Question

1-Researchers are interested in a new drug intervention for those people with an abnormally high heart rate. We accrue 90 people in our study and assign 30 patients to take the placebo (the subjects do not know that it is a placebo), another 30 are assigned the current drug regiment, and the remaining 30 are assigned the new drug. Determine if the three groups are equal and if all are not equal, which drugs are different? To answer this question, complete parts a)-c) below

To save you time, raw data is not provided but the ANOVA table is partially available. The p-value for each pairwise comparison is also shown.

Source of Variation	Sum of Squares	df	Mean Squares	F Ratio	Critical F	p-value
Between	1344.4					<0.0001
Within
Total	2053.6	89

Comparisons	Pvalue
H0:  µplacebo= µcurrent	<0.0001
H0:  µplacebo= µnew	<0.0001
H0:  µnew= µcurrent	0.0221

1. Fill out the blanks in the above ANOVA table
2. Test if the three groups are different.
3. If the three groups are not equal, which ones are different? Please use Bonferroni adjustments for multiple testing.

Answer 1

(a)

Source of Variation	Sum of Squares	df	Mean Squares	F Ratio	Critical F	p-value
Between	1344.4	2	672.2	82.46	3.10	<0.0001
Within	709.2	87	8.1517
Total	2053.6	89

(b) The hypothesis being tested is:

H₀: µ₁ = µ₂ = µ₃

H_a: Not all means are equal

The p-value is 0.0001.

Since the p-value (0.0001) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the three groups are different.

(c) There is a significant difference between placebo and current.

There is a significant difference between placebo and new.

There is a significant difference between the new and current.