Our mineral reserves

Bibliographic data

Monograph

Identifikator:: 867029366

URN:: urn:nbn:de:zbw-retromon-93011

Document type:: Monograph

Author:: Smith, George Otis http://d-nb.info/gnd/117634530

Title:: Our mineral reserves

Place of publication:: Washington, DC

Publisher:: Gov. Print. Off.

Year of publication:: 1914

Scope:: 1 Online-Ressource (48 Seiten)

Collection:: Economics Books

Usage license:: Get license information via the feedback formular.

SUPPLEMENTS—GOODNESS OF FIT. 371 relation there shown to hold between the normal curve and the surface of normal correlation, at once suggests that the same principle will apply when there are two variables. It was proved on pp. 319-321 that the contours of a normal surface are a system of concentric ellipses. Now suppose we have a normal system of frequency in two variables z and Ys then the chance that on simple sampling we should obtain the combination 2’ ' is measured by the corresponding ordinate of the surface, and the feet of all ordinates of equal height will lie upon an ellipse which will therefore be the locus of all combina- tions of z and y equally likely to occur as is z’ y. oF combina- tion more likely to occur than 2’ will have a talle ordinate, and as the locus of its foot must also be an ellipse, that ellipse will be contained within the 2" 3’ ellipse. Conversely, combina- tions less likely to occur than 2’ 7’ will be represented by ordinates located upon ellipses wholly surrounding the z' #’ ellipse. Hence, if we dissect the surface into indefinitely thin elliptical slices and determine the total volumes of the sum of the slices from az=2' and y=%' down to 2=0 and y=0, this volume divided by the total volume of the surface will be the probability of obtaining in sampling a result not worse than x’ y'; or, if we prefer, we may sum from x=2', y=% to z=y=ow, and then the fraction is the chance of obtaining as bad a result as 2" 7, or a worse result. The reader who has compared the figures on p- 166 and p- 246, and followed the algebra of pp. 331-332, will have no difficulty in seeing that, when the number of variables is 3, 4... .m the above principle remains valid although it ceases to be possible to give a graphic representation. With three variables the contour ellipse becomes an ellipsoidal surface, and the four-dimensioned frequency “volume” must be dissected into tridimensional ellipsoids; with four variables another dimension is involved, and so on; but throughout the equation of the contour of equal probability is of the ellipse type (cf. the generalisation of the theorems of Chapter IX. in Chapter XII). Let us now suppose that if a certain set of data is derived from a statistical universe conforming to a particular law, these data, & in number, should be distributed into n+ 1 groups con- taining respectively ny, m;,, n, . . . . n, each. Instead of this we actually find mg, m,, m, . . . .m,, where myt+m +... a=nytn +... n,=D. The problem to be solved is whether the observed system of deviations from the most probable values might have arisen in

Access restriction

Copyright

fullscreen: Our mineral reserves

Monograph

Table of contents

Download

Monograph

This page

Image fragment

Citation links

Citation recommendation