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A definition, appropriate to a test comparing groups, is as follows: If the null hypothesis is true, the P-value is the probability of obtaining a difference between the groups (as measured by the test statistic T) as large as or larger than that observed. , τ = 0), then differences between the treatment groups that are very extreme are unlikely to occur by chance and their improbability is reflected in small P-values. 05 is obtained, then this is generally accepted as providing evidence that the null hypothesis is false.

In general, this cannot happen with randomized studies, unless the person admitting patients to the RCT also prepared the randomization list. Preparing a randomization list in advance can be good practice but should never be done by anyone involved with the recruitment of patients — it is best done by the trial statistician. 2). 1 is a hypothetical example which, although rather stylized, illustrates the nature of the problem that can arise. 1: Hypothetical Example of Selection Bias Consider a trial to compare two treatments for a serious malignant disease.

Find the error in the approximation in Question 6 when there are 30 patients; 100 patients in the trial and each group has the same size. ) 8. Use a method analogous to the delta method to derive an approximate formula for E(arcsin R / N ) when R has a binomial distribution with parameters N and π. 9. Use Minitab to generate 10000 random variables R from a binomial distribution with parameters N and π. Calculate arcsin R / N and find its variance. Compare this with its approximate theoretical value.

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