# Suppose a hypertension trial is mounted and 18 participants are

1. https://www.medicalnewstoday.com/articles/150109#:~:text=Hypertension%20is%20another%20name%20for,walls%20of%20their%20blood%20vessels. 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.

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