1、BRITISH STANDARD BS 2987:1958 Notes on The application of statistics to paper testingBS2987:1958 This BritishStandard, having been approved by the Paper Industry Standards Committeeand endorsed by theChairman ofthe Chemical Divisional Council,was publishedunder theauthority ofthe General Council on
2、27May1958 BSI 03-2000 The following BSI references relate to the work on this standard: Committee reference PAC/11 Draft for comment CX(PAC)8756 ISBN 0 580 35830 5 The following is a list of members of the Paper Industry Standards Committee, who have had the preparation of this standard under consid
3、eration: Chairman: Mr. L. G. Cottrall Vice-Chairman: Mr. G. F. Underhay Mr. B. G. E. Heywood, M.C. Board of Trade Mr. A. Kirk British Federation of Master Mr. L. G. White Printers Dr. N. R. Hood British Paper and Board Industry Research Association Dr. C. Binns British Paper and Board Makers Associa
4、tion Mr. R. W. H. Bray Mr. F. D. Broadbent Dr. W. Burt Mr. E. E. Capon Mr. L. G. Cottrall Dr. Julius Grant Mr. A. Gemmell Dr. H. Ainsworth Harrison Mr. S. H. Hough Mr. H. G. Paul Dr. H. F. Rance Mr. S. F. Smith Mr. F. H. Llewellyn Thomas Mr. G. F. Underhay Mr. A. C. Vincent Mr. W. Whiteley, J.P. Mr.
5、 J. ONeill British Railways, The British Transport Commission Mr. G. Newman Coated Paper and Board Makers Mr. K. Timberlake Association Mr. H. L. Morbey Envelope Makers and Manufacturing Stationers Association Mr. L. G. Smith H.M. Stationery Office Mr. E. L. Hill Ministry of Supply Mr. J. E. Pickeri
6、ng National Association of Paper Mr. C. J. Thorne, O.B.E. Merchants Dr. V. G. W. Harrison Printing, Packaging and Allied Trades Research Association Mr. F. Bolam Technical Section of the British Dr. H. F. Rance Paper & Board Makers Association Mr. G. Thompson Co-opted. (Chairman of Technical Committ
7、ee on Methods of Test) BS2987:1958 BSI 03-2000 The following is a list of members of the Technical Committee on Methods of Test for Paper, Board and Pulp: the Committee actually responsible for the preparation of the standard: Chairman: Mr. G. Thompson Vice-Chairman: Mr. C. A. Chester Mr. A. Kirk Br
8、itish Federation of Master Printers Mr. W. E. Bennett British Paper and Board Industry Research Association Mr. A. Baker British Paper and Board Makers Mr. L. G. Cottrall Association Mr. L. G. S. Hebbs British Woodpulp Association Mr. R. Allum Crown Agents for Oversea Governments and Administrations
9、 Mr. E. Halson, M.B.E. H.M. Stationery Office Mr. K. MacIntyre Ministry of Supply Dr. C. Binns Technical Section of the British Paper and Board Makers Association Mr. F. Bolam Mr. F. Bridge Mr. C. A. Chester Mr. T. H. Farebrother Mr. G. F. Glover Mr. I. F. Hendry Mr. L. F. Hopkins Dr. F. L. Hudson M
10、r. L. A. Lawrence Mr. D. McNeill Dr. H. F. Rance Mr. G. Thompson Mr. A. F. Tout Mr. H. G. Tyler Mr. G. F. Underhay Dr. V. G. W. Harrison Printing, Packaging and Allied Mr. R. R. Coupe Trades Research Association Mr. J. Meighan Society of British Soap Makers Amendments issued since publication Amd. N
11、o. Date Comments BS2987:1958 ii BSI 03-2000 Contents Page Foreword ii Introduction 1 Section 1. A practical problem from paper testing 2 Section 2. Application of statistical tests to the example 4 Section 3. Introduction to statistical methods 6 1 Distribution of results 6 2 Sampling from a populat
12、ion 6 3 Standard deviation (B) 7 4 Coefficient of variation ( ) 7 5 Estimation of the mean and the standard deviation from a sample 7 6 Precision of the mean: Confidence limits 8 7 Number of tests required for a given precision of the mean 9 8 Significance of difference between means of two tests 9
13、9 Students t test 10 Section 4. Example of calculation of Standard deviation, precision of mean and application to t tests, together with recommended computing procedures 14 Section 5. Applications to paper testing 16 References 25 Appendix A Rejection of abnormal results 18 Appendix B Note on the u
14、se of range 19 Appendix C Coefficient of variation for various paper tests 19 Appendix D Table for t for various numbers of degrees of freedom 21 Appendix E Formulae for easy reference 21 Appendix F Glossary of statistical terms and symbols 22 Figure 1 6 Figure 2 8 Figure 3 10 Figure 4 11 Figure 5 1
15、2BS2987:1958 BSI 03-2000 iii Foreword This standard makes reference to the following BritishStandards: BS600, Application of statistical methods to industrial standardization and quality control. BS2846, The reduction and presentation of experimental results. BS . . . . Sampling paper for testing 1)
16、 . This BritishStandard is based upon British PBMA Method S1:1955, prepared by the Statistics Committee of the Technical Section of the British Paper and Board Makers Association, to which Committee grateful acknowledgment is made for the considerable amount of work involved in its preparation. The
