Question

Three different treatments for hypertension (high blood pressure) are being tested. A medical researcher takes volunteers and randomly assigns them into groups taking treatment A, B, and C. The reduction in blood pressure is measured for each patient with the following results:

In R: > dput(d$treatment)

c("A", "A", "A", "A", "A", "B", "B", "B", "B", "B", "B", "B", "B", "B", "C", "C", "C", "C", "C", "C"

) > dput(d$reduction)

c(2.6, 4.5, 4.3, 4, 1.5, 4, -0.2, -2.4, 5, -1.8, 4.4, -1.1, 3.4, 1.4, 8.5, 6.6, 0.1, 4.7, 0.7, 8.4)

Is there evidence that blood pressure reduction differs between the treatment groups?

(a) State a sensible null hypothesis

(b) State the precise definition of p-value and explain what “more extreme” means in this context

(c) Perform an ANOVA using lm() and interpret

Answer 1

(a)

denotes the mean reduction in presurrure through treatment.

(b)p-value: The probability of a test statistic having a value as extreme or more extreme under the null hypothesis than the actual observed value.

Here "most extreme" implies that average value of reduction in pressure which is most unlikely under the null hypothesis.

(c)

Analysis of Variance Table

Response: reduction

	Df	Sum Sq	Mean Sq	F value	Pr(>F)
treatment	2	43.512	21.7559	2.6114	0.1026
Residuals	17	141.63	8.3312
total	19	185.142

Here p-value>0.05, hence at 5% level of significance we can conclude that there is insufficient evidence to support the claim that blood pressure reduction differs between the treatment groups.