Embedded Markov chains may be used to describe rock sequences in which a lithology is not or cannot be observed following itself. Such chains lead to a transition matrix with zeros on the main diagonal. To test the hypothesis of randomness in an embedded Markov chain, we apply Goodman's (1968) model of quasi-independence and compare it to previously used methods (which we now believe are invalid) in the geological literature. Data in the literature show quite different results (depending on the original method) when reanalyzed in this way. We present tests for homogeneity, a spatial analogue to stationarity, of multiple embedded chains and for symmetry and Markov chain order. Matrices from vertical or laterally spaced sequences can be tested for homogeneity and conclusions drawn regarding variations of processes over space. A normalized difference is proposed as an aid in interpreting the difference between observed transition frequencies and transition probabilities estimated with a model of independence or quasi-independence.