Confidence and Significance

A criminal court of law needs to be convinced of a defendant s guilt beyond all reasonable doubt. Civil cases are decided on the balance of probabilities. What do these statements mean Courts are very careful to avoid putting actual figures on these statements, but the first (beyond all reasonable doubt) might be, say, 99.9% certain while the second might only be 60% or less. If we have the luxury of having data that do allow real probabilities to be determined then it is possible to give the court the chance to decide what is reasonable [Pg.68]

Consider what the consequences of setting the probability level for acceptance of H0 at 90, 95, and 99% might be. As an example suppose an analytical method has been used to analyze a certified reference material for the element zinc, that is, a material whose amount of substance of zinc has been established to a high metrological standard with low measurement uncertainty, with a view to deciding if there is any significant systematic error in the method. The mean of n measurement results has been determined and suppose that the population standard deviation (a), and therefore the standard deviation of the [Pg.69]

It seems that to make a small as possible Type I error (that is, wrongly rejecting the null hypothesis) all we have to do is to set higher and higher probability limits by choosing smaller and smaller a. This is up to the analyst, but as the limit for rejecting H0 is pushed farther [Pg.70]

The point about this example is that all analytical chemistry should be fit for purpose. When you make a decision based on a statistical test, the choice of the probability level at which the null hypothesis is rejected is made by the user, not by a book or software package. Do not adopt probability levels blindly, but consider the risk of making the different types of error. [Pg.72]

Big Chemical Encyclopedia

Chemical substances, components, reactions, process design ...