title: Estimation of type I error probability from experimental Dixon's "Q" parameter on testing for outliers within small size data sets.
abstract: Common significance tests carried out using statistical software packages usually return to the user the probability p of type I error as the result. Based on p and the preset confidence level the user will decide on the acceptance or the rejection of the associated null hypothesis. Dixon's test (Q-test) is commonly used for the detection of an outlier within a set of N observations (typically: N=3-12). Q-test can only be applied by comparing the experimental value of the statistic Q with tabulated critical Q-values corresponding to some standard values of p. Hence, for a given value of Q and a number of observations, N, the user knows only the range and not the value of the associated probability p of type I error (erroneous rejection). This is due to the lack of explicit expressions of the form p=F(Q,N). In this work, a simple stochastic (Monte Carlo) approach is presented for the estimation of p corresponding to a given experimental value of Q and size N of the data set. In addition, based on Dixon's equations, explicit expressions of p are given for N=3 and 4.
authors.affiliation: Laboratory of Analytical Chemistry, Department of Chemistry, University of Athens, University Campus, Athens, Greece. cefstath@chem.uoa.gr
authors.forename: Constantinos E
authors.initials: CE
authors.lastname: Efstathiou