SUPPLEMENTS—GOODNESS OF FIT. £7 
zero. The same statement must hold good for every row, Hence, 
if » be the number of rows, ¢ the number of columus, the number 
of algebraically independent values of é is (r—1)(c—1), and the 
tables must be entered with the value 
w=>r-1)c-1)+1. 
The student will realise that this is a reasonable rule if he 
considers that when we take n’ as the number of classes, the 
comparison frequencies being given a priori, we are taking it as 
one more than the number of algebraically independent frequencies, 
since the total number of observations is fixed. 
The following will serve as an illustration (Yule, ref. 5 of 
Chapter V.). Sixteen pieces of photographic paper were printed 
down to different depths of colour from nearly white to a very 
deep blackish brown. Small scraps were cut from each sheet and 
pasted on cards, two scraps on each card one above the other, 
combining scraps from the several sheets in all possible ways, so 
that there were 256 cards in the pack. Twenty observers then 
went through the pack independently, each one naming each tint 
either “light,” “medium,” or “dark.” 
TaBLE showing the Name (light, medium, or dark) assigned to each of two 
Pieces of Photographic Paper on a Card: 256 Cards and 20 Observers. 
Upper figure, observed frequency ; central figure, independence frequency ; 
bottom figure, difference 8. (Yule, ref. 5 of Chap. V., Table XXI.) 
. Name assigned to Upper Tint on Card. 
Name assigned to 
Lower Tint on Total. 
Card, Light. Medium. Dark. 
850 571 580 aang 
Light 785 633 583 
+65 - 62 - 3 
618 503 455 So 
Medium . 653 527 486 
—- 35 +66 - 31 
540 456 457 RE] 
Dark 570 460 423 
—-30 - 4 +34 
Tot? ro g 
377 
“OU; 
1660 
14D¢ 
aL 2008 1620 149% 512¢