Computation of Effects in (2^k)r Factorial Design

Use sign table to compute effects (i.e., q_0, q_A, q_B, q_{AB}).

Example:

Reconsider memory-cache size experiments. Repeat each three times ((2^2)3 design).

Cache          Memory       Memory
Size           Size         Size
(kbytes)       4 Mbytes     16 Mbytes
_____________________________________
1              15,18,12      45,48,51
2              25,28,19      75,75,81
_____________________________________

Sign Table Analysis

Sign table differs from the 2^2 case by

• enumerating all observations of y in y column,

• add one column containing mean response variable value per experiment (denoted "ybar"), and

• multiplying column ybar by I, A, B, and AB to get "totals."

Experiment  I     A      B      AB          y       ybar (mean)
_______________________________________________________________
1           1    -1     -1       1     (15,18,12)     15
2           1     1     -1      -1     (45,48,51)     48
3           1    -1      1      -1     (25,28,19)     24
4           1     1      1       1     (75,75,81)     77
_______________________________________________________________
Totals:   164  86.0   38.0    20
Totals/4:  41  21.5    9.5     5

The effects are close to those obtained earlier: