A researcher hypothesizes that distractions occur more for those with greater prior exposure to sugars when sugary snacks are placed in their work environment. Essentially, the researchers were attempting to see if the presence or absence of sugary treats affected the amount of time to distraction for three groups: those with low, moderate and high exposure to sugar. They measured time to distraction by timing the participants in completing a computer task – thus, longer times meant more distraction, while shorter times meant less distraction. To test this, the researchers conducted a twoway ANOVA with replication, for which the data and output are shown in the file “Sugar”. The researchers conducted the research by setting α = 0.01. Identify the independent variables and their levels. Identify the dependent variable. Interpret the ANOVA output for significance at α = 0.05 for each of the following: the effect of exposure on completion time; the effect of the absence or presence of sugary snacks on completion time; and the interaction effect of snack availability and prior exposure to sugars on completion time. Provide a layperson interpretation of the findings in (b). What is the next step in this study?
Previous Exposure to Sugar Low Moderate High Sugar at
Worksite
Absent 8 10 13 7 12 9 9 15 11 10 8 8 12 6 13 8 9 12
Present 5 15 15 8 9 12 5 7 15 6 6 16 5 4 12 7 11 14
a)
Since the data is not given, in proper format, rearranging the data as:
Sugary Snacks 

Completion time 
Absent 
Present 
Low 
8 
5 
10 
15 

13 
15 

7 
8 

12 
9 

9 
12 

Moderate 
9 
5 
15 
7 

11 
15 

10 
6 

8 
6 

8 
16 

High 
12 
5 
6 
4 

13 
12 

8 
7 

9 
11 

12 
14 
Independent Variables:
Sugary Snacks  2 Levels (Absent, Present)
Completion Time – 3 Levels (Low, Moderate, High)
Dependent Variable: Time to distraction
Null and Alternative Hypothesis:
We will have three hypotheses:
Completion time
H_{0}: µ_{Low} = µ_{Moderate}= µ_{High}
H_{1}: Not all Means are equal
Sugary Snacks
H_{0}: µ_{Absent} = µ_{Present}
H_{1}: Not all Means are equal
H_{0}: An interaction is absent
H_{1}: Interaction is present
Alpha = 0.05
Degress of Freedom:
Df_{Completion Time}(A) = a1 = 31 = 2
Df_{Sugary Snacks} (B) = b1 = 21 = 1
df _{Completion Time * Sugary Snacks} (A*B) = (a1) * (b1) = 2*1 = 2
df _{error} = N – ab = 36 – 3*2 = 30
df _{total}= N – 1 = 36 – 1 = 35
Decision Rule (3):
We have three hypotheses, so we have three decision rules:
Critical Values:
Completion Time (df_{Completion Time}(A), df _{error}): (2,30) = 3.32
Sugary Snacks (df_{Sugary Snacks} (B),df _{error}): (1,30) = 4.17
Interaction (df _{Completion Time * Sugary Snacks} (A*B), df _{error}) : (2,30) = 3.32
[Completion Time] If F is greater than 3.32, reject the null hypothesis
[Sugary Snacks] If F is greater than 4.17, reject the null hypothesis
[Interaction] If F is greater than 3.32, reject the null hypothesis
Test Statistics:
SS_{Completion Time} = ∑(∑a_{i})^{2}/b*n  T^{2}/N = 4.39
SS_{Sugary Snacks} = ∑(∑b_{i})^{2}/a*n  T^{2}/N = 1.78
SS_{Completion Time*Sugary Snacks} = ∑(∑a_{i} * b_{i})^{2}/n  ∑(∑a_{i})^{2}/b*n  ∑(∑b_{i})^{2}/a*n + T^{2}/N = 7.39
SS_{Total} = ∑(Y)^{2}  T^{2}/N = 400.22
SS_{Error} = SS_{Total}  SS_{Completion Time}  SS_{Sugary Snacks}  SS_{Completion Time*Sugary Snacks} = 386.67
MS = SS/df
F = MS_{effect} / MS_{error}
Hence,
F_{Completion Time} = 2.19/12.89 = 0.170
F_{Sugary Snacks} = 1.78/12.89 = 0.138
F_{Interaction} = 3.69/12.89 = 0.287
SS 
Df 
MS 
F 

Completion Time 
4.39 
2 
2.19 
0.170 
Sugary Snacks 
1.78 
1 
1.78 
0.138 
Interaction 
7.39 
2 
3.69 
0.287 
Error 
386.67 
30 
12.89 

Total 
400.22 
35 
Results:
[Completion Time] If F is greater than 3.32, reject the null hypothesis
Our F = 0.170, we retain the null hypothesis.
[Sugary Snacks] If F is greater than 4.17, reject the null hypothesis
Our F = 0.138, we retain the null hypothesis.
[Interaction] If F is greater than 3.32, reject the null hypothesis
Our F = 0.287, we retain the null hypothesis.
b)
Had we rejected the null hypothesis for any effect, we should have done a PostHoc Analysis.
PS: If the data is different, use the above approach to get the desired results.
A researcher hypothesizes that distractions occur more for those with greater prior exposure to sugars when...
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