April, ’24] 
hartzell: dosage estimation 
283 
lation. The relation between efficiency and open space seems also to 
be slight. 
Partial or Net Correlation 
In an ideal experiment, two factors are allowed to vary while all other 
influences are held as nearly constant as possible. Such investigations 
are practically impossible in the field. What is needed is a measure of 
the relationship between two variables when the other variables are 
held constant. This measure is provided by partial or net correlation 
coefficients. The notation needs explaining. Partial correlation coeffi¬ 
cient subscripts have a decimal form. The two subscripts to the left of 
the period are known as primary subscripts and indicate the variables 
measured, while the subscripts to the right of the point are designated 
secondary subscripts and show what factors are held constant. For 
example, ri 4 .23 shows that the correlation is measured between efficiency 
and percentage of open space, when the dosage and temperature are 
held constant. 
The chief problem to be solved is this: what is the net correlation 
between the percentage of efficiency and the dosage when all the trees 
are considered constant as regards temperature and percentage of open 
space? vStated otherwise, is . the difference between r ]2 and ri 2 .34 sig¬ 
nificant" Another question which demands an answer is; what is the 
effect of temperature on efficiency when dosage and open space is kept 
constant? The values of the first and second order coefficients are set 
forth in Table 2. 
It will be noted that the difference between r 42 and ri 2 . 34 is .038 ± .108, 
which is not significant since the probable error is greater than the differ¬ 
ence between the two coefficients. The objection may be raised that the 
number of observations is small (46). Suppose that there were 414 
observations and assume that the coefficients remain the same, all the 
probable errors would be only one-third those shown in Table 2. The 
difference between r 42 and r 42 . 34 would then be .038 ± .036 and would 
still lack significance. In other words, the variation due to temperature 
and open space have not, apparently, affected the relation between 
efficiency and dosage. The same might be said of the relation between 
efficiency and open space (r 44 . 23 ). It is vastly different as regards the 
effect of temperature on efficiency when dosage and open space is held 
constant, for r 43 . 24 is positive. The difference between r L3 and ri 3 . 24 - 
is .396 ± .134, which is almost significant notwithstanding the paucity 
