Answer:
Step-by-step explanation:
We have a factorial experiment with Factors A and B, levels a=2, b=3, and n=2 observations.
It's necessary to apply a Two-Factor with replication ANOVA by using Excel or calculating by hand.
1. Sum of Squares could be calculated with the following formulas:
[tex]SS_{T}=\sum\limits^a_{i=1}\sum\limits^b_{j=1}\sum\limits^n_{k=1} {(y_{ijk}-y_{...} ^{2} )}\\SS_{A}=bn\sum\limits^a_{i=1} {(y_{i..}^{2}) -Ny_{...} ^{2} }\\SS_{B}=an\sum\limits^b_{j=1} {(y_{.j.}^{2}) -Ny_{...} ^{2} }\\SS_{AB}=n\sum\limits^a_{i=1}\sum\limits^b_{j=1} {(y_{ij.}^{2}) -Ny_{...} ^{2} -SC_{A} -SC_{B}-SC_{AB}}[/tex]
2. Calculate Degrees of Freedom
Factor A: [tex]a-1[/tex]
Factor B: [tex]b-1[/tex]
Interaction: [tex](a-1)(b-1)[/tex]
Within: [tex]ab(n-1)[/tex]
Total: [tex]abn-1[/tex]
3. Mean Square:
Factor A: [tex]MS_{A}=\frac{SS_{A}}{a-1}[/tex]
Factor B: [tex]MS_{B}=\frac{SS_{B}}{b-1}[/tex]
Interaction: [tex]MS_{AB}=\frac{SS_{AB}}{(a-1)(b-1)}[/tex]
Within:[tex]MS_{E}=\frac{SS_{E}}{ab(n-1)}[/tex]
4. Estimate F and P-value
[tex]F_{A}=\frac{SS_{A} }{SS_{E}}[/tex]
[tex]F_{B}=\frac{SS_{B} }{SS_{E}}[/tex]
[tex]F_{AB}=\frac{SS_{AB} }{SS_{E}}[/tex]
Open the attachment to see the results.
5. Analysis of P-values
Factor A: P-value (0.1280
)>(0.05)
Factor B: P-value (0.0315 )<(0.05)
Interaction: P-value (0.2963
)<(0.05)
P-value of Factor B is less than 0.05, then type of language is insignifficant.
P-value of Factor A and interaction are greater than 0.05, then the translator system and the interaction of both factors are signifficant.