17、standard, which is one of a series for paper testing, is published under the authority of the Paper Industry Standards Committee. The other standards so far published in this series are: BS2644, Sizing properties of paper Method of testing the degree of water resistance. BS2699, The absorbency of bl
18、otting paper Determination of ink absorbency time. BS2916, Absorbency test for bibulous paper. BS2922, Methods for testing the strength of wet paper. BS2923, The printing opacity of paper. BS2924, Methods for determining the pH value of aqueous extracts of paper. BS2925, Methods for determining the
19、air permeability and air resistance of paper. This standard has two purposes. One is to arouse the interest of persons engaged on paper testing in elementary statistical methods. The other is to provide an easy source of reference to the formulae required for the treatment of data, so as to satisfy
20、the general reporting clauses included in most of the paper testing methods. To that extent it is complementary to the BritishStandards enumerated above. It is hoped that this explanation will make the layout of this standard more intelligible to the general reader, for the dual purpose has inevitab
21、ly resulted in the juxtaposition of elementary and more advanced concepts. A British Standard does not purport to include all the necessary provisions of a contract. Users of British Standards are responsible for their correct application. Compliance with a British Standard does not of itself confer
22、 immunity from legal obligations. Summary of pages This document comprises a front cover, an inside front cover, pagesi to iv, pages1to24, an inside back cover and a back cover. This standard has been updated (see copyright date) and may have had amendments incorporated. This will be indicated in th
23、e amendment table on the inside front cover. 1) In course of preparation.iii blankBS2987:1958 BSI 03-2000 1 Introduction The problems of sampling and the reliability of results obtained in paper testing are clearly cases for the application of statistical methods, and in recent years a number of pap
24、ers have been published indicating the growing interest in statistical methods in the paper trade. The results of paper tests are usually subject to appreciable variation, due not only to experimental error, but also to variation in the raw materials and to the operation of many unknown or random fa
25、ctors in the manufacturing process. The interpretation of test results therefore requires some care and the chief value of statistical methods in this connection lies in their ability to replace purely subjective judgments of the data by objective criteria such as the t test, which is described in t
26、he text. Statistical analysis of the data cannot add to the accuracy of an experiment by turning an uncertain result into a certainty, but it can enable the conclusions to be expressed more precisely in terms of a definite probability. Although statistical methods have their foundation in mathematic
27、al theories of probability, a knowledge of such theories is not required for the successful application of these methods. Only straightforward arithmetical processes are involved and, in many cases, the calculation does not require the use of a machine. One or two shortcut methods to simplify calcul
28、ations are given. The purpose of the present notes is to give only a brief outline of the subject, but with sufficient detail to enable the reader to carry out the simpler statistical calculations on his test data, such as those for ascertaining the precision of test means and the significance of di
29、fferences in test means. For the more advanced techniques, such as that of analysis of variance, which can be of great utility for the comparison of instruments and for the analysis of causes of variation in test readings, reference is made to appropriate textbooks. A secondary purpose of these note
30、s is to secure greater uniformity in the presentation of test results and in the use of statistical terms and symbols (see Glossary, Appendix F). In the opinion of the Committee responsible for the preparation of these notes, the problems of sampling depend too much on particular conditions (such as
31、 of manufacture and storage) to be capable of statistical treatment here, although some consideration has been given to these matters in the preparation of BS. . . . 2)“Sampling paper for testing.” Problems of sampling are being considered by the Statistics Committee of the Technical Section of the
32、British Paper and Board Makers Association and will be the subject of a future publication. 2) In course of preparation. Pending completion, see British PBMA Method PT2:1951, published by the Technical Section of the British Paper and Board Makers Association.BS2987:1958 2 BSI 03-2000 Section 1. A p
33、ractical problem from paper testing Imagine that a paper merchant is accustomed to supplying a certain kraft paper A for bag making. He knows from experience over a long period of time that this material is satisfactory, but recently he has been offered quantities of papers B, C and D at attractive
