Question

A pilot study is run to investigate the effect of a lifestyle intervention designed to increase medication adherence in patients with HIV. Medication adherence is measured as the percentage of prescribed pills that are taken over a one-week observation period. Ten patients with HIV agree to participate and their medication adherence before and after the intervention are shown below. Compute the standard deviation of the difference in adherence before versus after intervention. Please show your work and explain.Thank you!

Participant ID	Before Intervention	After Intervention
1	75%	80%
2	82%	84%
3	66%	70%
4	74%	70%
5	88%	90%
6	66%	75%
7	51%	60%
8	93%	90%
9	88%	90%
10	91%	95%

Answer 1

The standard deviation of the difference in adherence before versus after intervention is obtained as follows,

Form the data values,

Difference in adherence = Before Intervention - After Intervention

Participant ID	Before Intervention	After Intervention	Difference (Before - After)
1	75%	80%	-5%
2	82%	84%	-2%
3	66%	70%	-4%
4	74%	70%	4%
5	88%	90%	-2%
6	66%	75%	-9%
7	51%	60%	-9%
8	93%	90%	3%
9	88%	90%	-2%
10	91%	95%	-4%

The standard deviation for the differences is obtained using the formula,

Where, mean of differences,

Now,

Participant ID	After Intervention	Difference, D
1	80%	-5%	-2%	0.04%
2	84%	-2%	1%	0.01%
3	70%	-4%	-1%	0.01%
4	70%	4%	7%	0.49%
5	90%	-2%	1%	0.01%
6	75%	-9%	-6%	0.36%
7	60%	-9%	-6%	0.36%
8	90%	3%	6%	0.36%
9	90%	-2%	1%	0.01%
10	95%	-4%	-1%	0.01%
			Sum	1.66%