Chi-square tests for markov chain analysis

Markov chain analysis has become a popular and useful technique for the evaluation of stratigraphic information. Field data on frequencies of facies transitions are first assembled in a transition count matrix. Observed frequencies can be compared statistically with frequencies expected if no order, or memory, exists in the stratigraphic sequence. Two chi-square (²) tests have been proposed for this purpose. One of the previously proposed ² tests was observed to give anomalously large values of the test statistic during another study. This unsatisfactory behavior is verified here. Limiting values of the two ² tests (from tables) are compared with the distribution of values for both test statistics obtained by analyzing many random matrices generated by a simple computer program. In all cases, the logarithmic ² test, suggested by several previous authors, fails to provide any meaningful assessment of the presence or absence of order in stratigraphic sequences evaluated. Further use of this test should therefore be avoided.