### Abstract

Probability plots are commonly used as a technique for testing distributional assumptions. However, any conclusion about the linearity of such a plot is based strictly on the user's judgment. Regression tests of fit are supposed to make this procedure more objective, but these tests typically are not based on probability plots as they are constructed in practice. This is because the developers of these tests defined probability plots in terms of plotting positions which are not used by practitioners. In this paper, a class of goodness-of-fit test statistics which are calculated directly from probability plots as they are constructed in practice is described. Several realistic plotting positions for the normal distribution are chosen and empirical sampling methods are used to derive the null distribution of each of the corresponding test statistics. These tests are then compared on the basis of 5% power against certain nonnormal alternatives. Results of the comparisons indicate that the test based on the plotting position p_{i} =(i — 0.4)/(j + 0.2) is a reasonable choice for a powerful regression test of fit for normality.

Original language | English (US) |
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Pages (from-to) | 115-127 |

Number of pages | 13 |

Journal | Journal of Statistical Computation and Simulation |

Volume | 20 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jan 9 1984 |

Externally published | Yes |

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### Keywords

- Correlation coefficient
- Empirical power comparison
- Filliben test
- Plotting position
- Shapiro-Francia test
- Shapiro-Wilk test

### ASJC Scopus subject areas

- Statistics and Probability
- Modeling and Simulation
- Statistics, Probability and Uncertainty
- Applied Mathematics

### Cite this

*Journal of Statistical Computation and Simulation*,

*20*(2), 115-127. https://doi.org/10.1080/00949658408810761