Question

A randomised controlled trial was conducted to assess the effectiveness of a new eye drop to reduce eye pain in patients suffering from a systemic condition affecting both eyes. Each patient received the prescribed dose of the new eye drop in one eye and the same dose of an existing drop in the other eye. The investigators randomised which eye was treated with the new eye drop and which received the existing eye drop. 45 patients were asked to rate the level of pain in each eye on a 0–10 scale with higher scores indicating higher levels of pain.The dataset is provided below.The dataset contains the following variables.

• ID: Participant ID number

• Pain_ctl = pain score in the eye receiving the existing drop

• Pain_new = pain score in the eye receiving the new drop

a) What are the study factor and the outcome factor?

b) State the null hypothesis and alternative hypothesis for the study.

c) Which statistical test would be appropriate to test the null hypothesis you have stated and why?

d) Use Stata to conduct the statistical test you stated in part (e) report the key findings and interpret them.Report all the relevant statistics and graphs required for checking the assumptions with interpretations

e) Write a brief report summarising all the results you have obtained and state your conclusion.

id	pain_ctl	pain_new
1	9	1
2	7	4
3	2	5
4	8	6
5	9	9
6	5	4
7	6	6
8	9	5
9	6	2
10	3	2
11	4	1
12	2	4
13	9	2
14	7	0
15	7	6
16	4	0
17	6	2
18	5	5
19	5	8
20	10	3
21	6	6
22	11	0
23	7	6
24	8	3
25	6	11
26	7	3
27	9	0
28	4	1
29	10	3
30	3	1
31	5	3
32	5	3
33	5	4
34	5	2
35	8	3
36	6	2
37	7	0
38	2	5
39	7	4
40	2	2
41	5	6
42	6	1
43	5	6
44	9	0
45	2	0

Answer 1

(a): Study Factor is eye drop and one is existing eye and new eye drop to see which eye drops are help reduce the pain. So pain is outcome factor in this study.

(b):

Null Hypothesis (H₀): There is no difference between existing eye drop and new drop.

Alternative Hypothesis (HA): There is a difference between existing eye drop and new drop.

(c): Paired t test would be appropriate to test the null hypothesis because here we have before and after data means using existing eye drop and new eye drop to check pain.

(d): Using Stata:

Paired t test Command: ttest pain_ctl == pain_new

Here mean(diff) !=0 and mean(diff) > 0 are significant because p value is less than 0.05. it is means of existing eye drop pain is high from new drop.

Check assumption:

Normality: make a histogram of both variable

Here pain_clt is follow normality.

pain new variable not follow normality because pain new variable data is right skewed.

Outliers: make a boxplot of both variable.

Here we can see there is one outliers in pain new variable. why pain new variable follow normality assumption.