Question

Problem 1: 25 patients with blisters were randomly assigned to treatment A, treatment B and Placebo; the number of days until the blisters heal were recorded. Are these treatments significantly different? Use α = 5%.

Treatment A	5	6	6	7	7	8	9	10
Treatment B	7	7	8	9	9	10	10	11
Placebo	7	9	9	10	10	10	11	12	13

Sample size (n)

Median

Mean

Standard Deviation (S)

Treatment A

8

7

7.250

1.669

Treatment B

8

9

8.875

1.458

Placebo

9

10

10.111

1.764

1. Provide the null hypotheses.

2. Provide the alternative hypotheses.

3. Determine the appropriate statistic for this test

1. Z- test
2. T- test
3. Chi Square-test
4. F-Test
   

4. Determine the probability of type I error (α) for this test

1. 1%
2. 10%
3. 0.05
4. 95%
5. 0.005

5. Complete the ANOVA Table

ANOVA
Source of Variation	Sum of Squares	Degrees of freedom	Mean Squares	F	F Critical value	P-value
Treatments
Error			2.74
Total	85.83

6. Determine the test statistic critical value (s).

7. The Error Sum of Squares (SSE) for the ANOVA is __

8. Determine the test statistic value for this test
   

9. What conclusion should be drawn?
   

10. Compute the critical values (LSD) to test population 1 (Placebo) and population 2

(Treatment A) .    

11. What conclusion should be drawn when comparing population 1 (Placebo) and population 2 (Treatment A)?
    

Answer 1

The appropriate test is F test, since we are comparing more than 2 means.

SSTr = SST-SSE

MST = SSTr/df for treatments

MSE = SSE/error df

ANOVA
Source of Variation	SS	df	MS	F	P-value
Treatments	25.55	2	12.775	4.662	0.0205
Error	60.28	22	2.74
Total	85.83	24

Conclusion: Since p-value <0.05, so we reject H0 i.e. the treatments are significantly different.

Since 2.86>lsd, the the treatment A differs significantly from placebo