.The following table summarizes the results from a two-factor study (examining t
ID: 3257445 • Letter: #
Question
.The following table summarizes the results from a two-factor study (examining the effects of two factors: A and B) with 2 levels of factor A and 3 levels of factor B. A separate group of n = 8 participants are included in each of the 6 treatment conditions. Fill in the missing values. (Hint: Start by filling in the df values. Look at each relevant formula to figure out what you can calculate based on the values provided, starting with df. Remember that in ANOVA, we are partitioning variability [and df, SS, and MS] into different components, so each component should add up to the total. We are also partitioning “between treatments” variance into different components for the main effects and the interaction.)
Between Treatments: SS:60 df:___
Factor A: SS:______ df:___ MS:5 F:____
Factor B: SS:______ df:___ MS:___ F:____
Factor AxB interactions: SS:25 df:___ MS:___ F:____
Within Treatments: SS:______ df:42 MS:2.5
Total: SS 165 df:47
Please fill in the missing blanks, and show work. Thank you!
Explanation / Answer
There are 2 levels of factor A , hence we have,
dfFactor A = 2 -1 = 1
Also we have 3 levels of factor B , hence we have,
dfFactor B = 3 -1 = 2
dfBetween treatemnts = dfTotal - dfWithin treatments = 47- 42 = 5
dfFactor AxB interaction = dfBetween treatments - dfFactor A - dfFactor B = 5 - 1 - 2 = 2
SSFactor A = MSFactor A x dfFactor A = 5 x 1 = 5
SSWithin treatments = MSWithin treatments x dfWithin treatments = 2.5 x 42 = 105
SSFactor B = SSBetween treatments - SSFactor A - SSFactor AxB interactions = 60 - 5 - 25 = 30
MSFactor B = SSFactor B/dfFactor B = 30/2 = 15
MSFactor AxB interactions = SSFactor AxBinteractions/dfFactor AxB interactions = 25/2 = 12.5
FFactor A = MSFactor A/MSWithin treatments = 5/2.5 = 2
FFactor B = MSFactor B/MSWithin treatments = 15/2.5 = 6
FFactor AxB interactions = MSFactor AxB interactions/MSWithin treatments = 12.5/2.5 = 5
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