TY - JOUR
T1 - Approximate unconditional test procedure for comparing two ordered multinomials
AU - Tang, Man Lai
AU - Poon, Wai Yin
AU - Ling, Leevan
AU - Liao, Yijie
AU - Chui, Hang Wai
N1 - Funding Information:
The authors would like to thank the referees for their valuable comments. The research work of Tang, Man-Lai was supported by two research grants from the Hong Kong Baptist University ( FRG2/08-09/066 and FRG2/09-10/060 ).
PY - 2011/2/1
Y1 - 2011/2/1
N2 - The asymptotic and exact conditional methods are widely used to compare two ordered multinomials. The asymptotic method is well known for its good performance when the sample size is sufficiently large. However, Brown et al. (2001) gave a contrary example in which this method performed liberally even when the sample size was large. In practice, when the sample size is moderate, the exact conditional method is a good alternative, but it is often criticised for its conservativeness. Exact unconditional methods are less conservative, but their computational burden usually renders them infeasible in practical applications. To address these issues, we develop an approximate unconditional method in this paper. Its computational burden is successfully alleviated by using an algorithm that is based on polynomial multiplication. Moreover, the proposed method not only corrects the conservativeness of the exact conditional method, but also produces a satisfactory type I error rate. We demonstrate the practicality and applicability of this proposed procedure with two real examples, and simulation studies are conducted to assess its performance. The results of these simulation studies suggest that the proposed procedure outperforms the existing procedures in terms of the type I error rate and power, and is a reliable and attractive method for comparing two ordered multinomials.
AB - The asymptotic and exact conditional methods are widely used to compare two ordered multinomials. The asymptotic method is well known for its good performance when the sample size is sufficiently large. However, Brown et al. (2001) gave a contrary example in which this method performed liberally even when the sample size was large. In practice, when the sample size is moderate, the exact conditional method is a good alternative, but it is often criticised for its conservativeness. Exact unconditional methods are less conservative, but their computational burden usually renders them infeasible in practical applications. To address these issues, we develop an approximate unconditional method in this paper. Its computational burden is successfully alleviated by using an algorithm that is based on polynomial multiplication. Moreover, the proposed method not only corrects the conservativeness of the exact conditional method, but also produces a satisfactory type I error rate. We demonstrate the practicality and applicability of this proposed procedure with two real examples, and simulation studies are conducted to assess its performance. The results of these simulation studies suggest that the proposed procedure outperforms the existing procedures in terms of the type I error rate and power, and is a reliable and attractive method for comparing two ordered multinomials.
KW - Approximate unconditional test
KW - Asymptotic test
KW - Exact conditional test
KW - Exact unconditional test
KW - Two ordered Multinomials
KW - Wilcoxon statistic
UR - http://www.scopus.com/inward/record.url?scp=78049257742&partnerID=8YFLogxK
U2 - 10.1016/j.csda.2010.08.009
DO - 10.1016/j.csda.2010.08.009
M3 - Journal article
AN - SCOPUS:78049257742
SN - 0167-9473
VL - 55
SP - 955
EP - 963
JO - Computational Statistics and Data Analysis
JF - Computational Statistics and Data Analysis
IS - 2
ER -