Question

Is there any difference in conductivity due to coating type at 5% alpha level using Kruskal- Wallis test? (Do written calculations)

Conductivity Coating Type 141 1 143 150 146 2 152 137 143 149 3 136 132 127 134 129 4 129 127 132

Answer 1

H0 : there is no difference in the conductivity due to coating

H1: there is difference in the conductivity due to coating

Now arranging them in ascending order.

1	2	3	4
141	137	127	127
143	143	132	129
146	149	134	129
150	152	136	132

now giving them ranks

1	2	3	4
10	9	1.5	1.5
11.5	11.5	5.5	3.5
13	14	7	3.5
15	16	8	5.5

In this example R₁ = 49.5, R₂ = 50.5, R₃ = 22 and R4= 14

To check : the sum of ranks should be equal to n(n+1)/2

Here: verified

now calculating the H statistic

H 12/N (N1) 1- kRj2/nj 3(N 1)

where k=the number of comparison groups, N= the total sample size, n_j is the sample size in the j^th group and R_j is the sum of the ranks in the j^th group.

H= 12/16(17)4[(49.5)^2+(50.5)^2+(22)^2+(14)^2]

H= 17041.5/272-51

H= 11.6525

here k=4

hence critical value = 7.235( using table)

and since 11.6525>7.235

we reject Ho and conclude that there is difference in the conductivity due to coating .