Ixviii Tables for Statisticians and Biometricians [XXXY — XLYI 



It would look therefore as if /c, were significantly negative, but it is just possible 

 that «■, might be zero. Such a big probable error for k^ suggests our being 

 in the neighbourhood of a critical limit. This is verified on examining Table 

 XLIII to find the value of Vi\''S,„. We see that it is over 80, nnd we thus 

 conclude that the probable error of «•., may lie between 1 and 2. Thus we cannot 

 be definitely certain of the sign or magnitude of k„, when we are even relatively in 

 the neighbourhood of k^ = 0. 



If we turn to Diagram XXXV (p. 66) we see that the point y3i = "678 and 

 y82=3'734 is not very close but is approaching the line along which Type III is 

 applicable, and this is the source of the disturbance noted. 



We accordingly try to measure the probability that Type III would be as 

 satisfactory as Type I within the area of which our /3i, /Sa values actually lie. 

 We must take ri77\/FS, from Table XLIV and 1177VF2, from Table XLV. 

 We have 



/3, = -6789, ;8o = 3-7 then ri77Vi\^Si = 2-3 



„ /3. = 3-8 „ „ =2-5. 



Hence for /3, = 3-7342, 1-177 ViV'S, = 2-3 + f-^^ [2] = 2-37. 



Again: ;82=3-7 1-177\/FS,= 16 -|§|[1] = 15-43, 



/3o = 3-8 l-177\/iV'S, = 18 -|ff[l] = 17-43, 

 y8o = 3-7342 1-17 7 V JS = 15-43 + fU^ [2] = 16-11. 



Thus: 2i/22 = 2-37/16-11 = -147 = -15, say. Or, if we turn to Diagram XLVII 

 (p. 88), our system of ellipses is half-way between the 3rd (Sj/S., = '14) and the 

 4th (2i/22= -16). Now if such a system of ellipses be traced oti' and centred at 

 the point /Si = -678, ySo = 3-734 on Diagram XLVII to the right and then the 

 niajor-a.xis be brought into parallelism with the dotted lines, we find that the 

 biggest of these ellipses XSj = '5 fails to reach the critical line III. But the 

 semi-major axis of the probability-ellipse is 1-177S2 = 16-ll/ViV= -493. Hence 

 we must conclude that it is more probable that the curve is of Type I than of 

 Type III. This is readily determined and is usually sufficient guide. Actually 

 the value of XS2 must be about -6 before we get an ellipse to approximately touch 

 the Type III line. But to = -493/1-177 = -419, and accordingly X = •6/-419 = 1432, 

 which gives P = e~4^^ = -36 nearly, or the odds are 16 to 9 that the point would 

 not lie outside this contour. But if it did lie outside this contour, the chance 

 of its being on or over the Type III line corresponds to only a very small section 

 of the total frequency outside this contour. If we invert the problem and put the 

 system of ellipses on the nearest point of the Type III line we fiud that the odds 

 are very much in favour of the point /3i = -678, /So = 3734 lying outside such a 

 system. On the whole it is reasonable to conclude that Type I is properly used 

 although we should probably not get bad results from a Type III curve. In 

 some respects a suitable fit would be obtained by using Type I, and fixing its 



