# For the following, A = attract

For the following, A = attractiveness and B=time; same levels.Conduct a two-factor fixed effects ANOVA (alpha=.05).

A₁B₁: 10, 8, 7, 3

A₁ B₂: 15, 12, 21, 13

A₂ B₁: 13, 9, 18, 12

A₂B₂: 20, 22, 24, 25

A₃ B₁: 24, 29, 27, 25

A₃ B₂: 10, 12, 21, 14

A₄ B₁: 30, 26, 29, 28

A₄ B₂: 22, 20, 25, 15

Answer For the Fixed Effects Model of the above problem

Factors are

1 . Attracttiveness A: 4 levels(a) – A1,A2, A3 and A4

2. Time B 2 levels (b)B1 and   B2

There are 4 replications(n).

Hence for Anova Effect and noof degrees of freed om will be

EffectDegrees ofFreedom

A a-1= 4-1 =3

B b-1= 2-1=1

AB interaction(a-1)*(b-1)= 3*1 = 3

Error a*b*(n-1)=4*2*(4-1)=24

Total 4*2*4-1=31

ANOVA table can be derived using Minitab based on the data /ormanually calculated (lengthy)

in mintab use following steps to get the ANOVA results

1. put data as per following format in worksheet.

2.choose   Stat > ANOVA > Two-Way.

3. Select Response as Response ,Row Factor as “Attractivenessand Column Factor as “Time”

Check confidence level at 95%, Click OK . you will get ANOVA onsession window output. The same is given below

Two-way ANOVA: Response versus Attractiveness, Time

Source DF SS MS F PAttractiveness 3 738.59 246.198 21.35 0.000Time 1 1.53 1.531 0.13 0.719Interaction 3 732.84 244.281 21.18 0.000Error 24 276.75 11.531Total 31 1749.72

S = 3.396 R-Sq = 84.18% R-Sq(adj) = 79.57%

The above Table is the ANOVA table ,

As p value is lower for Attractiveness and Interaction it can besaid that there is significant effect for attractiveness andintercation of attractivess and time interaction. and effect oftime is not significant.

Datasheet ———————-

Attractveness   Time   ResponseA1 B1   10A1   B1   8A1   B1   7A1   B1   3A1   B2   15A1   B2   12A1   B2   21A1   B2   13A2   B1   13A2   B1   9A2   B1   18A2   B1   12A2   B2   20A2   B2   22A2   B2   24A2   B2   25A3   B1   24A3   B1   29A3   B1   27A3   B1   25A3   B2   10A3   B2   12A3   B2   21A3   B2   14A4   B1   30A4   B1   26A4   B1   29A4   B1   28A4   B2   22A4   B2   20A4   B2   25A4   B2   15

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