摘要:

SummaryPhysicists and chemists hardly ever use the standard deviation for expressing the errors of their observations. This is attributed to the facts that the error theory as commonly treated in textbooks on physics is based too exclusively on the normal frequency distribution, and leaves some of the most important practical problems unanswered.The main advantage of mean and standard deviation lies in the very simple mathematical relations satisfied by these quantities regardless of the shape of the frequency distribution. These relations are discussed in the first part of this paper, while in the second part they are employed for a thorough treatment of the degree of rounding off permissible in practice. The following rules of thumb are derived:The maximum permissible rounding interval should be(A)  one half of the standard deviation, or(B)  one sixth of the range computed from 5 to 10 observations, or(C)  one sixth of the maximum mutual difference observed in ten pairs of observations.The rounding interval should be at least one fifth of the maximum just specified.In setting up these limits the following principles were adopted: (1) that the changes in the mean and the standard deviation produced by rounding off must not be too large, and (2) that rounding off must be productive of an effective simplification in the numerical treatment of the data, in particular in the computation of the standard devi

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1948.tb00369.x

出版商:Blackwell Publishing Ltd    

年代:1948

数据来源: WILEY

摘要:

Summary (Superposition of two frequency distributions)Notation:n: number of observationsM: arithmetic means̀: standard deviationμr: rthmoment coefficientβ1: coefficient of skewnessβ2: coefficient of kurtosis.The suffixes a and b apply to the component distributions. The suffix t applies to the resulting distributions.The problem: Given the first r moments of two frequency distributions (to begin with μ0). Find the first r moments of the distribution resulting from superposition of the two components (r≥5).Formulae [1]. … [5] (§3) give the results in their most general form up to μ4.Some special cases are treated in § 4, and eight different cases of superposition of two normal distributions in § 5.In § 6 some remarks are made about the reverse situation, i.e. the splitting into two normal components of a combined frequen

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1948.tb00370.x

出版商:Blackwell Publishing Ltd    

年代:1948

数据来源: WILEY

摘要:

Summary (Sample size for a single sampling scheme).The operating characteristic of a sampling scheme may be specified by the producers 1 in 20 risk point (p1), at which the probability of rejecting a batch is 0.05, and the consumers 1 in 20 risk point (p2) at which the probability of accepting a batch of that quality is also 0.05.A nomogram is given (fig. 2) to determine for single sampling schemes and for given values of p1and p2the necessary sample size(n) and the allowable number of defectives in the sample (c).The nomogram may reversedly be used to determine the producers and consumers 1 in 20 risk points for a given single sampling scheme.The curves in this nomogram were computed from a table of percentage points of the χ2distribution. For v>30 Wilson and Hilferty's approximation to the χ2distribution was u

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1948.tb00371.x

出版商:Blackwell Publishing Ltd    

年代:1948

数据来源: WILEY

摘要:

Summary (Some remarks on the possibility of applying mathematical‐statistical methods to time‐study problems and in particular to the Bedaux system.)Time and motion study are based on observations of the workman's movements and an estimation of his efficiency.The time spent on a certain action in mass‐production is not constant but shows a considerable variation, due to various causes. The time‐study‐man who investigates this action and expresses it in a rate, causes still more variations by certain inaccuracies in using the stopwatch and calculating the rate itself. Considered from a statistical point of view, these cumulating variations result in a standard‐error in the calculated rate; this gives rise to some interesting phenomena.A more statistical approach tot the whole problem is shown in this article to be possible.In the discussion, the application of the Beaux‐system is assumed, but the conclusions hold good for all tim

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1948.tb00372.x

出版商:Blackwell Publishing Ltd    

年代:1948

数据来源: WILEY

摘要:

Summary (The treatment of the results of field experiments by reducing the yields in two directions)Ir J. J. Dijkveld Stol has shown that good results have been obtained by reducing the yields of field experiments both in columns and in rows.The mathematical foundation of this method is discussed in the preceding article and it is shown, that the method gives good results if the same supposition may be made as necessary for the application of the methods of Fisher, Knut Vik and the method of the differences.The variance s̀ of Dijkveld Stol's method is identical with Fisher's error varian

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1948.tb00373.x

出版商:Blackwell Publishing Ltd    

年代:1948

数据来源: WILEY

摘要:

Summary (A useful climatological application of regression theory) It is often required to estimate the 24th mean temperature from a few known temperatures, e.g. at 8h, 14h and 19h, when a sample of accurately known 24h means is available. The usual method is to add a constant to the mean of the three temperatures.It is better however to compute a regression equation of the accurate 24h means on the three temperatures.An example is given, showing that the efficiency of the regression method is about 6 times as great as that of the usual metho

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1948.tb00374.x

出版商:Blackwell Publishing Ltd    

年代:1948

数据来源: WILEY

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1948.tb00375.x

出版商:Blackwell Publishing Ltd    

年代:1948

数据来源: WILEY

摘要:

Book reviewed in this article:A. “Sampling Inspection”, Statistical Research Group, Columbia UniversityB. Selected techniques of statistical analy

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1948.tb00376.x

出版商:Blackwell Publishing Ltd    

年代:1948

数据来源: WILEY

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1948.tb00378.x

出版商:Blackwell Publishing Ltd    

年代:1948

数据来源: WILEY