In: Statistics and Probability
Suppose you are interested in the basic question of, “Is there an effect of mental health on amount of sleep?” You recruit 8 healthy individuals, 8 depressed individuals, and 8 anxious individuals and measure the amount they sleep. Given that SSb = 1902 and SSw = 3386 fill in a source table and find the obtained value of the appropriate statistic.
a.17 |
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b 5.90 |
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c. 24.00 |
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d. 4.45 |
Given your obtained value in the sleep study, what is the correct decision?
Significant. Reject the Ho. Mental health did not have a significant effect on amount slept. |
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Significant. Reject the Ho. Mental health had a significant effect on amount slept. |
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Not significant. Fail to reject the Ho. Mental health did not have a significant effect on amount slept. |
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Not significant. Fail to reject the Ho. Mental health had a significant effect on amount slept. |
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The Hypothesis:
H0: Mental health does not have a significant effect on amount slept. (There is no relationship between them)
Ha: Mental health has a significant effect on amount slept. (There is a relationship between them)
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Number of groups, k = 3
Total Observations N = 24
df b = k - 1 = 2
df w = N - k = 24 - 3 = 21
MS b = SSb / df b = 1902 / 2 = 951
MS w = SSw / df w = 3386 / 21 = 161.238
Therefore F test = MS b / MS w = 951 / 161.238 = 5.90 (Option b)
The ANOVA table is as below
Source | SS | DF | Mean Square | F | p | Fc |
Between | 1902.00 | 2 | 951.00 | 5.90 | 0.0093 | 3.467 |
Within/Error | 3386.00 | 21 | 161.24 | |||
Total | 5288.00 | 23 |
The p value is calculated for F = 5.9, df1 = 2, df2 = 21
The F critical value is calculated at Alpha = 0.05 (default) df1 = 2, df2 = 21
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Since F test is > Fcritical (3.467) and also p value is < 0.05, We reject the null hypothesis.
Option 2: Significant Reject the H0. Mental health had a significant effect on the amount slept.
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