ANOVA Source of Variation
ANOVA  
Source ofVariation  SS  df  MS  F  pvalue 
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?  

(b) 
Calculate each F test statistic and thepvalue for each F test using Excel’s function=F.DIST.RT(F,DF1,DF2). (Round yourF_{calc} values to 3 decimal places andpvalues to 4 decimal places.) 
Source ofVariation  F_{calc}  pvalue 
Factor A  
Factor B  
Interaction  
(c1) 
There is a significant effect due to Factor A. 


(c2) 
There is a significant effect due to Factor B. 


(c3) 
There is a significant interaction between the two factors. 


Answer:
(a) What Kind of ANOVA is this
Ans : Twofactor 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 levelsfor Factor A x Number of levels for Factor B = 4×3 = 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  pvalue  pvalue 
Factor A  Mean Sum of squares for Factor ‘A’ / Mean sum of squares forError = 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 forError = 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 forError = 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  pvalue 
Factor A  2.9538  0.04542 
Factor B  3.2104  0.05212 
Interaction  7.4605  0.00003 
If pvalue is less than level of significance : ; Reject null hypothesis i.e. Factor is significant(Nullhypothesis Factor is not significant). Else Fail to reject nullhypothesis.
(c1) If level of significance : = 0.05
Factor A : pvalue : 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 : pvalue : 0.0454 > 0.01; Fail to reject nullhypothesis. Factor ‘A’ is not significant; Significant effect dueto factor ‘A’ : FALSE
(c2) If level of significance : = 0.05
Factor B : pvalue : 0.0521 > 0.05; Fail to reject nullhypothesis; Factor ‘B’ is not significant; Significant effect dueto factor ‘B’ : FALSE
If level of significance : = 0.01
Factor B : pvalue : 0.0521 > 0.01; Fail to reject nullhypothesis; Factor ‘B’ is not significant; Significant effect dueto factor ‘B’ : FALSE
(c3) If level of significance : = 0.05
Interaction : pvalue : 0.00003 < 0.05; Reject nullhypothesis; Interaction is significant; Significant effect due toInteraction : True
If level of significance : = 0.01
Interaction : pvalue : 0.00003 > 0.01; Reject nullhypothesis; Interaction is significant; Significant effect due toInteraction : True