34、prices. As a safeguard against complaints, he decides to test the papers for strength before attempting to pass them on to his clients. He carries out burst tests, ten for each paper, under comparable conditions and gets the following results: The purpose of these tests is to show up differences of
35、strength of the four papers, and probably the first thing the merchant will do with the figures is to run his eye up and down the columns, This may be sufficient to answer the questions, but, if the figures are difficult to compare, he will calculate the means or average values of the sets of ten re
36、sults. In doing this, although he perhaps neither knows nor cares, he has applied statistical methods of analysis to the sets of figures. He has deduced a derived quantity or statistic which gives information in a succinct form about the readings. What do these mean values tell him? One person may c
37、onclude from the four means that papers B and C are stronger than A and paper D is weaker. Another may be more cautious. He knows that any test on paper is subject to considerable variability that is why he has done ten tests instead of one and there is therefore some uncertainty about the mean valu
38、es. He may conclude that, since the test average of C is8percent higher than that of A, C is appreciably stronger, and B possibly stronger than A. The result for D is about1percent weaker and, although he may have doubts about the significance of this result, he will perhaps reject paper D, just to
39、be on the safe side. The mean value is not enough The variability of the readings has to be considered. In the unrealistic case where all ten readings on paperA happened to be57.4 and those on B60.3 it could be confidently asserted that B is stronger than A. In practice, some variability is to be ex
40、pected, and the greater this is the more doubtful does the conclusion become. As the variability increases further, it becomes obvious that there is no reliable evidence of a difference of strength between the two papers. Ways of assessing variability A rough impression can be obtained by running ov
41、er the figures by eye, but conclusions drawn from this procedure are subjective. If the variability has to be expressed in a report the highest and lowest values can be used, or the range, but again the interpretation of these statements is open to doubt. The mean deviation (see Glossary, Appendix F
42、) is a better expression of variability but it is of limited usefulness. Burst tests (lb/sq. in.) A B C D 59 56 55 62.5 54 61.5 58.5 54.5 52.5 60 59 59 61.5 59 56.5 66.5 64 62.5 56 59 57 67.5 62 54 70 57 65.5 65 60 66 63.5 60.5 53 52.5 43 62.5 61 57 57.5 58 A B C D Mean 57.4 60.3 62.4 56.9BS2987:195
43、8 BSI 03-2000 3 The most satisfactory way to express variability is to calculate the standard deviation, also called the root mean square deviation. This is the most efficient way of expressing the variability, because it remains more constant than the others in repeated sets of figures. The range,
44、for example, may vary relatively more than the standard deviation from one set of readings to another because it depends only on the two extreme values in each set. The standard deviation is more difficult to calculate than the range or mean deviation, but this is more than compensated by its versat
45、ility. It is fundamental to statistical analysis. The coefficient of variation is closely related. It is the standard deviation expressed as a percentage of the mean value. It often has the useful property of typifying a material. If a series of kraft papers were made from the same stock the burstin
46、g strength and standard deviation should increase with basis weight, but the coefficient of variation should be relatively constant. The sample itself is another variable Only a small part of the consignment of paper A was tested and this sample has been assumed to be representative of the paper as
47、a whole. If another sample were to be tested, it is likely that a different value of burst would be obtained and this might lead to different conclusions. When a large series of similar samples is tested, however, a definite pattern begins to arise. Different values of the mean will occur with diffe
48、rent frequencies which will approach steady values as more and more samples are tested. On the basis of this phenomenon, statements can be made about a single sample which take care of the variability of the samples. Why use statistics in paper testing? In certain simple situations, conclusions can
49、be reached without any reasonable doubt. It should be recognized, however, that personal judgment often plays a large part in arriving at a decision. This may be tempered by experience but, unless statistical methods are used, at least one guess is involved. Statistics eliminates the guesses. Instead of a forthright statement that the bursting strength of paper A is57.4lb/sq. in. (which may be proved wrong by the next sample
