Question

The paper “Effect of long-term blood pressure control on salt sensitivity” [Journal of Medicine (1997) 28:147–156] describes a study evaluating salt sensitivity (SENS) after a period of antihypertensive treatment. Ten hypertensive patients (diastolic blood pressure between 90 and 115 mmHg) were studied after at least 18 months on antihypertensive treatment. SENS readings, which were obtained before and after the patients were placed on an antihypertensive treatment, are given in data 3. Is there significant evidence that the mean SENS value decreased after the patient received antihypertensive treatment?

'capacity'
23,28,35,42,21,19,14,25,45,49,36,44,29,23,27,12,15,17,29,39,41,46,51,18,44,43,36,33,14,18,19,25,47,48,13

My solution: I performed a paired t-test since the two samples are related each other. Hence, samples are dependent. Also, the sampling distribution of the differences follows a normal distribution.(checked ad.test)

One Sample t-test

diff<-data_3$Before-data_3$After

> diff

[1] 16.75 11.76   7.45   6.68   2.21   2.40   1.21 -0.23 -18.11 -4.28

mean(diff)

[1] 2.584

sd(diff)

[1] 9.490733

teststat

[1] 0.8609794

data: diff (paired t-test)

t = 0.86098, df = 9, p-value = 0.2058

alternative hypothesis: true mean is greater than 0

95 percent confidence interval:

-2.917599       Inf

sample estimates:

mean of x

    2.584

Or,

A paired t-test is appropriate because samples are dependent.

Ho: mu(diff)<=0

Ha: mu(diff)>0

t=0.8609793863

tcdf(0.860979386, 10^99,9)=0.2057995743

p-value>0.05, we fail to reject the H0.

The data don't provide sufficient evidence that the mean SENS value decreased after the patient received antihypertensive treatment.

Is that right??

Answer 1

Ten hypertensive patients (diastolic blood pressure between 90 and 115 mmHg) were studied after at least 18 months on antihypertensive treatment. SENS readings, which were obtained before and after the patients were placed on an antihypertensive treatment,

So data is paired because the before & after an treatment.

A paired t test to be carry out.

t = 0.86098, df = 9, p-value = 0.2058

P-value = 0.2058 which is large.

P-value > 0.05,0.01,0.10 level of significance

We fail to reject Ho.

Or do not reject Ho

So we can conclude that the data do not provide sufficient evidence to support claim that mean SENS value decreased after the patient received antihypertensive treatment.

So we can say that treatment is not effective.