《BS-2846-1-1991.pdf》由会员分享，可在线阅读，更多相关《BS-2846-1-1991.pdf（42页珍藏版）》请在三一文库上搜索。
1、BRITISH STANDARD BS 2846-1: 1991 Guide to Statistical interpretation of data Part 1: Routine analysis of quantitative data Licensed Copy: sheffieldun sheffieldun, na, Mon Nov 27 12:35:47 GMT+00:00 2006, Uncontrolled Copy, (c) BSI BS 2846-1:1991 This British Standard, having been prepared under the d
2、irection of the Quality, Management and Statistics Standards Policy Committee, was published under the authority of the Standards Board and comes into effect on 20 December 1991 BSI 07-1999 First published as BS 2846, April 1957 Second edition as BS 2846-1, June 1975 Third edition December 1991 The
3、following BSI references relate to the work on this standard: Committee reference QMS/12 Draft for comment 86/60257 DC ISBN 0 580 19793 X Committees responsible for this British Standard The preparation of this British Standard was entrusted by the Quality, Management and Statistics Standards Policy
4、 Committee (QMS/-) to Technical Committee QMS/12, upon which the following bodies were represented: Association for Consumer Research (ACRE) Clay Pipe Development Association Limited Institute of Quality Assurance Institute of Statisticians Ministry of Defence Royal Statistical Society Amendments is
5、sued since publication Amd. No.DateComments Licensed Copy: sheffieldun sheffieldun, na, Mon Nov 27 12:35:47 GMT+00:00 2006, Uncontrolled Copy, (c) BSI BS 2846-1:1991 BSI 07-1999i Contents Page Committees responsibleInside front cover Forewordiii Section 1. General principles 0Introduction1 1Scope1 2
6、Definitions1 3Frequency tables1 4Graphical methods1 5Representative measures1 6Uncertainty of estimates1 7Rounding2 8Comparing estimates2 9General recommendations3 Section 2. Rules for presentation of experimental results 10General4 11Example of presentation4 Section 3. Rounding of observations 12Re
7、asons for rounding5 13The effect of rounding on variation5 14Rounding interval: definition and choice5 15Caution on rounding6 Section 4. Frequency distributions 16Purpose7 17Grouping into classes7 18Rules for grouping7 19Example of grouping7 20Presentation of tables9 21Graphical representation12 22S
8、ymmetry of distribution15 Section 5. Further condensation: arithmetic mean and standard deviation 23Necessity for further condensation16 24Measures of central tendency16 25Measures of dispersion16 26Computation of the mean and of the standard deviation17 27Rounding of means and standard deviations21
9、 Section 6. Uncertainty in estimation 28General22 29Distributions of means and standard deviations22 30Confidence limits and confidence intervals22 31Homogeneity25 32The assumption of normality27 Appendix A Presentation of numerical values (fineness of expression; rounding of numbers)28 Figure 1 Fre
10、quency distribution of compressive strengths of 400 concrete cubes (equal class widths)13 Figure 2 Frequency distribution of compressive strengths of 400 concrete cubes (general case)13 Licensed Copy: sheffieldun sheffieldun, na, Mon Nov 27 12:35:47 GMT+00:00 2006, Uncontrolled Copy, (c) BSI BS 2846
11、-1:1991 ii BSI 07-1999 Page Figure 3 Frequency curve for compressive strengths of 400 concrete cubes14 Figure 4 Percentage cumulative distribution of compressive strengths of 400 concrete cubes15 Figure 5 Scatter diagram for % P2O5 in fertilizer (from Table 6)15 Figure 6 Control charts for compressi
12、ve strength of 400 concrete cubes26 Table 1 Compressive strengths of concrete cubes (after 7 days)8 Table 2 Methods of classifying observations10 Table 3 Two ways of presenting a frequency distribution11 Table 4 Alternative way of defining classes in a frequency distribution11 Table 5 Two ways of pr
13、esenting a cumulative frequency distribution12 Table 6 Analysis of fertilizer (% P2O5)18 Table 7 Analysis of fertilizer (% P2O5): (difference from 11.00 %)19 Table 8 Calculation of mean and standard deviation of a frequency distribution21 Table 9 Factors for control lines for mean and range charts25
14、 Publication(s) referred toInside back cover Licensed Copy: sheffieldun sheffieldun, na, Mon Nov 27 12:35:47 GMT+00:00 2006, Uncontrolled Copy, (c) BSI BS 2846-1:1991 BSI 07-1999iii Foreword This Part of BS 2846 has been prepared under the direction of the Quality, Management and Statistics Standard
15、s Policy Committee. It supersedes BS 2846-1:1975 which is withdrawn. The principal change made from the previous edition is the addition of an appendix on rounding of observations and estimates to augment the guidance on rounding already given. This new appendix, which is a shortened version of BS 1
16、957:1953, replaces the previous Appendix A which explained the statistical terms used and is now no longer needed following the publication of BS 5532 “Statistical terminology”. Other changes include the addition of text in clause 6 to introduce the concept of hypothesis testing and modifications of
