WALDEN
UNIVERSITY
YOLANDA N.
GEORGE-DAVID
WEEK
4. ASSIGNMENT
Scenario:
Imagine you are a
researcher who believes that a relaxation technique involving visualization
will help people with mild insomnia fall asleep faster. You randomly select a
sample of 20 participants from a population of mild insomnia patients and
randomly assign 10 to receive visualization therapy. The other 10 participants
receive no treatment.
You then measure
how long (in minutes) it takes participants to fall asleep. Your data are
below. The numbers represent the number of minutes each participant took to
fall asleep.
|
No Treatment (X1) |
Treatment (X2) |
|
22 |
19 |
|
18 |
17 |
|
27 |
24 |
|
20 |
21 |
|
23 |
27 |
|
26 |
21 |
|
27 |
23 |
|
22 |
18 |
|
24 |
19 |
|
22 |
22 |
Assignment:
• Explain whether you chose to
use an independent-samples t-test or a matched-samples t test. Provide a rationale
for your choice.
The two variables (No Treatment X1 and Treatment X2) are independent of
each other.
I chose to use an independent-samples t-test because our resource defines
Independent-samples t-test as the parametric procedure used to test sample
means from two independent samples (Heiman 2015).
• Identify the independent and
dependent variables.
The dependent variable is the variable that measures a behavior or
attribute of participants that we expect will be influenced by the independent
variable. (Heiman 2015). The Dependent variable is the time it takes
participants to fall asleep. Therefore, the independent variable is the
treatment.
• Knowing you believe the
treatment will reduce the amount of time to fall asleep, state the null and
alternate hypotheses in words (not formulas).
The null hypothesis is always the hypothesis of no difference (2015).
With the two variables, there’s no difference with the time to fall asleep
whether treatment was given or not given.
However, the Alternative Hypothesis is when the time to fall asleep is
lower when treatment is given as compared to when no treatment is given.
• Explain whether you would use
a one-tailed or two-tailed test and why.
To be able to see if the treatments reduce the sleeping time, I would use
a one-tailed test because a one-tailed test allows you to determine if one mean
is greater or less than another mean, but not both.
• Explain whether you have
homogeneity of variance, and explain how you know. Explain why it is important
to know if you have homogeneity of variance.
Null Hypothesis, H0: There is no difference between the variances of
Treatment X1 and No treatment X2. Compared to the alternative Hypothesis, H1:
there is a difference between the variances of Treatment X1 and No treatment X2
I fail to reject Ho at 5% level of significance because p-value is 1.00
which is greater than alpha (0.05).
Therefore, there is no difference between the variances of two groups
(Treatment and No treatment). Hence decide to proceed with independent sample
t-test with equal variances.
• Identify the obtained t value
for this data set using SPSS.
T value = 1.492
• Identify the degrees of
freedom and explain how you determined it.
Degree of freedom = n1+n2-2 = 10+10-2 = 18
• Identify the p value.
p-value = 0.153
• Explain whether you should
retain or reject the null hypothesis and why.
I reject H at 5% level of significance because P-Value = 1.00 and
conclude that the time to fall asleep when treatment is less as compared to
when no treatment is given.
• Explain what you can conclude
about the effectiveness of visualization therapy.
It is my conclusion that visualization therapy is effective.
References:
Heiman, Gary. Behavioral Sciences STAT 2, 2e, 2nd Edition. Cengage Learning,
2015. VitalBook file.
L. Lehmann, E., & P. Romano, J. (N.D.).
Testing Statistical Hypotheses (Third ed.).
SPSS Output
|
Group Statistics |
|||||
|
group |
N |
Mean |
Std. Deviation |
Std. Error Mean |
|
|
Observation |
no_treatment |
10 |
23.10 |
2.961 |
.936 |
|
treatment |
10 |
21.10 |
3.035 |
.960 |
|
Independent Samples Test |
||||||||||
|
Levene’s Test for Equality of Variances |
t-test for Equality of Means |
|||||||||
|
F |
Sig. |
t |
df |
Sig. (2-tailed) |
Mean Difference |
Std. Error Difference |
95% Confidence Interval of the Difference |
|||
|
Lower |
Upper |
|||||||||
|
Observation |
Equal variances assumed |
.000 |
1.000 |
1.492 |
18 |
.153 |
2.000 |
1.341 |
-.817 |
4.817 |
|
Equal variances not assumed |
1.492 |
17.989 |
.153 |
2.000 |
1.341 |
-.817 |
4.817 |
