Chi-Squared Test on the Triples

In order to test whether the Markov Property holds for a given process/transition matrix, we need to consider whether the probability p_jk is affected by state i (which immediately precedes state j). We do this using the Triples test.

My question is, is this chi-squared test one-tailed or two-tailed and why?

 

It's one-sided, because large differences between the actual and expected numbers of triples would suggest the Markov property didn't hold. Very small differences between the actual and expected numbers of triples would suggest the results were consistent with the Markov property.

 

Thank you, this makes sense

 

Hi, What would be the number of degrees of freedom here?