Student 
275 
Discussion of the Frequency Distributions obtained. 
Tables V and VI give the frequency distributions of /•, determined with 
Sheppard's corrections for grouping, of p and (jf R and their derivatives (from 
etjuations (iii) and (iv)) and 
In addition we have, in Table V, r determined without Sheppai'd's corrections 
and the theoretical disti'ibution of r calculated from the table {Biometrika, xi. 
p. 384), of the cooperative paper by interpolating between p ■ "65 and p = "70, 
drawing the frequency curve and estimating the areas by counting the squares: 
it is probably iiot very accurate, but fairly close to the truth. 
In Table VI is included r calculated from the fourfold table taken through 
the medians by Sheppard's formixla ?■= cos where B is the frequency in the 
'small' cells. This probably suffers a good deal from the coarse grouping which 
makes it necessary to divide the centre groups in an arbitrary manner. 
The most remarkable thing about these tables is the very wide spread of all 
the distributions. There is of course nothing new in this, but I cannot help 
thinking that an examination of these tables may be beneficial for all who try to 
work with very small samples. 
Besides this there is not very much to be found in these tables which is not 
seen to greater advantage in Tables VIII and IX of the means and s.D.'s, but as 
a matter of interest I have compared lines 2 — 4 of Table V with line 1 by the 
test with the following results : 
TABLE VII. 
25 groups 
16 groups 
P 
X^ 
P 
r with Sheppard'8 corrections . . . 
7- without Sheppard's corrections 
'/•p actual ... 
„ 
30-10 
20-43 
60-25 
74-10 
-18 
-67 
-000,064 
-000,002 
20-49 
12-39 
30-63 
55-65 
-17 
-66 
•01 
(say) -000,002 
The 25 groups were the 24 groups on the right of the table and the tail, 
which includes all groups which are less than I'O in line 1 : the 16 groups were 
taken so that no group in line 1 was less than 10. 
With such a small sample as 875 the x' test is only decisive for considerable 
departures from the theoretical and the regular excess over the theoretical for all 
groups less than -40 avoids detection. 
At the same time it is interesting to note that judged by the test Sheppard's 
corrections do not seem to have improved the calculation of r. 
