A note on the expected value of the Rand index.

@article{Steinley2018ANO,
  title={A note on the expected value of the Rand index.},
  author={Douglas L. Steinley and Michael J. Brusco},
  journal={The British journal of mathematical and statistical psychology},
  year={2018},
  volume={71 2},
  pages={
          287-299
        }
}
Two expectations of the adjusted Rand index (ARI) are compared. It is shown that the expectation derived by Morey and Agresti (1984, Educational and Psychological Measurement, 44, 33) under the multinomial distribution to approximate the exact expectation from the hypergeometric distribution (Hubert & Arabie, 1985, Journal of Classification, 2, 193) provides a poor approximation, and, in some cases, the difference between the two expectations can increase with the sample size. Proofs concerning… CONTINUE READING

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