ERIC Number: ED339752
Record Type: RIE
Publication Date: 1991-Nov
Reference Count: N/A
Generating an Empirical Probability Distribution for the Andrews-Pregibon Statistic.
Jarrell, Michele G.
A probability distribution was developed for the Andrews-Pregibon (AP) statistic. The statistic, developed by D. F. Andrews and D. Pregibon (1978), identifies multivariate outliers. It is a ratio of the determinant of the data matrix with an observation deleted to the determinant of the entire data matrix. Although the AP statistic has been used many times, no probability distribution has been available for it. The AP statistic is based on the volume of confidence ellipsoids and is a function of leverage and residual. Small values of the AP statistic are associated with outlying observations. A probability distribution was developed through computer generation of 10,438 samples of n=150 and p=3 from a multivariate normal population using a FORTRAN program. The AP statistic was calculated for each observation in each sample. A data file was created with the statistics and sorted by the ratios, and a frequency distribution was run. This distribution was used to obtain the critical values for the various error rates. Changing the parameters in the FORTRAN program could allow development of the probability distribution for other values of n and p, including data that are other than multivariate normal. Eight brief appendixes summarize computer programs that were run on the calculations. One data table and seven references are provided. (SLD)
Publication Type: Reports - Evaluative; Speeches/Meeting Papers
Education Level: N/A
Authoring Institution: N/A
Identifiers: Andrews Pregibon Statistic; Empirical Research; FORTRAN Programing Language; Outliers
Note: Paper presented at the Annual Meeting of the Mid-South Educational Research Association (20th, Lexington, KY, November 12-15, 1991).