Problem: 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 1: Restate the question as a research hypothesis and a null hypothesis about the populations. Pop 1: Pop 2: Pop 3: Null hypothesis: Research hypothesis: Step 2: Determine the characteristics of the comparison distribution. What type of distribution is this What is the df for the between-groups variance estimate: What is the df for the within-groups variance estimate: Step 3: Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected. Use the F table (table A-3) in the textbook to look up the cutoff score using the degrees of freedom we just stated in Step 2. Cutoff score = 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. ************************************************************************************************************ 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 ************************************************************************************************************ Between-groups variance estimate: This is the number that goes on the top of your F ratio. To get this number, you have to do a few more calculations. You will use the formulas from the book. Use the table below to help get you started (where I inserted the names of groups in parentheses is where you actually input the mean of each group and delete the group names I inserted—I just put them there to guide you). What is the value of the Grand Mean: ??? Sample Means Deviation from Grand Mean (GM) Sq Dev from GM (sheep mean) ? ? (breathing mean) ? ? (control mean) ? ? Now you have to use the formula for the between-groups variance estimate (given below). S2Between = S2M (n) To find the S2M, you have to use the calculations from above with the squared deviation scores from the Grand Mean. Look in your text at the examples if you need help plugging numbers in. Your quick hint is to fill out the table I made you by subtracting the GM from each sample mean, then squaring those answers, adding them all up, and then dividing them by the dfBetween. The dfBetween is simply the number of groups minus 1. Once you have the S2M, don’t forget the last step of multiplying it by ‘n’, which is the number of participants in each sample (in this case, that number is 4). I hope this helps you get the correct numbers to plug into your F ratio! *********************************************************************************************************** What is the F ratio??? ____ / ____ = ______ When you divide out the F ratio, what is your final F value? Step 5: Decision Is your F value extreme enough to reject the null hypothesis? What is your final decision and why are you making this decision?
Problem:
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 1: Restate the question as a research hypothesis and a null hypothesis about the populations.
Pop 1:
Pop 2:
Pop 3:
Null hypothesis:
Research hypothesis:
Step 2: Determine the characteristics of the comparison distribution.
What type of distribution is this
What is the df for the between-groups variance estimate:
What is the df for the within-groups variance estimate:
Step 3: Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected.
Use the F table (table A-3) in the textbook to look up the cutoff score using the degrees of freedom we just stated in Step 2. Cutoff score =
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.
************************************************************************************************************
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
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
************************************************************************************************************
Between-groups variance estimate: This is the number that goes on the top of your F ratio.
To get this number, you have to do a few more calculations. You will use the formulas from the book. Use the table below to help get you started (where I inserted the names of groups in parentheses is where you actually input the mean of each group and delete the group names I inserted—I just put them there to guide you).
What is the value of the Grand Mean: ???
Sample Means Deviation from Grand Mean (GM) Sq Dev from GM
(sheep mean) ? ?
(breathing mean) ? ?
(control mean) ? ?
Now you have to use the formula for the between-groups variance estimate (given below).
S2Between = S2M (n)
To find the S2M, you have to use the calculations from above with the squared deviation scores from the Grand Mean. Look in your text at the examples if you need help plugging numbers in. Your quick hint is to fill out the table I made you by subtracting the GM from each sample mean, then squaring those answers, adding them all up, and then dividing them by the dfBetween. The dfBetween is simply the number of groups minus 1. Once you have the S2M, don’t forget the last step of multiplying it by ‘n’, which is the number of participants in each sample (in this case, that number is 4).
I hope this helps you get the correct numbers to plug into your F ratio!
***********************************************************************************************************
What is the F ratio??? ____ / ____ = ______
When you divide out the F ratio, what is your final F value?
Step 5: Decision
Is your F value extreme enough to reject the null hypothesis? What is your final decision and why are you making this decision?
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