurements of
43、sample A and of sample B. B.2 Calculate the mean values of measurements of samples A and B, denoted byYA and Xe, respectively, and express them by inverting the transformation B.4 Calculate the unbiased estimates of variance, denoted by VA and Vs, respectively: VA = 2 I . . . (8) VB = A- B J where A
44、 and a are the respective degrees of freedom of sample A and of sample B, A = nA - 1, #a = ne - 1; in this method n A = “B = n. B.5 Calculate the ratio of vs of Method B to VA of the reference Method A using equation (9). rounding off to the second decimal place. NOTE - In this method it is assumed
45、that the variance of the reference Method A would be smaller than that of Method B (V, Va), change the denominator for the numerator so that the ratio is greater than unity, and use equa- tion (IO). F, = v, vA F, 1 . . . (9) or ,rB=(+$,xBi)+c2 j F, = -!- VB F, 1 . . . . . . (6) B.3 Calculate the squ
46、are sums denoted by SA and sa, respectively : sA;( $,xiie ;($,xAi)2j$ 1 B.6 Obtain the statistical F point at a 5 % level of significance for e and #A degrees of freedom (s = A = I, denoted by F; 0,051, from table 4. Table 4 - Point of F(d; 0.05) 9 10 12 15 20 F 3,18 2,98 2,69 2.40 2,12 . . . (7) sB
47、=$,i-$($,xBi)2)+2 J 6 Copyright International Organization for Standardization Provided by IHS under license with ISO Licensee=NASA Technical Standards 1/9972545001 Not for Resale, 04/21/2007 10:22:46 MDTNo reproduction or networking permitted without license from IHS -,-,- IS0 7347 : 1987 (E) Annex
48、 C Method of calculation of the t-test for unpaired data (This annex forms an integral part of the Standard.) The observed value of the statistic t, denoted by to, shall be calculated by rounding off to the third decimal place as follows: to= /-$j-$Q . . . Hence to= ;fgy$ where A = nA - 1, 4 = nB - 1 and A = B = . . . (12) 7 Copyright International Organization for Standardization Provided by IHS under license with ISO Licensee=NASA Technical Standards 1/9972545001 Not for Resale, 04/21/2007 10:22:46 MDTNo reproduction or networking permitted without license from IHS -,