In a completely randomized design 12 experimental units were

In a completely randomized design, 12 experimental units were used for the first treatment, 15 for the second treatment, and 20 for the third treatment. Complete the following analysis of variance (to 2 decimals, if necessary). At a .05 level of significance, is there a significant difference between the treatments? The p-value is Select : What is your conclusion? Select

Solution

Here we have given that in a completely randomized design

12 experimental units were used for the first treatment.

15 for the second treatment.

20 for the third treatment.

H0 : All the means are same.

H1 : At least one of the means is different from one of the other means.

There are 3 treatments.

d.f. for treatment are ( 3 - 1 ) = 2

d.f. for total = total observations - 1 = (12 + 15 + 20) - 1 = 47 - 1 = 46

d.f. for error = 46 - 2 = 44

Sum of squares for error = sum of squares for total - sum of squares for treatments.

sum of squares for error = 1700 - 1200 = 500

Mean square for treatment = sum of squares for treatments / d.f. for treatments

= 1200 / 2 = 600

Mean square for error = sum of squares for error / d.f. for error

= 500 / 44 = 11.36

F = Mean square for treatment / Mean square for error

F = 600/11.3636 = 52.8169

P-value = fdist(x , deg_freedom 1 , deg_freedom 2)

where x is the F-statistic value

deg_freedom 1 are degrees of freedom for treatment.

deg_freedom 2 are degreeso of freedom for error.

P-value = 2.01979E-12

P-value = 0.00000

P-value < alpha (0.05)

Reject H0 at 5% level of significance.

At least one of the means is different from one of the other means.

Source of Variation	Sum of Squares	Degrees of Freedom	Mean square	F
Treatment	1200	2	600	52.8169
Error	500	44	11.36
Total	1700	46