A Nonparametric Test for Differences in the Dispersion of Dependent Samples

✍ Scribed by Dr. K. Boehnke

• Publisher: John Wiley and Sons
• Year: 1989
• Tongue: English
• Weight: 477 KB
• Volume: 31
• Category: Article
• ISSN: 0323-3847
• DOI: 10.1002/bimj.4710310403

✦ Synopsis

A new statistic A to test the hypothesis of a difference in the dispersion of two dependent samples of ordinal data quality is proposed. It draws on the idea of rank assignment originally forwarded by SIEGBL and TWEY (1960). No exact probability levels can be given for this statistic for the time being, but i t is shown that the statistic is linearly related to the so-called Hotelling-Pabst statistic D, and that one can use exact tablee of the latter as a substitute in the statistical decision p r o m with small samples. For larger samples, an approximation of A to the standard normal distribution is given. The problem of tied observations is not sufficiently solved yet. A conservative procedure of rank assignment is proposed 88 long a8 the exact distribution of A in the presence of ties is unknown. Key mds: Nonparametric ; Dispersion ; Dependent srtmples ; Siegel-Tukey extension ; Hotelling-Pabst statistic.

NERT (1974), but if data quality is only ordinal an appropriate test seems to be missing for dependent samples. A test for this cme is proposed here.