Question

In a randomized block design with one factor having 5 levels and another factor having 5 levels, the degree of freedom for the error sum of squares are equal to

• A. 16
• B. 15
• C. 14
• D. 18

Hint:

For any two-way table with $R$ rows and $C$ columns, the residual (error) degrees of freedom is always $(R-1)(C-1)$. This is a fundamental rule in ANOVA.

Answer 1

The Correct Option is A

We need to calculate the error degrees of freedom (df) for a two-way classification in a Randomized Block Design (RBD).

Step 1: \color{redIdentify the Parameters
Number of levels for Factor 1 (say treatments, $t$) = 5.
Number of levels for Factor 2 (say blocks, $b$) = 5.

Step 2: \color{redApply the Error df Formula for RBD
In a standard RBD without interaction, the error degrees of freedom is calculated as the product of (number of treatments - 1) and (number of blocks - 1).
Error df = $(t - 1) \times (b - 1)$.

Step 3: \color{redSubstitute the Values
Error df = $(5 - 1) \times (5 - 1)$
Error df = $4 \times 4 = 16$.
The degree of freedom for the error sum of squares is 16.