Background
I am trying to extract data from scientific publications. Sometimes an experiment can test two factors, e.g. a standard two-way factorial ANOVA.
Call these factors $A$ and $B$. If factor $A$ has two levels and $B$ has three, there are six total treatments.
If the effects of $A$ and $B$ are significant, but there is no interaction, only the 'Main' effects might be presented, e.g. five results, one for each level of $A$ and one for each level of $B$, averaged across all of the levels of the other factor.
Here is an example from Ma 2001 Table 2, in which $A$ would be the row spacing and $B$ would be the nitrogen rate.
Thus,
$7577 = \frac{X_{A_{20},B_{0}} + X_{A_{20},B_{112}} + X_{A_{20},B_{224}}} {3}$
$9186 = \frac{X_{A_{80},B_{0}} + X_{A_{80},B_{112}} + X_{A_{80},B_{224}}} {3}$
$3706 = \frac{X_{A_{20},B_{0}} + X_{A_{80},B_{0}}} {2}$ $9402 = \frac{X_{A_{20},B_{112}} + X_{A_{80},B_{112}}} {2}$ $12038 = \frac{X_{A_{20},B_{224}} + X_{A_{80},B_{224}}} {2}$
Question
Is it possible to calculate the means of each of the six treatments $X_{A,B}$, for $A\in[20,80]$ by $B\in[0,112,224]$ from these results?