Suppose a hypertension trial is mounted and 18 participants are

 

 

 

  1. Suppose a hypertension trial is mounted and 18 participants are randomly assigned to one of the comparison treatments. Each participant takes the assigned medication and their systolic blood pressure (SBP) is recorded after 6 months on the assigned treatment. The data are as follows.

 

 

 

 

 

Standard Treatment

Placebo

New Treatment

124

134

114

111

143

117

133

148

121

125

142

124

128

150

122

115

160

128

 

 

 

Is there a difference in mean SBP among treatments? Run the appropriate test at =0.05.

 

 

 

Step 1. Set up hypotheses and determine level of significance

 

H0: = 2= 3

 

H1: Means are not all equal =0.05

 

 

 

Step 2. Select the appropriate test statistic. F=MSB/MSE.

 

 

 

Step 3. Set up decision rule.

 

df1=k-1=3-1=2 and df2=N-k=18-3=15. Reject H0 if F > 3.68.

 

 

 

Step 4. Compute the test statistic.

 

 

 

 

 

Standard

Placebo

New Treatment

n1=6

n2=6

n3=6

1= 122.7

2= 146.2

3= 121.0

 

 

 

If we pool all N=18 observations, the overall mean is = 130.0.

 

 

 

We can now compute .

 

SSB = 6(122.7-130.0)2 + 6(146.2-130.0)2 + 6(121.0-130.0)2

 

SSB = 2380.4.

 

Next, .

 

 

 

Standard Treatment

(X – 122.7)

(X – 122.7)2

124

1.3

1.69

111

-11.7

136.89

133

10.3

106.09

125

2.3

5.29

128

5.3

28.09

115

-7.7

59.29

 

 

337.34

 

Thus, (X- 1)2 = 337.34.

 

 

 

Placebo

(X – 146.2)

(X – 146.2)2

134

-12.2

148.84

143

-3.2

10.24

148

1.8

3.24

142

-4.2

17.64

150

3.8

14.44

160

13.8

190.44

 

 

384.84

 

Thus, (X- 2)2 = 384.84.

 

 

 

New Treatment

(X – 121.0)

(X – 121.0)2

114

-7

49

117

-4

16

121

0

0

124

3

9

122

1

1

128

7

49

 

 

124

 

Thus, (X- 3)2 = 124.0

 

 

 

= 846.18.

 

 

 

We can now construct the ANOVA table.

 

 

Source of

Variation

 

Sums of Squares

SS

Degrees of freedom df

 

Mean Squares

MS

F

Between Treatments

2380.4

2

1190.2

21.1

Error or Residual

846.2

15

56.4

 

Total

3226.6

17

 

 

 

 

 

Step 5. Conclusion.

 

We reject H0 because 21.1 > 3.68. We have statistically significant evidence at =0.05 to show that there is a difference in mean systolic blood pressure among treatments.

 

 

 

 

——————————————–

 

 

Do the following problems using SPSS and provide a copy of the ANOVA table for each as your answer:

 

Sullivan pp. 162-168:  14

 

 

 

PLUS the following problems:

 

 1. A manufacturer wants to know which new coffee sells the best and distributes 3 types (Blue-Label, Green-Label and Red Label) to 6 of his stores. After letting customers taste the three types, the number of pounds purchased of each type of coffee on one day are recorded for the six stores.  Perform an ANOVA using SPSS to determine whether there is a significant difference in sales.

 

 Blue-Label   Green-Label     Red-Label 
            13              1              5 
              4              1              2 
            10              2              2 
            13              2              2 
            11              2              6 
              3              4              4

 

 

 

  1. Three topical antibiotics are tested to see how quickly they eliminate a rash in 4 people who have a history of repeated rashes of this type.

 

 

 

The number of days to eliminate the rash in the 4 people is given in the table below:  

 

Topical antibiotic 1

Topical antibiotic 2

Topical antibiotic 3

3

5

8

9

1

2

5

2

6

11

5

4

 

 

 

      Conduct a one-way ANOVA to determine whether there is a significance difference in the number of days to eliminate the rash.