γ | n | S | 95% critical value | Fraction rejected
assuming χ^{2}_{} |
---|---|---|---|---|

−4 | 25 | 100 | 3.54 | 0.04 |

1,000 | 4.23 | 0.061 | ||

10,000 | 4.06 | 0.056 | ||

50 | 100 | 3.81 | 0.049 | |

1,000 | 4.04 | 0.054 | ||

10,000 | 3.78 | 0.048 | ||

4 | 25 | 100 | 3.64 | 0.045 |

1,000 | 3.89 | 0.052 | ||

10,000 | 3.86 | 0.051 | ||

50 | 100 | 3.78 | 0.048 | |

1,000 | 3.83 | 0.050 | ||

10,000 | 4.15 | 0.065 | ||

20 | 25 | 100 | 3.86 | 0.051 |

1,000 | 3.94 | 0.053 | ||

10,000 | 3.42 | 0.033 | ||

50 | 100 | 3.52 | 0.039 | |

1,000 | 3.91 | 0.051 | ||

10,000 | 3.65 | 0.044 |

Asymptotic likelihood theory predicts that the 95% critical value is 3.84. Also shown is the null rejection rate at

*P*= 0.05 under the asymptotic assumption that the LRT statistic is chi-square distributed.