Would just like to make sure I completed each step correctly and have feedback/c
ID: 3232864 • Letter: W
Question
Would just like to make sure I completed each step correctly and have feedback/corrections.
For the following problem you need to:
1. identify the independent and dependent variables
2. give the null and alternative hypothesis
3. determine the critical value (use alpha = .05)
4. calculate the F statistic and all the required intermediate steps
5. what conclusion can you make at this point (using the statistic and critical value)
6. calculate a measure of effect size (R2)
8. calculate the contrasts (post-hoc tests) to determine which groups significantly differ from eachother
9. what conclusion can you make now (using the results of the contrasts).
A student interested in alternative sleep aids has heard that valerian root, melatonin and 5-htp have very few side effects and may be able to help with her recent insomnia. She decides to run a little experiment with her sorority sisters to determine which of the three makes people fall asleep the fastest. The following data is the amount of time, in minutes, between consumption and sleep for each of the three natural sleep aids.
Valerian Root
Melatonin
5- HTP
29
39
25
32
32
30
27
34
31
30
36
27
26
35
33
34
34
28
31
33
32
34
37
30
28
31
31
32
30
27
Independent Variables: Sleep aid types (Valerian Root, Melatonin, and 5-HTP)
Dependent Variables: Amount of time (in minutes) between consumption and sleep
Null Hypothesis : There is no any significant difference in the average amount of time between consumption and sleep for the three natural sleep aids.
Alternative hypothesis : There is a significant difference in the average amount of time between consumption and sleep for the three natural sleep aids.
For finding critical value, we must find degrees of freedom for F value.
Total number of groups: k=3
Total number of observations: N= 30
Level of significance:
So, we will find the F critical value with using F-Table
By using excel we can compute one way Anova table below to find the F-statistic ,
Anova: Single Factor
SUMMARY
Groups
Count
Sum
Average
Variance
Valerian Root
10
303
30.3
7.788888889
Melatonin
10
341
34.1
7.655555556
5-HTP
10
294
29.4
6.488888889
ANOVA
Source of Variation
SS
df
MS
F
P-value
F crit
Between Groups (BG)
124.466666
2
62.23333333
8.512158055
0.001360068
3.354130829
Within Groups (WG)
197.4
27
7.311111111
Total (T)
321.866666
29
Since , reject the null hypothesis and accept the alternative hypothesis as there is sufficient evidence at 5% level of significance to support the claim that groups significantly differ from each other.
Turkey HSD Test Results:
Below color coded results (red for insignificant, green for significant) of evaluating whether Qi,j>Qcritical for all relevant pairs of treatments.
treatments
Tukey HSD
Tukey HSD
Tukey HSD
pair
Q statistic
p-value
inferfence
A vs B
4.4442
0.0108953
* p<0.05
A vs C
1.0526
0.7253757
insignificant
B vs C
5.4968
0.0016706
** p<0.01
Scheffé Test results:
Below color coded results (red for insignificant, green for significant)
treatments
Scheffé
Scheffé
Scheffé
pair
T-statistic
p-value
interfence
A vs B
3.1425
0.0148754
* p<0.05
A vs C
0.7443
0.7602008
insignificant
B vs C
3.8868
0.0024809
** p<0.01
Valerian root and Melatonin are significant.
Valerian root and 5-HTP are insignificant.
Melatonin and 5-HTP are significant.
5-HTP has least mean, implying it takes less time to go to sleep.
Valerian Root
Melatonin
5- HTP
29
39
25
32
32
30
27
34
31
30
36
27
26
35
33
34
34
28
31
33
32
34
37
30
28
31
31
32
30
27
Explanation / Answer
Need following corrections:
Level of signficance: 0.05
Since p-value of F test is less than 0.05 so we reject the null hypothesis as there is sufficient evidence at 5% level of significance to support the claim that groups significantly differ from each other.
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