Question

Some common strategies for treating hypertensive patients by nonpharmacologic methods include (1) weight reduction and (2) trying to get the patient to relax more by meditational or other techniques. These strategies were evaluated by randomizing hypertensive patients to four groups who receive the following types of nonpharmacologic therapy: Group 1: patients receive counselling for both weight reduction and meditation. Group 2: patients receive counselling for weight reduction but not for meditation. Group 3: patients receive counselling for meditation but not for weight reduction. Group 4: patients receive no counselling at all. 20 hypertensive patients were assigned at random to each of the four groups, and the change in diastolic blood pressure (DBP) was recorded in these patients after a 1-month period. These data are summarized as follows:
Group n Mean change in DBP    sd of change (baseline - followup) (mm Hg)

1 20 8.6 6.2

2 20 5.3    5.4

3 20 4.9    7.0

4 20 1.1    6.5

(a)Complete the following ANOVA table:
Source of variation    DF Sum of Squares Mean Square    F-statistic p-value

Model (between group) _________ 565.35 _______    _______    < 0.05

Error (Within group)    __________ ________ ____________ __________ _________

Total    3583.31    ___________ _____________    ________    ____________

(b)Interpret this p-value. Be sure to clearly state what is being tested and what this means in the context of the problem of interest. Comment on our ability to draw causal inference in this setting.

[PLEASE CLEARLY STATE WHAT ALL THE PARAMETERS USED IN THIS QUESTION MEAN]

Answer 1

(a)

There are 4 groups so degree of freedom of between is

There are total 20+20+20+20 = 80 data values so degree of freedom of error is

The degree of freedom of total is

The sum of squares of within is

Now,

The F test statistics is

(b)

Since p-value is less than 0.05 so we reject the null hypothesis. That is we can conclude that change in diastolic blood pressure (DBP) is not same for all groups.