Question

.   Complete the analysis of variance table for the following data. Treat it as a two

      way Block Design. (Use α = 0.05). In each cell there are 2 observations, except for

      the last cell, which has only one observation.

DATA

Source A				Means
	I	II	III
Source B Level 1	20    18	12    14	9   11	14
Source B Level 2	12    10	10      8	8	9.6
Means	15	11	9.33	Grand Mean = 12

ANOVA TABLE

Sources	D.F.	S.S.	M.S.	F
Source A
Source B
Error
TOTAL

State the Alternate Hypothesis Ha for both sources of variability.

Source A   Ha:                                             Source B    Ha:

How many degrees of freedom for A? …….       What is the Critical Point for A?............

How many degrees of freedom for B? …….        What is the Critical Point for B?............

Do you reject Ho for Source A? ……..                  Do you reject Ho for Source B? ……..

So, is Source A statistically significant? …………..      And Source B? ………………..

Answer 1

ANOVA table

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
A	2	68.625	34.313	21.45	0.004
B	1	48.286	48.286	30.18	0.003
A*B	2	18.625	9.313	5.82	0.049
Error	5	8.000	1.600
Total	10	149.636

If p-value < 0.05 results are significant.

State the Alternate Hypothesis Ha for both sources of variability.

Source A   Ha: Atleast one mean is significantly different from the other.

Source B    Ha: Atleast one mean is significantly different from the other.

How many degrees of freedom for A= (3-1 = 2) What is the Critical Point for A=  F0.05,2,5 = 5.786

How many degrees of freedom for B = (2-1 = 1) What is the Critical Point for B= F0.05,1,5 = 6.608

Do you reject Ho for Source A = Yes Reject H0 Do you reject Ho for Source B = Yes Reject H0

So, is Source A statistically significant? Yes Significant And Source B? Yes Significant