ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1951.tb00577.x

出版商:Blackwell Publishing Ltd    

年代:1951

数据来源: WILEY

摘要:

SummaryThe Use of Random NumbersA table of random numbers gives a sequence of numbers in which no order can be detected; the probability of finding a certain number respectively a certain combination of numbers in a specified place in the table is the same for all numbers respectively combinations of numbers.Tables of random numbers have been constructed by using other tables (I) or by using a mechanical device (see [2] [4]).The randomness of these tables can be tested by means of the %2 test of goodness of fit.In applying statistical procedures it is often essential that the required sample is taken at random from a given collection.In applying the ratio‐delay method in making time studies it is necessary to make „snap readings” of a group of machines at random moments. This can be done by numbering the consecutive time intervals of the period in which the snap readings will be taken, choosing the required number of intervals from the available intervals by means of a table of random numbers and making observations at the beginning of each interval.Certain properties of industrial sampling schemes may be determined experimentally by constructing, by means of random sampling numbers, lots containing a wanted percentage defectives.A lot containing e.g. 4 % defectives is constructed by regarding pairs of numbers in the table as items in the lot and denoting the pairs 01 — 02 — 03 — 04, which are expected to occur 4 times in every 100 pairs, as „defectives”. In this way samples of n items, can easily be taken from such a lot. An application of this method is given in [7] where the sample size distribution when applying sequential tests, is discussed.In the manner described in [I] a continuous population of a specified mathematical form can be constructed.This has been useful when a sampling scheme had to be developed for testing the duration of life of the carbon brushes of small electric motors.Significance tests for determining a lower boundary for the median of a distribution have been developed by Walsh [9] which seemed to be appropriate in the case.A lower boundary for the median of the universe can for samplesize 12 be determined from the first 6 items in the sample which „end their life” (see table 2). This method however can only be applied if the probability distribution from which the samples are taken is symmetric. In the case under consideration this distribution might be supposed to be bell‐shaped but symmetry was not assured.In order to test the outcome of min [1/2(x1+ x6), 1/2 (x3+ x4)] as a lower boundary for the median and max. [1/2 (x7+ x12), 1/2 (x9+ x10)] as an upper boundary for the median duration of life in case the universe is decidedly skew, a hundred samples of 12 items were taken from the universe depicted in fig. 1.The frequency distribution of the 1200 items chosen in this way is given in fig. 2. In the figs. 3 and 4 frequency distributions are given of the lower and upper boundaries estimated by means of the above mentioned formules.The test chosen has, according to Walsh, a two sided significance level of 0.011. It appeared from the sampling experiment that the estimation of the lower boundary was wrong in 2% of the cases while the upper boundary was never lower than the median of the universe.This divergence was so small that the test could without difficulties be applied to th

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1951.tb00578.x

出版商:Blackwell Publishing Ltd    

年代:1951

数据来源: WILEY

摘要:

SummaryDistribution‐free methods in the regression analysis of two variables.This paper gives an expository survey of the distribution‐free methods of A. Wald (1940), G. W. Housner and J. F. Brennan (1948) and H. Theil (1950). A discussion of the efficiency in a simple case is gi

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1951.tb00579.x

出版商:Blackwell Publishing Ltd    

年代:1951

数据来源: WILEY

摘要:

SummaryThe usual deductions of the well known relation between B‐ en T‐functions have some disadvantages. In this article a simple straightforward method is gi

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1951.tb00580.x

出版商:Blackwell Publishing Ltd    

年代:1951

数据来源: WILEY

摘要:

SummaryFree‐hand curves in estimating the potency of human sera against Toxoplasma1)The observations of 70 human sera, selected on clinical and epidemiological grounds, where the only material available. Three doses of every serum, with ratios 1: 5: 25, were subjected to the “Sabin‐test”, counting the number of killed Toxoplasmas out of 50, exposed to every dose.The chief problem was the estimation of the active dose in every medium serum dose. The percentage kill was used as response y (table I). For the active doses x, a logarithmic scale was used, with the origin at the median letal dose and the dilution I: 5 as unity. The three active doses of every serum were named x–I, x and x + I. The problem was solved by fitting three parallel free‐hand curves, Y (X – I), Y (X) and Y (X + I), to the 3 × 14 mean responses y of five subsequent sera, when ranked in order of magnitude of Σy (table 2, figure 3). The x of every single serum was estimated in principle by shifting the responses y (x – I), y (x) and y (x + I) along the abscis till the condition Σy=ΣY was satisfied; and in practice by reading from a previous y prepared double scale with Σy and xThe chief difficulty in drawing figure 3, the unknown value of x, was overcome by means of two accessory figures. In figure I, ȳ (x̄) is plotted on the abscis for the points and Y (X) for the curves. The points in this figure are not in the right position because the condition Σy =ΣY is not satisfied. Their shifting to the right position, or the substitution of their abscis ȳ (x̄) by Y (¯), was rather cumbersome, because every correction of the curves would imply corrections of the rrbscisses. Therefore figure 2 was drawn, with Σȳ=ΣY plotted on the abscis, to avoid the need of shifting.Because the curves of figure 3 should be parallel, the curves of figures 1 and 2 shorild satisfy the following condition: Of any rectangle, parallel to the axes, with two diagonal summits on the medium curve and one summit on the upper curve, the fourth summit should ly upon the lower curve. In each figure a set of such rectangles is drawn, yielding the positions of x = ‐4, ‐3, ‐2, ‐1, 0, 1, 2, which were used for the construction of figure I. Every correction in one of the curves, caused corresponding. corrections in the other curves. The three graphs were jointly accomplished.The most remarkable feature about figure 3 is an upper asymptote at about 82%. It is suggested that about 18% of the Toxoplasmas would be colored after death, or that the active component would have a maximum concentration, corresponding to some chemical balance in the staining mixture, which would be survived by 18% of the Toxoplasmns.The differences y — Y have only two degrees of freedom for every serum. One of this was used to construct an orthogonal component Xb, designed to absorb individual differences of dose response curves. The remaining component xawas used for error variance. These components appeared to be independent (figure 4).The following significant results were found:I. The variance of Xais somewhat larger than would follow from the binomial distribution of y.2. The variance of xbis larger than that of xa.3. The distribution of x b is negatively skew (table 3).4. A serial correlation exists among the signs of Xb(table 4).5. A serial correlation exists among the values of xb2(table 5).It is apparent that the individual dose response curves do not possess the same shape. So the curves of figure 3 represent some kind of a mean dose response curve and the Toxoplasma killing properties cannot be fully described by a single parameter x. Xbmay be conside

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1951.tb00581.x

出版商:Blackwell Publishing Ltd    

年代:1951

数据来源: WILEY

摘要:

SummaryA nomograph is given for the multiple correlation coefficient defined by (I).

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1951.tb00582.x

出版商:Blackwell Publishing Ltd    

年代:1951

数据来源: WILEY