Prediction of Rainfall in Hawaii— Wentworth 
Even where the individual group shows 
a smaller standard deviation, the groups are 
so small that the measure is not reliable. 
We have no basis for assuming any mean to 
be closer than average probable errors for the 
whole series. In Table 4, as an example, an 
attempt is made to apply the 16- and 20- 
year cycles, the most promising two cycles, 
to the prediction of the index for the years 
from 1939 to 1948 inclusive. 
In this table, the actual index up to date 
is given in column 2. The indexes predicted 
by the 16-year cycle alone are given in col¬ 
umn 4, and those predicted by the 16-year 
cycle followed by the 20-year cycle are 
shown in column 6. Columns 3, 5, and 7 
show errors of prediction by use of the mean 
(column 3), by use of the 16-year cycle 
(column 5), and by use of the 20-year cycle 
after the 16-year (column 7). These show 
that, on the average, there is a moderate im¬ 
provement of prospective accuracy of esti¬ 
mate by using the 16-year cycle, and a still 
smaller improvement by using the 20-year 
cycle in addition. However, anyone desiring 
to use such data for practical purposes should 
have his doubts aroused by noting that in two 
of the predicted years, 1946 and 1947, the 
219 
predicted values in column 4 are quite dif¬ 
ferent from those in column 6 and of oppo¬ 
site deviation from normal. In both 1946 
and 1947, there is marked change on using 
the 20-year cycle. It is easy to trace this 
effect, since these dates are 20 years after 
the phenomenally low and high years of 
1926 and 1927. The indexes for these 2 
years are so aberrant that in much statistical 
procedure they would be rejected. The 20- 
year average is based only on two pairs— 
1906 and 1926, 1907 and 1927—and the 
effect of the latter year in each case is dis¬ 
proportionate. The figures for 1947 and 
1948 are not offered as predictions but 
simply as working data. 
The conclusion drawn from the table and 
other data presented is that by progressive 
use of cycles, the prospective average errors 
of estimation can be made slightly smaller 
than those shown by predicting the mean. 
However, the practical utility of any such 
improvement is marred by the knowledge 
that it is gained through the introduction of 
group averages having probable errors that 
we cannot reasonably assume to be less than 
approximately 5 per cent. The problem 
comes down to whether an estimate having 
TABLE 4 
Prediction by 16-Year and 20-Year Cycles 
1 
2 
3 
4 
5 
6 
7 
INDEX BY 
ACTUAL 
DEVIATION 
INDEX BY 
DEVIATION 
16- AND 20- 
DEVIATION 
YEAR 
INDEX 
FROM 
16- YEAR 
FROM 
YEAR 
FROM 
MEAN 
CYCLE 
ACTUAL 
CYCLES 
ACTUAL 
1939 
117 
17 
112 
5 
102 
15 
1940 
70 
30 
83 
13 
65 
5 
1941 
79 
21 
87 
8 
85 
6 
1942 
109 
9 
98 
11 
10 4 
5 
1943 
91 
9 
120 
29 
119 
28 
1944 
74 
26 
77 
3 
79 
5 
1945 
64 
36 
79 
15 
71 
7 
1946 
86 
14 
108 
22 
85 
1 
1947 
94 
116 
1948 
114 
119 
Average deviation, 
8 years . 
20.2 
12.8 
9 
