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A clinical oncologist is investigating the efficacy of a new treatment on reduction in tumour size. She randomly assigns patients to the new treatment or old treatment and compares the mean reduction in tumour size between the two treatment groups. She carries out a statistical test to assess whether the new treatment results in greater reductions. The resulting P-value is 0.001. Which of the following are valid interpretations of the P-value?
I) The probability of observing a difference between the treatment groups as large or larger than she observed if the new treatment has the same efficacy as the old treatment.
II) The probability that the new treatment works the same as the old treatment.
III) The probability that the new treatment, on average, reduces tumour size more than the old treatment.
Please explain your reasoning.
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