Question: A web-designing company wants to learn about the effect of one-click checkouts. The target audiences of the web site were randomized into four groups, with 4 in each group. Each group was shown a page with either high or low graphics layout, and with one, or two click out options. After using the page, customers rated the convenience of the design on a 0-50 scale. At α = 0.05, find FA × B and analyze the interaction effect using a two-way ANOVA. [ A : Page layout and B : Mouse click ]
A ) 44.1, the combination of page layout and mouse click does not affect the scores B ) 44.1, the combination of page layout and mouse click does affect the scores C ) 0.1, the combination of page layout and mouse click does not affect the scores D ) 4.75, the combination of page layout and mouse click does affect the scores
Steps to derive
1 H0: There is no interaction effect between the page layout and the mouse click on the mean score.
H1: There is an interaction effect between the page layout and the mouse click on the mean score. [Hypotheses for the variables interaction.]
2a = 2, b = 2, and n = 4. The degrees of freedom(d.f.) are
Factor A: d.f.N = a - 1 = 2 - 1 = 1
Factor B: d.f.N = b - 1 = 2 - 1 = 1
Interaction (A × B): d.f.N = (a - 1)(b - 1) = (2 - 1)(2 - 1) = 1
Within(error): d.f.D = ab(n - 1) = 2·2 (4 - 1) = 12 [a, b are levels of factors A, B respectively and n is the number of data values in each group.]
3 The critical value FA corresponding to α = 0.05, d.f.N = 1, and d.f.D = 12 is 4.75
4 The critical value FB corresponding to α = 0.05, d.f.N = 1, and d.f.D = 12 is 4.75
5 The critical value FA × B corresponding to α = 0.05, d.f.N = 1, and d.f.D = 12 is 4.75
6 SSA = 1, SSB = 1, SSA × B = 441 and SSW = 120
7 The mean squares are as follows:
MSA = SSAa-1 = 1
MSB = SSBb-1 = 1
MSA × B = SSA×B(a-1)(b-1) = 441
MSW = SSWab(n-1) = 10 [Substitute and simplify.]
8 MSA = 1, MSB = 1, MSA × B = 441 and MSW = 10
9 The F values are computed as follows:
FA = MSAMSW = 0.1
FB = MSBMSW = 0.1
FA × B = MSA×BMSW = 44.1 [Substitute and simplify.]
10 Since FA × B = 44.1 > 4.75, the null hypothesis concerning the interaction effect should be rejected.
11 Since the null hypothesis for the interaction effect was rejected, it can be concluded that the combination of page layout and mouse click does affect the scores.
