| The purpose of this work is to develop Analysis of Means (ANOM) based tests of the homogeneity of variance (HOV) hypothesis using independent samples from three or more populations. Six tests are developed. Methods and examples are provided for performing these tests with a one-way layout as well as p x q designs. Each of these tests can be performed using decision charts that resemble Shewart control charts. The decision charts make it easy for practitioners to assess statistical and practical significance.;A test (ANOMV) that assumes one has samples from normal populations is presented, along with tables of critical values required in this test. A large sample version (ANOMV-LN) that uses critical values from ANOM tables is also presented.;Two nonparametric (rank-based) HOV tests and two tests intended to be robust against nonnormality are presented. One robust test employs subsampling; the other robust test employs jackknifing.;The tests are evaluated using simulation. The simulation shows that ANOMV has power competitive with other commonly used normal-based HOV tests; but, like other normal based HOV tests, ANOMV has dangerously large Type I error rates when samples from fat-tailed distributions are tested. The nonparametric test based on the expected normal scores of the absolute deviations from the median and the test employing jackknifing show good robustness and are recommended when fat-tailed distributions cannot be ruled out. |
