Changes

===Limitations of null hypothesis tests===

===Limitations of null hypothesis tests===

One considerable limitation of hypothesis testing is described above: namely, hypothesis tests do not relate to the main question of interest (whether or not there is a true difference in the population), and only provide degrees of evidence in favour or against there being no true difference. Another limitation is that there will always be a difference of some magnitude between the two groups, even if this is of no relevance. Consider a cohort study where 1 million nondiseased individuals are followed up to see whether or not exposure to substance x is associated with disease. It may be that in this whole population of 1 million animals, 10.0% of exposed individuals develop the disease and that 9.9% of unexposed individuals develop the disease. Of course, this difference is not of any '''biological relevance''', and yet there is a difference there (as this is a whole population rather than a sample, we would not conduct a hypothesis test). As the size of any sample increases, the ability to detect a true difference increases. As there will be a 'true difference' (however small) in most populations, This means that with large sample sizes, the chance of a hypothesis test detecting a difference increases (indeed, some statisticians view hypothesis testing as a method of determining whether or not the sample size is sufficient to detect a difference). This problem can be reduced by ensuring that the appropriate measure of effect is always presented along with the hypothesis test p-value. In this example, the

One considerable limitation of hypothesis testing is described above: namely, hypothesis tests do not relate to the main question of interest (whether or not there is a true difference in the population), and only provide degrees of evidence in favour or against there being no true difference. Another limitation is that there will always be a difference of some magnitude between the two groups, even if this is of no relevance. Consider a cohort study where 1 million nondiseased individuals are followed up to see whether or not exposure to substance x is associated with disease. It may be that in this whole population of 1 million animals, 10.0% of exposed individuals develop the disease and that 9.9% of unexposed individuals develop the disease. Of course, this difference is not of any '''biological relevance''', and yet there is a difference there (as this is a whole population rather than a sample, we would not conduct a hypothesis test). As the size of any sample increases, the ability to detect a true difference increases. As there will be a 'true difference' (however small) in most populations, this means that hypothesis tests on large sample sizes will tend to give low p-values (indeed, some statisticians view hypothesis testing as a method of determining whether or not the sample size is sufficient to detect a difference). This problem can be reduced by ensuring that the appropriate measure of effect is always presented along with the hypothesis test p-value.