Accession Number : ADA119475

Title :   Conflict among Testing Procedures?

Corporate Author : RAND CORP SANTA MONICA CA

Personal Author(s) : Kohler,Daniel F

PDF Url : ADA119475

Report Date : Apr 1982

Pagination or Media Count : 11

Abstract : Savin (1976) and Berndt and Savin (1977), among others, have pointed out that an inequality relation exists between the Lagrange Multiplier Test, the Wald Test, and the Likelihood Ratio Test. However, since all tests converge to the same limiting Chi-square distribution they are usually compared against the same critical value. This raises the possibility of conflicting conclusions from the three tests. Kohler (1979) and Vandaele (1981) have shown that the three tests are monotonic functions of each other. This implies that they have identical power characteristics. In particular, if the probabilities of Type I errors are equal among the three tests, they have to have the same probability of Type II errors as well. In essence we are dealing with one and the same test. In this paper, we review briefly how the tests are related and why the inequality relation exists. We then derive criteria which allow us to determine which test is more appropriate in a given situation. This should resolve possible conflicts for at least some sets of circumstances.

Descriptors :   *Statistical tests, *Lagrangian functions, *Maximum likelihood estimation, Conflict, Multiplication, Comparison, Chi square test, Convergence, Rejection, Probability

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE