Sample size significance with large trials

The null distribution for the t-test depended on the number of subjects in the trial. For the chi-square test comparing two proportions, and providing the sample size is reasonably large, this is not the case the null distribution is always x i- As a consequence we become very familiar with x i- The critical value for 5 per cent significance is 3.841 while 6.635 cuts off the outer 1 per cent probability and 10.83 cuts off the outer 0.1 per cent. 

Now, from (13.7) for given prior odds and fixed a, the posterior odds are greater the smaller the value of (3, which is to say the greater the power of the test. But the power increases with sample size. Hence, other things being equal, significant results are more indicative of efficacy if obtained from large trials rather than small trials. 

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