Question

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). Round p-value to four decimal places. If your answer is zero enter "0".

Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value Treatments 1,300 Error Total 1,800

At a .05 level of significance, is there a significant difference between the treatments?

The p-value is

What is your conclusion?

Answer 1

From the table,

The sum of square values are,

SS (Treatment) = 1200

SS (Total) = 1600

SS (Error) = SS (Total) - SS (Treatment) = 1600 - 1200 = 400

The degree of freedom values are,

df (Treatment) = k - 1 = 3 - 1 = 2

df (Error) = N - k = 47 - 3 = 44

df (Total) = N - 1 = 47 - 1 = 46

The mean square values are,

MS (Treatment) = SS (Treatment) / df (Treatment) = 1200/2 = 600

MS (Error) = SS (Error) / df (Error) = 400/44 = 9.0909

The F-value is,

F = MS (Treatment)/ MS (Error) = 600/9.0909 = 66

P-value

The p-value is obtained from the F-distribution table for F = 66, numerator degree of freedom = 2 and denominator degree offreedom = 44.

P-value = 0.0000

The ANOVA table is shown below,

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	P-value
Treatments	1200	2	600	66	0.0000
Error	400	44	9.090909	.	.
Total	1600	46	.	.	.

Conclusion:

Since, the p-value is less than 0.05 at a 5% significance level, the null hypothesis is rejected, hence we can conclude that there is a significant difference in 3 treatment group means.