Question

A researcher is studying treatments for agoraphobia with panic disorder. The treatments are to be the drug Imipramine at the two doses 1.5 mg per kg of body weight and 2.5 mg per kg of body weight. There will also be a control group given a placebo. Thirty patients were randomly divided into three groups of ten each. One group was assigned to the control, and the other two groups were assigned to the two drug treatments. After twenty-four weeks on treatment, each of the subject's symptoms were evaluated through a battery of psychological tests, where high scores indicate a lessening of symptoms. Assume the data for the three groups are independent and approximately Normal with the same variance. An ANOVA F test tested the null hypothesis that there were no differences among the means for the three treatments that had a P-value less than 0.001. Which conclusion is correct?

Question 5 options:

	A. No choice is correct.
	B. There is strong evidence that the population mean scores for the higher dose group of 2.5 must be larger than the population mean for the lower dose group of 1.5.
	C. There is strong evidence that the three population mean scores must all be different from each other because the P-value is so small.
	D. There is little evidence that the three population mean scores must all be different from each other because the P-value is so small.

Options C and D were marked INCORRECT so I am trying to find the correct answer. I chose C originally so I don't understand why it's wrong. If you could explain!

Answer 1

Option C would have been the right choice if the word "all" were not to be there in it. The fact that the p-value is so small implies that at least two of the three groups have significantly different means, not necessarily that all three groups have significantly different means.

Option D is wrong because with a small p-value we reject the null hypothesis of equal means.

Option B may be correct if we assume that high potency dosage (2.5 mg) leads to much better-improved symptoms than low potency dosage (1.5 mg). (But this may not be necessarily true of drugs, so can't say).

Option A, therefore, appears to be the correct choice.