By Swinscow T.D.V., Campbell M.J.
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The level at which a result is declared significant is known as the type I error rate, often denoted by α. We try to show that a null hypothesis is unlikely, not its converse (that it is likely), so a difference which is greater than the limits we have set, and which we therefore regard as “significant”, makes the null hypothesis unlikely. However, a difference within the limits we have set, and which we therefore regard as “non-significant”, does not make the hypothesis likely. To repeat an old adage, absence of evidence is not evidence of absence.
Thus the variation between samples depends partly also on the size of the sample. Usually, however, we are not in a position to take a random sample; our sample is simply those subjects available for study. This is a “convenience” sample. For valid generalisations to be made we would like to assert that our sample is in some way representative of the population as a whole and for this reason the first stage in a report is to describe the sample, say by age, sex and disease status, so that other readers can decide if it is representative of the type of patients they encounter.
Given a sample of disease free subjects, an alternative method of defining a normal range would be simply to define points that exclude 2·5% of subjects at the top end and 2·5% of subjects at the lower end. This would give an empirical normal range. Thus in the 140 children we might choose to exclude the three highest and three lowest values. However, it is much more efficient to use the mean ±2 SD, unless the data set is quite large (say, greater than 400). Confidence intervals The means and their standard errors can be treated in a similar fashion.