17、 the techniques to take account of the use of calculators and computers. In particular, the guidance formerly given on the estimation of the standard deviation from the range has been deleted, since the standard deviation can be easily obtained directly from a calculator, many of which are pre-progr
18、ammed for this purpose. (In practice, however, it seems likely that the mean range will continue to be used to calculate the numerical values for the action and warning lines used on control charts for the mean and the range.) The importance of correct interpretation and presentation of test results
19、 has been increasingly recognized in the analysis of data obtained from manufacturing processes based on sample determinations and prototype evaluations in industry, commerce and educational institutions. It was for this reason that subcommittee 2 of Technical Committee 69 “Application of statistica
20、l methods” of the International Organization for Standardization (ISO), was charged with the task of establishing a guide to statistical methods for the interpretation of test results. International agreement has already been reached on the specification of several techniques and these have been pub
21、lished as Parts of BS 2846, as follows. Part 1: Routine analysis of quantitative data; Part 2: Estimation of the mean: confidence interval (identical to ISO 2602); Part 3: Determination of a statistical tolerance interval (identical to ISO 3207); Part 4: Techniques of estimation and tests relating t
22、o means and variances (identical to ISO 2854); Part 5: Power of tests relating to means and variances (identical to ISO 3494); Part 6: Comparison of two means in the case of paired observations (identical to ISO 3301); Part 7: Tests for departure from normality (technically equivalent to ISO/DIS 547
23、9). Part 1 is concerned with the routine analysis, presentation and reduction of quantitative data, such as rounding of test results, which should be considered prior to applying the statistical tests given in later Parts. Part 2 specifies techniques for the calculation of confidence intervals for t
24、he mean of a normal population based on the results of a test applied to each of a random sample of individuals drawn from this population. It deals only with the case where the variance of the population is unknown. Part 3 specifies techniques for the estimation of statistical tolerance limits, i.e
25、. intervals containing, with a fixed probability, at least a given fraction of the population. It also includes a brief introduction to distribution-free methods of determining statistical tolerance limits, which are consequently valid when no assumptions can be made regarding the distribution of th
26、e underlying population. Part 4 relates the estimates of the means and variances of a sample to the population parameters and specifies the techniques required to examine certain hypotheses concerning the numerical values of those parameters. Licensed Copy: sheffieldun sheffieldun, na, Mon Nov 27 12
27、:35:47 GMT+00:00 2006, Uncontrolled Copy, (c) BSI BS 2846-1:1991 iv BSI 07-1999 Part 5 on the other hand specifies procedures for assessing the risks of drawing wrong conclusions from sample data when applying the techniques of Part 4. It permits the determination of appropriate sample sizes to keep
28、 the risks down to acceptable levels, and the determination of the most appropriate acceptance criterion to keep the risks in balance. Part 6 deals with the special case known as the method of paired comparisons, which Part 4 touches on briefly. Such cases can arise, for example, when two tests are
29、performed on each specimen in the sample, a first prior to the application of some treatment and the second after, in order to ascertain whether the treatment is effective or not. It is important to be aware of the various assumptions underlying the application of the methods, as stated in the text
30、of Parts 1 to 6. These assumptions can be satisfied in almost any situation if the experiment has been designed properly from a statistical standpoint and this standard is concerned with data arising from experiments that are satisfactory in this respect. Although not dealt with in the following pag
31、es, the design of experiments is an important subject to which experimenters should give careful thought, more thought than is sometimes given before an experiment is started. Most of the techiques for the analysis of quantitative data described in this standard assume that the items in the sample c
32、ome from a population which has a normal distribution. In certain cases this assumption is not critical but in others, unless it can be shown to be at least approximately true, the techniques should not be applied. This applies particularly to the estimation of statistical tolerance intervals as spe
33、cified in Part 3 and to the tests for variances in Part 4. This problem is discussed briefly in Parts 1 and 4 and in more detail in Part 7. Part 7 describes procedures which may be used to test whether apparent departures from normality can be regarded as sampling fluctuations or represent a signifi
