1、BRITISH STANDARD BS2846-1: 1991 Guide to Statistical interpretation of data Part1: Routine analysis of quantitative dataBS2846-1:1991 This British Standard, having been prepared under the directionof the Quality, Management and Statistics Standards Policy Committee, waspublished under the authorityo
2、f the Standards Boardand comes into effect on 20December1991 BSI07-1999 First published as BS2846, April1957 Second edition as BS2846-1, June1975 Third edition December1991 The following BSI references relate to the work on this standard: Committee reference QMS/12 Draft for comment86/60257DC ISBN 0
3、 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 Committee (QMS/-) to Technical Committee QMS/12, upon which the following bodies were represented: Association for Consumer
4、Research (ACRE) Clay Pipe Development Association Limited Institute of Quality Assurance Institute of Statisticians Ministry of Defence Royal Statistical Society Amendments issued since publication Amd. No. Date CommentsBS2846-1:1991 BSI 07-1999 i Contents Page Committees responsible Inside front co
5、ver Foreword iii Section 1. General principles 0 Introduction 1 1 Scope 1 2 Definitions 1 3 Frequency tables 1 4 Graphical methods 1 5 Representative measures 1 6 Uncertainty of estimates 1 7 Rounding 2 8 Comparing estimates 2 9 General recommendations 3 Section 2. Rules for presentation of experime
6、ntal results 10 General 4 11 Example of presentation 4 Section 3. Rounding of observations 12 Reasons for rounding 5 13 The effect of rounding on variation 5 14 Rounding interval: definition and choice 5 15 Caution on rounding 6 Section 4. Frequency distributions 16 Purpose 7 17 Grouping into classe
7、s 7 18 Rules for grouping 7 19 Example of grouping 7 20 Presentation of tables 9 21 Graphical representation 12 22 Symmetry of distribution 15 Section 5. Further condensation: arithmetic mean and standard deviation 23 Necessity for further condensation 16 24 Measures of central tendency 16 25 Measur
8、es of dispersion 16 26 Computation of the mean and of the standard deviation 17 27 Rounding of means and standard deviations 21 Section 6. Uncertainty in estimation 28 General 22 29 Distributions of means and standard deviations 22 30 Confidence limits and confidence intervals 22 31 Homogeneity 25 3
9、2 The assumption of normality 27 Appendix A Presentation of numerical values (fineness of expression; rounding of numbers) 28 Figure 1 Frequency distribution of compressive strengths of400 concrete cubes (equal class widths) 13 Figure 2 Frequency distribution of compressive strengths of400 concrete
10、cubes (general case) 13BS2846-1:1991 ii BSI 07-1999 Page Figure 3 Frequency curve for compressive strengths of400 concrete cubes 14 Figure 4 Percentage cumulative distribution of compressive strengths of400 concrete cubes 15 Figure 5 Scatter diagram for% P 2 O 5in fertilizer (from Table 6) 15 Figure
11、 6 Control charts for compressive strength of400 concrete cubes 26 Table 1 Compressive strengths of concrete cubes (after7 days) 8 Table 2 Methods of classifying observations 10 Table 3 Two ways of presenting a frequency distribution 11 Table 4 Alternative way of defining classes in a frequency dist
12、ribution 11 Table 5 Two ways of presenting a cumulative frequency distribution 12 Table 6 Analysis of fertilizer (% P 2 O 5 ) 18 Table 7 Analysis of fertilizer (% P 2 O 5 ): (difference from11.00%) 19 Table 8 Calculation of mean and standard deviation of a frequency distribution 21 Table 9 Factors f
13、or control lines for mean and range charts 25 Publication(s) referred to Inside back coverBS2846-1:1991 BSI 07-1999 iii Foreword This Part of BS2846 has been prepared under the direction of the Quality, Management and Statistics Standards Policy Committee. It supersedes BS2846-1:1975 which is withdr
14、awn. 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 BS1957:1953, replaces the previous Appendix A which explained the st
15、atistical terms used and is now no longer needed following the publication of BS5532 “Statistical terminology”. Other changes include the addition of text in clause 6 to introduce the concept of hypothesis testing and modifications of the techniques to take account of the use of calculators and comp
16、uters. 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-programmed for this purpose. (In practice, however, it seems likely tha
17、t 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 has been increasingly recognized in the analysis of data obtained
18、 from manufacturing processes based on sample determinations and prototype evaluations in industry, commerce and educational institutions. It was for this reason that subcommittee2 of Technical Committee69 “Application of statistical methods” of the International Organization for Standardization (IS
19、O), 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 published as Parts of BS2846, as follows. Part1: Routine analysis of qu
20、antitative data; Part2: Estimation of the mean: confidence interval (identical to ISO2602); Part3: Determination of a statistical tolerance interval (identical to ISO3207); Part4: Techniques of estimation and tests relating to means and variances (identical to ISO2854); Part5: Power of tests relatin
21、g to means and variances (identical to ISO3494); Part6: Comparison of two means in the case of paired observations (identical to ISO3301); Part7: Tests for departure from normality (technically equivalent to ISO/DIS5479). Part1 is concerned with the routine analysis, presentation and reduction of qu
22、antitative data, such as rounding of test results, which should be considered prior to applying the statistical tests given in later Parts. Part2 specifies techniques for the calculation of confidence intervals for the mean of a normal population based on the results of a test applied to each of a r
