Question

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

		Treatments
		A	B	C
Blocks	1	10	9	8
	2	12	6	5
	3	18	16	14
	4	20	18	18
	5	8	7	8

Use α = 0.05 to test for any significant differences.

Find the value of the test statistic. (Round your answer to two decimal places.)

__________.

Find the p-value. (Round your answer to three decimal places.)

p-value = ________.

Answer 1

For this question we use MS-EXCEL.

Go to data analysis toolpack and select ANOVA : two factors without replication.

Randomized Block Design

Test hypothesis is,

H₀₁ : There is no significant difference between treatments.

H₁₁ : There is significant difference between treatments.

H₀₂ : There is no significant difference between blocks.

H₁₂ : There is significant difference between blocks.

ANOVA Table

Source of Variation	SS	df	MS	F	P-value	F crit
Treatments(columns)	25.2	2	12.6	6	0.0256	4.45897
Blocks(rows)	320.4	4	80.1	38.14286	2.96E-05	3.837853
Error	16.8	8	2.1
Total	362.4	14

level of significance = 0.05

For treatements

The value of test statistic is 6

p-value is 0.0256

Therefore, p-value <

Hence, Reject H₀₁

Conclusion : There is significant difference between treatments.

For Blocks

The value of test statistic is 38.14286

p-value is 2.96E-05

Therefore, p-value <

Hence, Reject H₀₂

Conclusion : There is significant difference between blocks.