6 BULLETIN 1351, tJ. S. DEPARTMENT OP AGRICULTURE 
Incidentally, an understanding of the size of the market is of con- 
siderable importance to farmers who are considering the shifting of 
acreage between wheat and oats, for a change in production which 
would cause a relatively small change in wheat prices might cause 
a great change in the price of oats, because oats are sold in a narrower 
market. 
TREND OF PRICES OF OATS 
The trend of oat prices for the period 1881 to 192:2 has been 
less uniform than the trend of production. It tended downward 
from 1881 until the low point was reached during the nineties. 
After 1896 the trend was gradually upward until the close of the war 
period. The lack of uniformity in trie trend of prices makes it im- 
possible of representation by a straight line. There are actually 
two trends, one downward until 1896 and the other an irregular trend 
from 1S96 to the present year in a general upward direction. Two 
methods of representing this trend are illustrated in Figure 2. One 
is the use of two straight lines to show the downward and upward 
trends; the other is the use of a third degree parabola curve. 
A comparative examination of the graphs of production and price 
in Figure 1, where 1 the prices haye been corrected for changes in the 
price level, shows that during the period from 1881 to 1913 prices 
were usually below the normal, represented by the trend line, when 
production was above, and aboye when production was below. In 
fact, during much of the period one cuiwe seems almost the exact 
opposite of the other, if allowance is made for the difference in 
trends. The closeness of the relationship as indicated l>y the two 
graphs shows clearly that the size of the oat crop in the United 
States has an important influence upon the year-to-year changes in 
price. Prices used in these two graphs are averages for crop years, 
September to August, instead of July to June, as used in the resl oi 
the bulletin. 
Graphs like these, useful as they are in showing the nature of the 
relationship between two factors, furnish no measure of the close- 
ness of that relationship, nor do they provide a method of estimal ing 
one when the other is known. To obtain these two results it is 
necessary to make use of the statistical device of correlation. 4 
The relation between these two factors, when the ratio of production 
to the trend of production is correlated with the ratio of price to the 
trend of price, is expressed by a correlation coefficient of —0.82. 
The negative sign indicates that a change in one factor is accom- 
panied by a change in the opposite direction in the other; and the 
size of the coefficient measures both the extent to which changes 
in one factor are associated with changes in the other and the accuracy 
with which values of one factor may be predicted from known values 
of the other during the period covered by the study, assuming that 
perfect correlation is represented by the coefficient ±1.00. 
Not the actual value of the coefficient, however, but the square 
of the value represents the proportion of the change in price that is 
accounted for by the change in the other variable. 
A coefficient of correlation, squared, measures between X and Y 
the proportion of variation in Y that can be accounted for by vari- 
ations m X, provided one is defining variability as the standard 
* The method of obtaining the coefficient of correlation is explained in Appendix A, Table II. p. 28. 
