Question

Problem 1:

Strategies for treating hypertensive patients by nonpharmacologic methods are compared by establishing three groups of hypertensive patients who receive the following types of nonpharmacologic therapy: Group 1:   Patients receive counseling for weight reduction Group 2:   Patients receive counseling for meditation Group 3:   Patients receive no counseling at all The reduction in diastolic blood pressure is noted in these patients after a 1-month period and are given in the table below. Group 1 Group 2 Group 3 4.2 4.5 1.2 6.4 2.3 −0.3 3.4 2.3 0.1 2.3

Work through Example 13 (which starts on p. 36 of the lab manual) and then do the following using the data from Problem #1 above. (a) Find the p-value for the hypothesis test in Problem #1(a) above. (b) Construct a normal probability plot of the residuals which includes the p-value for the normality test (similar to Figure 9, p. 41 of the lab manual). Enter the p-value into the answer box. (c) Find the p-value for the hypothesis test of equality of population variances (using Bartlett's test).

Answer 1

Q1a) As there are One Factor with 3 levels One Way Anova is conducted to test the Hypothesis , Using Minitab

use Stat > ANOVA > One-Way (Unstacked).

Here are the results As p value is <0.05 Null Hypothesis is rejected.indicating there is a difference between the groups (atleast 1 group is different from the other

One-way ANOVA: BP Reduction versus Group

Source DF SS MS F P
Group 2 28.74 14.37 9.31 0.014
Error 6 9.26 1.54
Total 8 38.00

S = 1.242 R-Sq = 75.63% R-Sq(adj) = 67.50%

Individual 95% CIs For Mean Based on
Pooled StDev
Level N Mean StDev -------+---------+---------+---------+--
Gr1 3 4.667 1.553 (-------*--------)
Gr2 3 3.033 1.270 (--------*--------)
Gr3 3 0.333 0.777 (--------*-------)
-------+---------+---------+---------+--
0.0 2.0 4.0 6.0

Pooled StDev = 1.242

Q1b ) Normal Prob Plot for Residuals Use Minitab (Stat > Basic Statistics > Normality Test)

Output is enclosed p value 0.82 indicates a good fit

Q2c

Test of Equality of Population variances

Use Minitab- Stat > ANOVA > Test for Equal Variances

Test for Equal Variances: BP Reduction versus Group

95% Bonferroni confidence intervals for standard deviations

Group N Lower StDev Upper
Gr1 3 0.709994 1.55349 16.9821
Gr2 3 0.580508 1.27017 13.8850
Gr3 3 0.354997 0.77675 8.4910

Bartlett's Test (Normal Distribution)
Test statistic = 0.73, p-value = 0.693

Levene's Test (Any Continuous Distribution)
Test statistic = 0.18, p-value = 0.841

Test for Equal Variances: BP Reduction versus Group