Question

Consider the experimental results for the following randomized block design. Make the calculations necessary to set up the analysis of variance table.

		Treatment
		A	B	C
	1	11	10	8
	2	12	6	6
Blocks	3	18	16	15
	4	20	18	18
	5	9	7	9

Use a=.05 to test for any significant differences. Show entries to 2 decimals, if necessary. Round all intermediate values to two decimal places in your calculations. If your answer is zero enter "0".

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
Treatments
Blocks
Error
Total

The -value is - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 14

What is your conclusion?
- Select your answer - Conclude not all treatment means are equal  Do not reject the assumption that the treatment means are equal Item 15

Answer 1

I used Excel to solve this question:

Step.1 Enter data in excel sheet.

Step.2 Go to 'Data' menu ---> 'Data Analysis' ---> Select 'ANOVA : Two Factor Without Replication'.

Step.3 New window pop-up on screen. Provide input and output range. Refer following screen shot:

Excel output:

Anova: Two-Factor Without Replication
SUMMARY	Count	Sum	Average	Variance
1	3	29	9.67	2.33
2	3	24	8.00	12.00
3	3	49	16.33	2.33
4	3	56	18.67	1.33
5	3	25	8.33	1.33
A	5	70	14.00	22.50
B	5	57	11.40	28.80
C	5	56	11.20	25.70
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Block	293.73	4	73.43	41.18	0.00	3.84
Treatment	24.40	2	12.20	6.84	0.02	4.46
Error	14.27	8	1.78
Total	332.40	14

Hypothesis:

All treatment means are equal.

H1 : At least one treatment mean is significantly different than others.

P-value for F test statistic is 0.02 which is less than 0.05, hence we reject null hypothesis and conclude that not all treatment means are equal.