It is known that a two-factorial design is balanced if and only if each combination of the level of the two factors have the same replication. As an example, if $A$ has $2$ levels and $B$ has $2$ levels, then the replications for treatment $A_1 B_1$, $A_2 B_2$, $A_1 B_2$, $A_2 B_1$ are all the same. But, how is balance considered inside an ANCOVA design? For example, say I have a model with a factor $A$ of $2$ levels and one continuous covariate, $X$. Does it mean that the design is balanced if $A_1$ and $A_2$ have the same replications (ignoring the continuous covariate)?



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