Yates s Kontinuitätskorrektur
Transkription
3 Freiheit. Yates [17] argumentiert, daß die χ 2 1 Verteilung nur ungefähre Schätzungen der diskreten Wahrscheinlichkeiten zugeordnet Frequenzdaten und somit die p-Werte auf Basis von Pearson s wird im allgemeinen unterschätzt X 2-Statistik gibt die wahren Werte p. Im Allgemeinen, wenn eine Statistik nimmt diskrete Werte a < b < c, the p value corresponding to b is estimated by the tail of the continuous function defined by the point a+b 2. Therefore, the tail of the continuous function computed at b will underestimate the p value. In this context, Yates suggested that X 2 should be corrected for continuity and proposed the corrected test statistic N( AD BC 1 2 N)2 (A + B)(C + D)(A + C)(B + D). Although Yates s correction is best known for its use in the analysis of 2 2 contingency tables, it is also applicable to the analysis of 2 1 contingency tables. A 2 1 contingency table displays the frequencies of occurrence of two categories in a random sample of size N, drawn from a population in which the proportions of cases within the two categories are p and 1 p. The research question is usually whether the observed numbers of cases x and N x in the two categories have been sampled from a population with some pre specified value of p. This can be tested using Pearson s statistic, X 2 = (x Np)2 Np(1 p), which asymptotically has a χ 2 1 distribution under the null hypothesis. Yates showed that, in this case as well, the use of Pearson s X 2 results in p values which systematically underestimate the true p values based on the binomial 3