### Abstract

To deal with the problem of non-normality and heteroscedasticity, the current study proposes applying approximate transformation trimmed mean methods to the test of simple linear regression slope equality. The distribution-free slope estimates are first trimmed on both sides and then the test statistic t is transformed by Johnson's method for each group to correct non-normality. Lastly, an approximate test such as the James second-order test, the Welch test, or the DeShon-Alexander test, which are robust for heterogeneous variances, is applied to test the equality of regression slopes. Bootstrap methods and Monte Carlo simulation results show that the proposed methods provide protection against both unusual y values, as well as unusual x values. The new methods are valid alternatives for testing the simple linear regression slopes when heteroscedastic variances and non-normality are present.

Original language | English |
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Pages (from-to) | 843-857 |

Number of pages | 15 |

Journal | Journal of Applied Statistics |

Volume | 27 |

Issue number | 7 |

DOIs | |

Publication status | Published - 2000 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

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*Journal of Applied Statistics*, vol. 27, no. 7, pp. 843-857. https://doi.org/10.1080/02664760050120533

**Approximate transformation trimmed mean methods to the test of simple linear regression slope equality.** / Luh, Wei-Ming; Guo, Jiin Huarng.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Approximate transformation trimmed mean methods to the test of simple linear regression slope equality

AU - Luh, Wei-Ming

AU - Guo, Jiin Huarng

PY - 2000/1/1

Y1 - 2000/1/1

N2 - To deal with the problem of non-normality and heteroscedasticity, the current study proposes applying approximate transformation trimmed mean methods to the test of simple linear regression slope equality. The distribution-free slope estimates are first trimmed on both sides and then the test statistic t is transformed by Johnson's method for each group to correct non-normality. Lastly, an approximate test such as the James second-order test, the Welch test, or the DeShon-Alexander test, which are robust for heterogeneous variances, is applied to test the equality of regression slopes. Bootstrap methods and Monte Carlo simulation results show that the proposed methods provide protection against both unusual y values, as well as unusual x values. The new methods are valid alternatives for testing the simple linear regression slopes when heteroscedastic variances and non-normality are present.

AB - To deal with the problem of non-normality and heteroscedasticity, the current study proposes applying approximate transformation trimmed mean methods to the test of simple linear regression slope equality. The distribution-free slope estimates are first trimmed on both sides and then the test statistic t is transformed by Johnson's method for each group to correct non-normality. Lastly, an approximate test such as the James second-order test, the Welch test, or the DeShon-Alexander test, which are robust for heterogeneous variances, is applied to test the equality of regression slopes. Bootstrap methods and Monte Carlo simulation results show that the proposed methods provide protection against both unusual y values, as well as unusual x values. The new methods are valid alternatives for testing the simple linear regression slopes when heteroscedastic variances and non-normality are present.

UR - http://www.scopus.com/inward/record.url?scp=1542630619&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1542630619&partnerID=8YFLogxK

U2 - 10.1080/02664760050120533

DO - 10.1080/02664760050120533

M3 - Article

AN - SCOPUS:1542630619

VL - 27

SP - 843

EP - 857

JO - Journal of Applied Statistics

JF - Journal of Applied Statistics

SN - 0266-4763

IS - 7

ER -