 Solution

Use two crossed sets of blocks in experimental design: volunteers as rows and afternoons as columns. Volunteer blocks control persistent ability, drawing style and prior experience; afternoon blocks control conditions shared that day, including common task difficulty and general practice over time. Neither partition is nested in the other.

Give every volunteer each program twice, and use each program twice each afternoon. The row-column design is then balanced for both block systems. In the additive modelthe program contrasts are orthogonal to both centered block spaces. This controls additive volunteer and afternoon effects; it does not automatically eliminate individual learning differences or carryover effects.