Question

How many degrees of freedom will the error have in a randomized block design with five treatments and three blocks?

Answer 1

df = 8

Therefore, the number of degree of freedom is 8

Explanation:

the number of degrees of freedom can be defined as the number of values in the final calculation of a statistic that are free to vary.

In randomised block design, It can be represented by the equation.

df = (b-1)(t-1) ..... 1

Where;

df is the degree of freedom

b is the number of blocks

t is the number of treatments

From the questions above.

b = 3

t = 5

Using equation 1

df = (3-1)(5-1)

df = 2×4

df = 8

Therefore, the number of degree of freedom is 8

Answer 2

8

Explanation:

In a randomnized block design, the formula for calculating the degrees of freedom for error is given by:

(r-1)(c-1)

where: r is the number of treatments and c is the number of blocks

Applying the above formula to this case;

The number of treatments is 5 and the number of blocks is 3, which means we can calculate the degrees of freedom for error as :

(5-1)x(3-1) = 4 x 2 = 8