Question

ANOVA
Source of Variation	SS	df	MS	F	p-value
Factor A	33,443.41	3	11,147.80
Factor B	24,232.44	2	12,116.22
Interaction	168,937.71	6	28,156.29
Error	135,865.32	36	3,774.04
Total	362,478.88	47

(a)	What kind of ANOVA is this?
	One-factor ANOVA Two-factor ANOVA with replication Two-factor ANOVA without replication

(b)	Calculate each F test statistic and the p-value for each F test using Excel's function =F.DIST.RT(F,DF1,DF2). (Round your Fcalc values to 3 decimal places and p-values to 4 decimal places.)

   

Source of Variation	Fcalc	p-value
Factor A
Factor B
Interaction

(c-1)	There is a significant effect due to Factor A.
	True False

        

(c-2)	There is a significant effect due to Factor B.
	False True

        

(c-3)	There is a significant interaction between the two factors.
	True False

Answer 1

(a) What Kind of ANOVA is this

Ans : Two-factor ANOVA with replication

In this We are studying two factors and their interaction.

Factor A has four levels

(For Factor A :As degrees of freedom(df)=number of levels -1; Number of levels=df+1=3+1=4)

Factor B has three Levels

(For Factor B: As degrees of freedom(df)=number of levels -1; Number of levels=df+1=2+1=3)

Number of observations for one replication = Number of levels for Factor A x Number of levels for Factor B = 4x3 = 12

Degrees of Freedom for Total= Total number of observations -1 ;

Total number of observations = Degrees of Freedom for Total + 1 = 47+1 = 48

Total number of replications = Total number of observations / Number of observations for one replication = 48/12 = 4

(b)

Source of Variation	Fcalc	F calc	DF1	DF2	p-value	p-value
Factor A	Mean Sum of squares for Factor 'A' / Mean sum of squares for Error = 11,147.80/ 3,774.04	2.9538	DF for Factor A = 3	DF for Error = 36	F.DIST.RT(2.9538,3,36)	0.04542
Factor B	Mean Sum of squares for Factor 'B' / Mean sum of squares for Error = 12,116.22/ 3,774.04	3.2104	DF for Factor B = 2	DF for Error = 36	F.DIST.RT(3.2104,2,36)	0.05212
Interaction	Mean Sum of squares for Interaction / Mean sum of squares for Error = 28,156.29/ 3,774.04	7.4605	DF for Interaction = 6	DF for Error = 36	F.DIST.RT(7.4605,6,36)	0.00003

Source of Variation	F calc	p-value
Factor A	2.9538	0.04542
Factor B	3.2104	0.05212
Interaction	7.4605	0.00003

If p-value is less than level of significance : ; Reject null hypothesis i.e. Factor is significant(Null hypothesis Factor is not significant). Else Fail to reject null hypothesis.

(c-1) If level of significance : = 0.05

Factor A : p-value : 0.0454 < 0.05; Reject null hypothesis; Factor 'A' is significant; Significant effect due to factor 'A' : TRUE

If level of significance : = 0.01

Factor A : p-value : 0.0454 > 0.01; Fail to reject null hypothesis. Factor 'A' is not significant; Significant effect due to factor 'A' : FALSE

(c-2) If level of significance : = 0.05

Factor B : p-value : 0.0521 > 0.05; Fail to reject null hypothesis; Factor 'B' is not significant; Significant effect due to factor 'B' : FALSE

If level of significance : = 0.01

Factor B : p-value : 0.0521 > 0.01; Fail to reject null hypothesis; Factor 'B' is not significant; Significant effect due to factor 'B' : FALSE

(c-3) If level of significance : = 0.05

Interaction : p-value : 0.00003 < 0.05; Reject null hypothesis; Interaction is significant; Significant effect due to Interaction : True

If level of significance : = 0.01

Interaction : p-value : 0.00003 > 0.01; Reject null hypothesis; Interaction is significant; Significant effect due to Interaction : True