To study the effectiveness of possible treatments for insomnia, a sleep researcher conducted a study in which four participants were instructed to count sheep (the Sheep Condition), four were told to concentrate on their breathing (the Breathing Condition), and four were not given any special instructions. The average number of minutes taken for each participant to fall asleep over the next seven days were 14, 28, 27, and 31 minutes for the Sheep condition; 25, 22, 17, and 14 minutes for those in the Breathing condition; and 45, 33, 30, and 41 for the Control condition. Using the .05 significance level, did the different techniques have different effects?
To study the effectiveness of possible treatments for insomnia, a sleep researcher conducted a study in which four participants were instructed to count sheep (the Sheep Condition), four were told to concentrate on their breathing (the Breathing Condition), and four were not given any special instructions. The average number of minutes taken for each participant to fall asleep over the next seven days were 14, 28, 27, and 31 minutes for the Sheep condition; 25, 22, 17, and 14 minutes for those in the Breathing condition; and 45, 33, 30, and 41 for the Control condition. Using the .05 significance level, did the different techniques have different effects?
Step 4: Determine your sample’s score on the comparison distribution.
This is where you determine the sample’s F ratio (the numerator and denominator). To do that, you have to find the between-groups variance estimate and the within-groups variance estimate.
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Within-groups variance estimate: This is the number that goes on the bottom of your F ratio.
I have a table started to help you come up with the numbers you need. I have filled in the given numbers. You must fill in the blanks, add things up, etc., according to what you learned from the chapter.
Sheep Condition Deviation from Mean Squared Dev from Mean
14
28
27
31
Mean of Sheep Condition People = ???
S2 = ???
Breathing Condition Deviation from Mean Squared Dev from Mean
25
22
17
14
Mean of Breathing Condition People = ???
S2 = ???
Control Condition Deviation from Mean Squared Dev from Mean
45
33
30
41
Mean of Control Condition People = ???
S2 = ???
Now you have to use the numbers you just came up with to plug into the formula for the within-groups variance estimate (given below). The “answer” you get is your final number for the within-groups variance.
S2Within= S21 + S22 + S23 / NGroups
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