ANOVA Source of Variation
| ANOVA | |||||
| Source ofVariation | 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? | ||||||
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| (b) |
Calculate each F test statistic and thep-value for each F test using Excel’s function=F.DIST.RT(F,DF1,DF2). (Round yourFcalc values to 3 decimal places andp-values to 4 decimal places.) |
| Source ofVariation | Fcalc | p-value |
| Factor A | ||
| Factor B | ||
| Interaction | ||
| (c-1) |
There is a significant effect due to Factor A. |
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|
| (c-2) |
There is a significant effect due to Factor B. |
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|
| (c-3) |
There is a significant interaction between the two factors. |
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Answer:
(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 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 | p-value | p-value |
| 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 | 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(Nullhypothesis Factor is not significant). Else Fail to reject nullhypothesis.
(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 nullhypothesis. Factor ‘A’ is not significant; Significant effect dueto factor ‘A’ : FALSE
(c-2) If level of significance : = 0.05
Factor B : p-value : 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 : p-value : 0.0521 > 0.01; Fail to reject nullhypothesis; Factor ‘B’ is not significant; Significant effect dueto factor ‘B’ : FALSE
(c-3) If level of significance : = 0.05
Interaction : p-value : 0.00003 < 0.05; Reject nullhypothesis; Interaction is significant; Significant effect due toInteraction : True
If level of significance : = 0.01
Interaction : p-value : 0.00003 > 0.01; Reject nullhypothesis; Interaction is significant; Significant effect due toInteraction : True
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