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**Exact tests in simple growth curve models and one-way ANOVA with equicorrelation error structure.**
*(English)*
Zbl 1014.62067

Summary: We consider exact tests with several equicorrelation error structures and combination of equicorrelation covariance structures in simple growth curve models having single or multiple treatments and in one-way ANOVA models. Exact inferences using generalized \(p\)-values are obtained. Tests for equal treatment effects under equal equicorrelation error terms and for unequal equicorrelation error terms are also developed. Two examples are given to illustrate the importance of our results. According to our findings, we would be better off dropping the assumption of equal variance when the heteroscedasticity is serious. Therefore, tests based on generalized \(p\)-values without the assumption of equal variance are much more powerful than tests with this assumption.

### MSC:

62H15 | Hypothesis testing in multivariate analysis |

62J10 | Analysis of variance and covariance (ANOVA) |

62F03 | Parametric hypothesis testing |

### Keywords:

combination of equicorrelation covariances; generalized p-values; repeated measures; measure; testing fixed treatment effects; multiple comparisons
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\textit{S.-H. Lin} and \textit{J. C. Lee}, J. Multivariate Anal. 84, No. 2, 351--368 (2003; Zbl 1014.62067)

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### References:

[1] | Ananda, M.M.A.; Weerahandi, S., Testing the difference of two exponential means using generalized p-values, Comm. statist.-simulation comput., 25, 2, 521-532, (1996) · Zbl 0875.62086 |

[2] | Chi, E.M.; Weerahandi, S., Comparing treatments under growth curve modelsexact tests using generalized p-values, J. statist. plann. inference, 71, 179-189, (1998) · Zbl 0931.62046 |

[3] | Gamage, J.; Weerahandi, S., Size performance of some tests in one-way ANOVA, Comm. statist.-simulation, 27, 3, 625-640, (1998) · Zbl 0954.62016 |

[4] | Krutchkoff, R.G., One-way fixed effects analysis of variance when the error variances may be unequal, J. statist. comput. simulation, 30, 259-271, (1998) · Zbl 0731.62124 |

[5] | Lee, J.C., Prediction and estimation of growth curve with special covariance structures, J. amer. statist. assoc., 83, 432-440, (1988) · Zbl 0648.62074 |

[6] | C.R. Rao, Least-squares theory using an estimated dispersion matrix and its application to measurement of signals, Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1, 1967, pp. 355-372. |

[7] | Thursby, J.G., A comparison of several exact tests and approximate tests for structural shift under heteroscedasticity, J. econometrics, 53, 363-386, (1992) |

[8] | Tsui, K.; Weerahandi, S., Generalized p-values in significance testing of hypotheses in the presence of nuisance parameters, J. amer. statist. assoc., 84, 602-607, (1989) |

[9] | Weerahandi, S., ANOVA under unequal error variances, Biometrics, 51, 589-599, (1995) |

[10] | S. Weerahandi, D. Amaratunga, A performance comparison of methods in mixed models, Statistics Med., 2003, to appear. |

[11] | Weerahandi, S.; Berger, V.W., Exact inference for growth curves with intraclass correlation structure, Biometrics, 55, 921-924, (1999) · Zbl 1059.62731 |

[12] | Zhou, L.; Mathew, T., Some tests for variance components using generalized p-values, Technometrics, 36, 4, 394-402, (1994) · Zbl 0825.62603 |

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