Question

In a \(2^n\) factorial, all effects and their sum of squares can be obtained directly at a stretch by :

• A. Yates' method
• B. Modulo technique
• C. Both (A) and (B)
• D. Neither (A) nor (B)

Hint:

Think of the systematic addition-subtraction algorithm applied to treatment totals in standard order.

Answer 1

The Correct Option is A

Step 1: In a \(2^n\) factorial design there are \(2^n\) treatment totals and \(2^n - 1\) effects (main effects and interactions) to be estimated.

Step 2: Yates' method arranges the treatment totals in standard order and applies successive cycles of addition and subtraction of adjacent pairs.

Step 3: After \(n\) such cycles, the resulting column directly gives every factorial effect total, and squaring each entry and dividing by \(N \times 2^n\) (with \(N\) the number of replications) gives the sum of squares for that effect, all obtained in one systematic sweep.

Step 4: The modulo technique, by contrast, is used to decide which interaction is confounded with blocks (through the defining contrast), not to compute the effects or their sums of squares.

Final Answer: (A) Yates' method.