Gambar halaman
PDF
ePub

for. This paper dealt almost entirely with methods, and he had hoped that Mr. Loch, than whom there was no one more conversant with statistics of pauperism, was going to tell them whether, in his view, the results of this mathematical reduction were in harmony with the tendency in England generally. The way in which the widely spread curve of 1850 had shrunk to the narrow and concentrated curve of 1891, seemed to him to prove most clearly that there had been remarkable inclination towards greater uniformity of administration, that is, the great improvement shown in the ratios dealt with in the paper was due to the much more uniform system on which the unions all over the country were administering relief; this feature being far more striking in the curves than the variation in the actual numbers.

Mr. N. A. HUMPHREYS said that no one felt more strongly than himself the necessity of a more frequent census, but at the same time he thought several speakers had suggested difficulties with regard to the arithmetical method of determining the proportion of pauperism to population which were scarcely valid. It was quite true that during a current decennium it was impossible to make satisfactory local estimates of population, but when a decennium was completed, there was no great difficulty in estimating the population of defined areas for any given year with quite sufficient accuracy to serve as a basis for calculating ratios of pauperism, and for testing the effects of variations in poor law administration.

Mr. R. H. HOOKER, referring to the statement on p. 340, that the distributions appeared to be slowly passing over to the simple. binomial type, in which the curve was limited at one end and tailed off to infinity at the other, pointed out that inspection of the diagrams of pauperism led one to expect this result, which the author had arrived at by calculation. For as the general tendency of the mode was to approach the ordinate of no pauperism, the rates less than the mode were all crowded into a smaller space, and the tendency of the curve to cut the axis instead of to touch it, i.e., to be limited towards the left, became greater, while there was still room for them to extend indefinitely to the right. This passage from one type to another led to the consideration of the method of determining the class of curve to be used. This was ascertained by examination of the value of . If was "approximately zero the curve would be of the binomial type; if it was positive, the curve would be of the limited range type. The question thus was, What amount would be considered "approximately zero?" and what indication would one have that a wrong kind of curve had been taken? Would there be any abnormal result? As the curve actually seemed to be passing from one type to another, the point was of practical interest.

On p. 330 it was mentioned that the ratio of skewness was zero for a symmetrical curve where the mode and the mean coincided, and was never greater than unity. A geometrical interpretation of a skewness unity would be useful, and he would like to know if he was right in deducing that the skewness would be unity in the

improbable case, for instance, of pauperism being the exception, i.e., if the maximum number of unions had a pauperism of less than per cent., so that the mode coincided with the lowest value of the variable.

With regard to the author's endeavour to ascertain the form of the curve for 1886, he should not himself expect any reliable result from an interpolation based upon the usual estimates of the population in intercensal periods. These were notoriously uncertain; in fact, had the author obtained a reasonable value for K, he (Mr. Hooker) would have been inclined to take this result as indicating that the estimate of population for 1886 was a correct one. He was, however, rather disposed to think that the distribution of population, as between urban and rural districts, might be materially different in 1886 to what it was both in 1881 and 1891, in which two years it was probably somewhat similar. He was inclined to think that such a different distribution would result from the fact that 1881 was near a year of maximum trade prosperity, and 1891 still more so, while 1886 was a year of minimum trade prosperity. The population estimates for 1886 being thus probably peculiarly inaccurate, it would follow that the estimates of pauperism would be so also. In 1870 the country was beginning to revive from a depression, and in this year pauperism was practically a maximum, so that a very different type of curve to that for 1881 would naturally be expected. These facts, Mr. Hooker thought, would account in part, possibly only to a slight extent, for the great difference in the type of curve between 1870 and 1881, and the great similarity between 1881 and 1891. 1886 having been somewhat similar, as regards trade, to 1870, it would therefore have been interesting if it had been possible to work out the values of and other particulars for 1886, to ascertain whether the curve showed any tendency (however slight) to revert to the form of 1870.

σ

Sir RAWSON W. RAWSON, K.C.M.G., C.B., said that the Society and statistical science generally were greatly indebted to Mr. Yule for showing how valuable and important, under careful management, mathematical processes were in testing and correcting the masses of statistical information which it is the province of the Society to collect and apply. He thought it was an advantage to the Society that the Council had admitted this paper for discussion, in order that other persons might be encouraged to use similar efforts to apply mathematical processes scientifically to statistical investigations. He also hoped it would encourage Mr. Francis Galton to give them an explanation of his method of working out problems of the same character.

The CHAIRMAN (The Right Hon. the Earl of Verulam) then moved a very cordial vote of thanks to Mr. Yule for the great care, labour, and accuracy he had displayed in bringing forward this very difficult subject. He would not attempt to deal with the details of the paper, but it was obvious what value such a paper must have, by showing the effect of a given policy upon the amount

of pauperism prevailing in the country, so that the lessons taught by such statistics could be acted upon by those who had the management of affairs; and without such methods of ascertaining the actual facts, obviously their policy could not be directed on the best possible lines. With regard to the statistics given by Mr. Flux in connection with the one hundred unions in Lancashire, Yorkshire, and Cheshire, it struck him that the reason for the variation he spoke of might possibly be that certain industries had ceased and others had sprung up in the respective districts. They often heard of towns being depleted of population in consequence of the cessation of a normal industry, the working out of mines, or the transference of industries from one place to another. One important point which Mr. Yule had very properly urged, was the necessity for more frequent censuses. He had no doubt that, to be of any real value, a quinquennial census certainly was desirable, and he was inclined to say that an annual one would be most valuable.

Mr. YULE, in reply, said he would deal first with a point raised by Mr. Galton, and again by Mr. Sheppard, as to the position of the mode. The latter speaker (Mr. Sheppard) appeared to think the mode corresponded to the greatest ordinate actually occurring; of course this was not so, it corresponded to the maximum ordinate of the fitted curve. Being thus determined (in a somewhat similar way to the mean) from the totality of the observations, the mode was entirely unaffected by the shifting of a few units from one side to the other near the actual maximum, and Mr. Sheppard's criticisms on this point were entirely beside the mark. Such a shifting of a few units would however be quite sufficient to entirely upset the judgment of one's eye, and for that reason he (Mr. Yule) did not consider that any great weight could be attached to simple estimates of the mode such as Mr. Galton had made.

With the use of percentiles, advocated by Mr. Galton, he preferred not to deal at length on the present occasion; the chief fault of the method in his eyes was that it did not lend itself to theoretical treatment. The value of a given form of diagram was always more or less a matter for personal opinion, but it seemed to him that five frequency distributions (without the fitted curves at all) really gave much more than five decile systems.3

With Mr. Bailey's remark, that the cases of pauperism and mortality were not parallel, he was in complete agreement. It was however quite as important to have a concise statement of facts in the first case, where changes were rapid, as in the second case, where changes were slow. The "law" of pauperism was a law of distribution round an average.

Mr. Flux's criticism, that an investigation of causes was most required, seemed to him perfectly just. But for such an investigation it was necessary to deal with a distribution in three dimensions, i.e., a frequency-surface, not a frequency-curve. He (Mr.

3 Some future remarks on the use of deciles and normal curves will be found on p. 396, in a note on Mr. Galton's memorandum, p. 392.

Yule) had used this method for one investigation' in pauperism, and hoped to be able to do further work in the same direction. The method of the present paper simply served to illustrate, without reference to causation, the breadth and character of the changes that had taken place; it did not profess to do more.

Mr. Flux's further remarks on the compactness of the distribution in a group of unions from one district were of great interest, and in complete agreement with what he (Mr. Yule) had noticed. A group, for instance, from a single registration division nearly always gave a much smaller standard deviation than that given by the whole country. The geographical limitations of pauperism in England were very marked.

Passing on to Mr. Sheppard's more theoretical criticisms, be differed from that speaker on one point of fact: the normal curve was by no means predominant in statistics, it was (on the contrary) decidedly exceptional. As regards the skew-curves employed, Mr. Sheppard did not appear to have followed the method. The normal curve was given its chance; i.e., the criterion was calculated, and if it had been near zero the normal curve would have been used. But the criterion was distant from zero by forty to eighty times its probable error! Under any circumstances how could a normal curve give a distribution sharply limited at one end, as these are at zero pauperism?

He (Mr. Yule) also failed to understand why the median was any better" criterion of the degree of pauperism" than the average; the one was no more the type than the other.

Mr. Humphreys had suggested that it was quite sufficiently accurate in most cases to interpolate for population; but surely the process was very uncertain for small areas like unions, largely affected by migration? For the country as a whole it might possibly serve.

5

With regard to Mr. Hooker's queries, by the statement that the criterion must be small, was meant that it should not be large compared with its own probable error. There would be no very noticeable differences between one type of curve and another, when the criterion was small; no abnormal results would be obtained by using the wrong form under these circumstances.

The skewness would be unity, for example, in the type of binomial curve, with the maximum at one end of the range."

The questions as to the condition of 1886, suggested by Mr. Hooker, were interesting, but it seemed impossible to arrive at any conclusions owing to the wretched population difficulty. Redistribution actually discovered for 1886, showed no tendency to revert to the form of 1870, but the reverse. The standard deviation found for 1886 was smaller than that for 1891! But of course no weight could be attached to these results.

“On the Correlation of Total Pauperism with proportion of Out-relief.” "Economic Journal." December, 1895.

5 The phrase in Sec. 6, to which Mr. Hooker referred, has been altered since the proofs were issued.

Curve II, fig. v, plate 9, Skew Variation, &c." Karl Pearson. "Phil.

Trans.," 186 A. 1895.

[blocks in formation]

STATISTICS, according to some authorities, must be defined so as to relate to society; but must the society be human? It is rather in the unprogressive communities of the lower gregarious animals that we may look for the realisation of that statistical ideal which Quetelet called Physique Sociale: the stable averages obtained from large numbers of statistics being compared to the dimensions of a body ascertained by repeated measurements. I have attempted to determine some statistical constants for one of the most orderly societies, that of wasps.'

I. The first inquiry which presents itself is one initiated by Sir John Lubbock, How long does a wasp take in loading herself with sweets? What is the average interval of time between the moment at which she sets to work at honey or jam or fruit, and the moment when she flies off with her fragrant load? Some answers to this question obtained from Sir John Lubbock's observations are given in Table I.

1 My observations have been made at intervals in the course of the last eleven years. They all, as far as I know, relate to the same species, which may be popularly denominated the common or ground wasp. The observations were made in three localities: Edgeworthstown in Ireland, Winchfield in Hampshire, and Hampstead Heath. Of the nests referred to by letters of the alphabet, A, B, C, D were at Edgeworthstown; E, F, G, H at Hampstead.

"Ants, Bees and Wasps," second edition and fifth edition.

« SebelumnyaLanjutkan »