When calculating the value of our test statistic I noticed that 0.5 has been deducted from the value of X(=18). In other examples(cant remember which specifically) we ADDED 0.5 to the value rather than deducting. Therefore my question is, when carrying out a hypotheses test what determines whether we add or subtract 1/2 after contuity correction. I am guessing that it has to do with the direction of the alternative hypothesis, and if this is the case how will we carry out continuity correction if the alternative hypothesis is a simple one e.g H0: p = 0.9 H1: p != 0.9 (!= is "not equal") thanks
Hi John, Thanks for the comments and this is what the study material also mentions. Could you please elaborate on the reason and logic behind adding/subtracting 0.5 towards mean as I am unable to locate it in the study pack. Many thanks. Sunil
So this "towards the mean" is only used in hypothesis tests in Chapter 10. This is because when we calculate the p-value for the binomial/Poisson we include the observed value. So if H0=0.8 vs H1>0.8 and we observe X=42 successes out of 50 trials for X~Bin(50,0.8), then the p-value will be P(X>=42) which continuity corrects to P(X>=41.5) which is closer to the mean of np=50*0.8=40. Similarly, if we were testing H0=0.8 vs H1<0.8 and we observe X=36 successes out of 50 trials for X~Bin(50,0.8), then the p-value will be P(X<=36) which continuity corrects to P(X<=36.5) which is closer to the mean of np=50*0.8=40.
