Question: Five different methods of analysis are used to determine in parts per million the amount of a certain constituent in a sample. Three analysts use each method two times and the results are given below. Write the levels of (i) first, (ii) second variable and the degrees of freedom for the (iii) variables, (iv) interaction, (v) within (error).
A ) (i) 5 (ii) 3 (iii) 4, 2 (iv) 8 (v) 15 B ) (i) 5 (ii) 3 (iii) 5, 3 (iv) 8 (v) 15 C ) (i) 4 (ii) 2 (iii) 5, 3 (iv) 8 (v) 15 D ) (i) 5 (ii) 3 (iii) 4, 2 (iv) 15 (v) 8
Steps to derive
1 The levels of the first variable, a = 5, the second variable, b = 3, and number of data values in each group, n = 2
2 The degrees of freedom(d.f.) are
First variable, d.f.N = a - 1 = 5 - 1 = 4
Second variable, d.f.N = b - 1 = 3 - 1 = 2
Interaction : d.f.N = (a - 1)(b - 1) = (5 - 1)(3 - 1) = 8
Within(error): d.f.D = ab(n - 1) = 5 · 3 · (2 - 1) = 15
