Question

STAT
PatientID	Age	Sex	County	CardioRisk	Height	Weight	BloodGroup	Stroke	RegularEx	Group	Cholesterol1	Cholesterol2
225	58	Male	Offaly	Low	179.2	103.5	AB	N	N	Placebo	6.1	4.6
226	61	Male	Carlow	Medium	174.9	63	AB	Y	N	Control	2.2	5.7
227	57	Female	Donegal	Medium	161.9	76.1	B	N	Y	Control	5.8	5
228	43	Male	Offaly	High	176	83.7	AB	Y	N	Control	3.6	2.4
229	37	Female	Longford	Low	157.8	68	B	N	Y	Control	4.9	6
230	29	Male	Leitrim	Medium	166.1	79.1	A	Y	Y	Placebo	3.5	5.3
231	52	Male	Cavan	Low	167.6	60.4	A	Y	Y	Placebo	2.9	4
232	47	Female	Westmeath	Low	167.8	63.6	B	N	Y	Control	4	3.2
233	28	Male	Wicklow	Low	170.5	67.2	O	Y	N	Control	4.2	4

the commands for these questions using rstudio

Q1

a. Is there a difference in the risk of cardiovascular disease between males and females?

b. Is there a difference in weight between the Control and Placebo groups?

c. Do the data suggest that the new drug reduces cholesterol level compared to the placebo?

Answer 1

Q.a

We perform chi-square test of independence to check this claim.

> d=read.table('data1.csv',header=T,sep=',')
> head(d)
PatientID Age Sex County CardioRisk Height Weight BloodGroup Stroke
1 225 58 Male Offaly Low 178.2 103.5 AB N
2 226 61 Male Carlow Medium 173.9 63.0 AB Y
3 227 57 Female Donegal Medium 160.9 76.1 B N
4 228 43 Male Offaly High 175.0 83.7 AB Y
5 229 37 Female Longford Low 156.8 68.0 B N
6 230 29 Male Leitrim Medium 165.1 79.1 A Y
RegularEx Group Cholesterol1 Cholesterol2
1 N Placebo 6.1 4.6
2 N Control 2.2 5.7
3 Y Control 5.8 5.0
4 N Control 3.6 2.4
5 Y Control 4.9 6.0
6 Y Placebo 3.5 5.3
> attach(d)
The following objects are masked from d (pos = 3):

Age, BloodGroup, CardioRisk, Cholesterol1, Cholesterol2, County,
Group, Height, PatientID, RegularEx, Sex, Stroke, Weight

> t=table(Sex,CardioRisk);t
CardioRisk
Sex High Low Medium
Female 0 2 1
Male 1 3 2
> chisq.test(t)

Pearson's Chi-squared test

data: t
X-squared = 0.6, df = 2, p-value = 0.7408

Warning message:
In chisq.test(t) : Chi-squared approximation may be incorrect

Hypothesis:

H0 : Cardio risk does not depend upon sex

H1 :  Cardio risk does depend upon sex.

Since p-value is greater than 0.05, we accept null hypothesis and conclude that there is no difference in the risk of cardiovascular disease between males and females.

Que.b

> t.test(Weight[which(Group=='Placebo')],Weight[which(Group=='Control')])

Welch Two Sample t-test

data: Weight[which(Group == "Placebo")] and Weight[which(Group == "Control")]
t = 0.83162, df = 2.2847, p-value = 0.4835
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-38.66752 60.13418
sample estimates:
mean of x mean of y
81.00000 70.26667

Since p-value is greater than 0.05, there is no difference in weight between the Control and Placebo groups.

Que.c

> chol1=Cholesterol2[which(Group=='Control')] - Cholesterol1[which(Group=='Control')]
> chol2=Cholesterol2[which(Group=='Placebo')] - Cholesterol1[which(Group=='Placebo')]
> t.test(chol1,chol2,alternative='less')

Welch Two Sample t-test

data: chol1 and chol2
t = -0.16147, df = 4.1791, p-value = 0.4396
alternative hypothesis: true difference in means is less than 0
95 percent confidence interval:
-Inf 2.408399
sample estimates:
mean of x mean of y
0.2666667 0.4666667

Since p-value is greater than 0.05, we conclude that the new drug does not reduces cholesterol level compared to the placebo.