Detecting Relationships between Categorical Variables Observed Over Time: A Problem of Deflating a Chi‐Squared Statistic

Patricia M. E. Altham

Journal of the Royal Statistical Society Series C, 1979, vol. 28, issue 2, 115-125

Abstract: The problem considered is the investigation of the interdependence of categorical variables, when the observations on these variables take place in a sequence over time, so that consecutive observations are distinctly non‐independent, and standard χ2 tests based on a multinomial distribution are inappropriate. Using fairly weak assumptions about the underlying probability distribution, upper and lower bounds for the appropriate χ2 test statistics are found. This is deliberately done without writing down the full likelihood of the data. Although some matrix algebra is necessary for the proofs of the inequalities, the application of the results of this paper does not require mathematical expertise, and should be intelligible to anyone used to doing χ2 tests. The particular problem considered here arose in an animal behaviour context, and is illustrated numerically in that context, but it is quite a common problem in behavioural data.

Date: 1979
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