Consider the following ANOVA table a What design was employe

Consider the following ANOVA table.

a) What design was employed?
(b) How many treatments were compared?
(c) How many observations were analyzed?
(d) At the .05 level of significance, can one conclude that the treatments have different effects? Why?

Solution

a) It is Randomized Block Design or Two way classification Since two facotrs exist in this design

b) The df of treatment (k-1) = 2 from the table. We required number of treatments k = 2 + 1 = 3.

c) Given the df of treatments k-1 = 2, that means, number of treatments k = 3

     and   the df of blocks r -1 = 7 , the means, number of blocks r = 8

and also the df of Error (r-1)(s-1) = (8-1)(3-1) = 14.

Therefore, the total number of observations are rk = 3*8 = 24.

d)

H0: There is no significance different between the treatment effects

H1: There is significance diference between the treatment effects.

From the table, variance ration F= 2.824

Table value F ( 5%, (2,14)df)) = 3.74 .

Here F < F(5%,(2,14)df)), therefore, we accept H0.

That is , There is no significance difference between the treatment effects.i.e. the treatments have not different effects.