34、cant degree of non-normality. Standards giving guidance on other techniques being developed at international level are: Estimation of a median Estimation of a proportion Comparison of a sample proportion with a given value Comparison of two proportions When these guides are published as internationa
35、l standards they will be considered for publication as dual-numbered British Standards, to provide further Parts of this standard. This standard does not contain methods for the collection of individuals in the random sample. In this respect references should be made to the particular British Standa
36、rds which specify the sampling procedures for a specific product. In the case of discrete items BS 6000, BS 6001 and BS 6002 contain general descriptions. The following British Standards also provide practical guidance on the application of statistical methods: BS 600, BS 2564, BS 5497, BS 5700, BS
37、5701, BS 57021), BS 5703, BS 6000, BS 60012), BS 6002. 1) In preparation. 2) BS 6001-0 is in preparation. Licensed Copy: sheffieldun sheffieldun, na, Mon Nov 27 12:35:47 GMT+00:00 2006, Uncontrolled Copy, (c) BSI BS 2846-1:1991 BSI 07-1999v A British Standard does not purport to include all the nece
38、ssary provisions of a contract. Users of British Standards are responsible for their correct application. Compliance with a British Standard does not of itself confer immunity from legal obligations. Summary of pages This document comprises a front cover, an inside front cover, pages i to vi, pages
39、1 to 32, 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 the amendment table on the inside front cover. Licensed Copy: sheffieldun sheffieldun, na, Mon Nov 27 12:35:47 GMT+00:00 2006, Uncon
40、trolled Copy, (c) BSI vi blank Licensed Copy: sheffieldun sheffieldun, na, Mon Nov 27 12:35:47 GMT+00:00 2006, Uncontrolled Copy, (c) BSI BS 2846-1:1991 BSI 07-19991 Section 1. General principles 0 Introduction It is generally agreed that reports of the results of investigations should preferably in
41、clude the observations that have been made, unless limitations of space preclude this. Even when it is possible to give the observations in full, it is preferable also to give the essential information in a condensed form for ease of interpretation. It is desirable, not only to do this in a uniform
42、way to avoid confusion, but also to ensure that the form adopted should follow the methods that have been found most satisfactory in practice. 1 Scope This Part of BS 2846 gives rules which are recommended for use in the condensation, interpretation and presentation of data; it is, however, restrict
43、ed to the consideration of observations of one variable only. This Part also deals with the uncertainty of various quantities estimated from the data, arising from the complex of variations which are termed errors. The applicability of the various measures of uncertainty depends on the validity of c
44、ertain assumptions, which are referred to in the text. Many of these assumptions are satisfied only if the experimental part of the investigation is designed properly from a statistical standpoint. NOTEThe titles of the publications referred to in this standard are listed on the inside back cover. 2
45、 Definitions For the purposes of this British Standard the definitions given in BS 5532 apply. 3 Frequency tables Although it may be desirable to present the whole of the original data, it is not always convenient to do so if the data are numerous. While a few values may be reported in the text and
46、cause no confusion, such a procedure with a large body of data might cause considerable interruption of the discussion. It is often better, therefore, to give full results in an appendix, and to include a condensed form of the data in the text. Some condensation is achieved by grouping. Grouped resu
47、lts may be presented in two ways, namely, as frequency tables or as cumulative frequency tables, and both ways are described in section 4. For most purposes grouping is of little value if fewer than thirty results are available. 4 Graphical methods In general, it is not difficult to grasp the inform
48、ation in a comparatively small number (ten or fewer) of values. It is, however, beyond the ability of most people to visualize the general features of a mass of data, even when grouped into classes, and the use of diagrams will usually facilitate interpretation. The diagrams most frequently used for
49、 this purpose are stem-and-leaf displays, the histogram and the cumulative diagram; these are described in section 4. 5 Representative measures Even the grouped data cannot be used readily for comparison with other data or information; further condensation is required for this purpose. Two statistics, the sample arithmetic mean and the sample standard deviation, are for many purposes adequate to represent the given data; these are described in section 5 and methods of calculating them are given. In some circumstances other statistics