Question

 

Chronic insomnia

10 people with chronic insomnia received a study in 4 studies that were intended to increase the number of hours of sleep. One of these treatments was placebo.

1- Calculate the average number of hours of sleep for each of the 4 treatments. Also enter a 95% confidence interval for the average.

2- Create box plot for each of the 4 treatments in the same graph. How will you describe the distribution of treatments?

3- Calculate how much extra sleep patients have received after each treatment compared to when they received a placebo. How many have had more sleep and how many have had less sleep in each of the treatment groups? What will be the average extra sleep for each treatment?

4- Test if there is statistically significant difference between each of the treatments and placebo (beh1 vs. placebo, beh2 vs. placebo, beh3 vs. placebo). Be sure to check the assumptions that are the basis for performing a t-test.

5- Is treatment 2 more effective than treatment 3? Make an analysis based on both confidence interval and p-value.

SPSS FILE 1

Patients

1
2
3
4
5
6
7
8
9
10

SPSS FILE 2

Placebo

.6
3.0
4.7
5.5
6.2
3.2
2.5
2.8
1.1
2.9

SPSS FILE 3

Treatment 1

1.3
1.4
4.5
4.3
6.1
6.6
6.2
3.6
1.1
4.9

SPSS FILE 4

Treatment 2

2.5
3.8
5.8
5.6
6.1
7.6
8.0
4.4
5.7
6.3

SPSS FILE 5

Treatment 3

2.1
4.4
4.7
4.8
6.7
8.3
8.2
4.3
5.8
6.4

Answer 1

The SPSS output for the above problem is attached below.

Here are the answers for the above questions:

1. The average no. of hours of sleep for each of the treatments is placebo = 3.25 hrs, treatment 1 = 4 hrs, treatment 2 = 5.58 hrs, treatment 3 = 5.57 hrs.

The 95% confidence interval for each of the treatments is given by

placebo : (1.978, 4.522)

treatment 1: (2.496, 5.504)

treatment 2: (4.392, 6.768)

treatment 3: (4.205, 6.935)

2. The box plots are drawn for all the treatments and it depicts that placebo and treatment 3 are negatively skewed and treatment 1 and 2 are positively skewed data. All the four treatments exhibit no outliers.

3. Extra sleep receieved by patients after treatments when compared with placebo:

Treatment Vs Placebo	No. of patients received extra sleep hours	average extra sleep
Treatment 1	6 out of 10	1.77
Treatment 2	9 out of 10	2.6
Treatment 3	9 out of 10	2.66

4. From the outputs of the paired t test it is clear that

a) Between Treatment 1 and placebo: p value= 0.218 indicates there is no significant difference in increasing the average sleep hours of patients i.e. Treatment 1 is not effective.

b) Between Treatment 2 and placebo: p value= 0.005 indicates there is a significant difference in increasing the average sleep hours of patients i.e. Treatment 2 is effective.

c) Between Treatment 3 and placebo: p value= 0.010 indicates there is a significant difference in increasing the average sleep hours of patients i.e. Treatment 3 is effective.

5. The p value and 95% confidence interval for treatment 2 Vs placebo is 0.005 and (0.8977, 3.7623) and for treatment 3 vs placebo the values are 0.010 and (0.6989, 3.9411). The standard error is minimum for treatment 2 than treatment 3. Hence treatment 2 is more effecitve than treatment 3