The statistics for testing for monotonic trend
To test for monotonic trend, the following five statistics are implemened in the package:
1. The likelihood ratio test (Barlow et al. 1972, and Robertson et al. 1988)
2. Williams (Williams, 1971 and 1972)
3. Marcus (Marcus, 1976)
4. The M statistic (Hu et al., 2005)
5. The modified M statistic (Lin et al., 2007)
The formulas for the statistics are presented below:

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where
References:
Barlow, R., Bartholomew, D., Bremner, M. and Brunk, H. (1972) Statistical Inference Under Order Restriction. New York: Wiley.
Hu, J., Kapoor, M., Zhang, W., Hamilton, S. and Coombes, K. (2005) Analysis of dose response effects on gene expression data with comparison of two microarray platforms. Bioinformatics, 21(17), 3524–3529.
Marcus, R. (1976) The powers of some tests of the quality of normal means against an ordered alternative. Biometrika, 63,177–83.
Lin, D., Shkedy, Z., Yekutieli, D., Burzykowski, T., G¨ohlmann, H., De Bondt, A., Perera, T., Geerts, T. and Bijnens, L. (2007) Testing for trends in dose-response microarray experiments: A comparison of several testing procedures, multiplicity and resamplingbased inference. Statistical Applications in Genetics and Molecular Biology, 6(1), Article 26.
Robertson, T., Wright, F. and Dykstra, R. (1988) Order Restricted Statistical Inference. Wiley.
Williams, D. (1971) A test for differences between treatment means when several dose levels are compared with a zero dose control. Biometrics, 27, 103–117.
Williams, D. (1972) The comparison of several dose levels with a zero dose control. Biometrics, 28, 519–531.