Amit Almor, a psychology researcher at the University of South Carolina, conducted a series of experiments on conversation and attention level. He found that subjects were four times more distracted while preparing to speak or speaking than when they were listening. This research has many implications, including those for the issue of using cell phones while driving. You decide to explore this issue by having three different groups try tracking a fast-moving target on a computer screen. The first group is preparing to speak, the second group is speaking, and the third group is listening to a conversation. The sample mean and sum of squares of the scores for each of the three groups are presented in the following table. Group Sample Mean Sum of Squares Preparing to speak 98.3 7,2810.0900 Speaking 101.5 6,6156.8100 Listening 103.2 70,277.7600

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Amit Almor, a psychology researcher at the University of South Carolina, conducted a series of experiments on conversation and attention level. He found that subjects were four times more distracted while preparing to speak or speaking than when they were listening. This research has many implications, including those for the issue of using cell phones while driving.
You decide to explore this issue by having three different groups try tracking a fast-moving target on a computer screen. The first group is preparing to speak, the second group is speaking, and the third group is listening to a conversation.
The sample mean and sum of squares of the scores for each of the three groups are presented in the following table.
Group
Sample Mean
Sum of Squares
Preparing to speak 98.3 7,2810.0900
Speaking 101.5 6,6156.8100
Listening 103.2 70,277.7600
 
After collecting the data, you analyze the data using an ANOVA. The results of your analysis are presented in the following ANOVA table.
ANOVA Table
Source of Variation
SS
df
MS
F
Between Treatments 3,095.00 2 1,547.50 5.52
Within Treatments 209,244.66 747 280.11  
Total 212,339.66 749    
 
These findings are significant at α = 0.05, which tells you that the difference is very unlikely to have occurred just by chance, but it does not tell you the size of the effect. A simple measure of the effect size is given by    .
 
What is the formula for this measure of the effect size?
MSbetweenbetween/MStotaltotal
 
SSbetweenbetween/SSwithinwithin
 
SSbetweenbetween/SStotaltotal
 
MSbetweenbetween/MSwithinwithin
 
 
Based on the data given, the effect size is    . (Round your answer to two decimal places)
 
The percentage of variability in the scores accounted for by the effect due to treatments is    .
Expert Solution
Step 1

ANOVA table is:

Source of variation

SS

df

MS

F

Between treatments

3095.00

2

1547.50

5.52

Within treatments

209244.66

247

280.11

 

Total

212339.66

249

 

 

 

These findings are significant at α = 0.05.

A simple measure of the effect size can be calculated as:

η2=SSbetweenSStotal

The correct option is:

  1. SSbetween/SStotal.
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