23、andom sample of individuals drawn from this population. It deals only with the case where the variance of the population is unknown. Part3 specifies techniques for the estimation of statistical tolerance limits, i.e.intervals containing, with a fixed probability, at least a given fraction of the pop
24、ulation. 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 the underlying population. Part4 relates the estimates of the means and variances of a s
25、ample to the population parameters and specifies the techniques required to examine certain hypotheses concerning the numerical values of those parameters.BS2846-1:1991 iv BSI 07-1999 Part5 on the other hand specifies procedures for assessing the risks of drawing wrong conclusions from sample data w
26、hen applying the techniques of Part4. It permits the determination of appropriate sample sizes to keep the risks down to acceptable levels, and the determination of the most appropriate acceptance criterion to keep the risks in balance. Part6 deals with the special case known as the method of paired
27、 comparisons, which Part4 touches on briefly. Such cases can arise, for example, when two tests are 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 b
28、e aware of the various assumptions underlying the application of the methods, as stated in the text of Parts1 to6. 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 fr
29、om experiments that are satisfactory in this respect. Although not dealt with in the following pages, 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
30、the analysis of quantitative data described in this standard assume that the items in the sample come 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
31、 be applied. This applies particularly to the estimation of statistical tolerance intervals as specified in Part3 and to the tests for variances in Part4. This problem is discussed briefly in Parts1 and4 and in more detail in Part7. Part7 describes procedures which may be used to test whether appare
32、nt departures from normality can be regarded as sampling fluctuations or represent a significant 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
33、 a given value Comparison of two proportions When these guides are published as international 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 t
34、he random sample. In this respect references should be made to the particular British Standards which specify the sampling procedures for a specific product. In the case of discrete items BS6000, BS6001 and BS6002 contain general descriptions. The following British Standards also provide practical g
35、uidance on the application of statistical methods: BS600, BS2564, BS5497, BS5700, BS5701, BS5702 1) , BS5703, BS6000, BS6001 2) , BS6002. 1) In preparation. 2) BS6001-0 is in preparation.BS2846-1:1991 BSI 07-1999 v A British Standard does not purport to include all the necessary provisions of a cont
36、ract. 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, pagesi tovi, pages1to32, an inside back cover a
37、nd 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.vi blankBS2846-1:1991 BSI 07-1999 1 Section 1. General principles 0 Introduction It is generally agreed that reports
38、of the results of investigations should preferably include 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 interpretatio
39、n. It is desirable, not only to do this in a uniform 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 BS2846 gives rules which are recommended for use in the condensation, interpretatio
40、n and presentation of data; it is, however, restricted 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
41、measures of uncertainty depends on the validity of certain 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
42、this standard are listed on the inside back cover. 2 Definitions For the purposes of this British Standard the definitions given in BS5532 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.
43、While a few values may be reported in the text and 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
44、 condensation is achieved by grouping. Grouped results may be presented in two ways, namely, as frequency tables or as cumulative frequency tables, and both ways are described in section4. For most purposes grouping is of little value if fewer than thirty results are available. 4 Graphical methods I
45、n general, it is not difficult to grasp the information 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 int
46、erpretation. The diagrams most frequently used for this purpose are stem-and-leaf displays, the histogram and the cumulative diagram; these are described in section4. 5 Representative measures Even the grouped data cannot be used readily for comparison with other data or information; further condens
47、ation 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 section5 and methods of calculating them are given. In some circumstances other statistics may be more
48、appropriate. Some of these alternative statistics are also described in section5. 6 Uncertainty of estimates It is a matter of experience that observations made under apparently identical conditions usually show some variation, because of factors outside the experimenters control. Such variation in
49、the observations leads to related, but smaller, variation in means and in standard deviations calculated from the observations. Thus, since experiments when repeated usually give results with slightly different means and standard deviations, the mean and the standard deviation estimated from a single group of results are subject to some uncertainty.BS2846-1:1991 2 BSI 07-1999 This uncertainty can lead to results which apparently run counter to an established hypothesis about the process producing the data. It is then necessary to te
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