### 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) |
---|---|

Pages (from-to) | 115-127 |

Number of pages | 13 |

Journal | Journal of Statistical Computation and Simulation |

Volume | 20 |

Issue number | 2 |

DOIs | |

State | Published - Jan 9 1984 |

### Fingerprint

### 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

**Regression Tests of Fit and Probability Plotting Positions.** / Looney, Stephen W.; Gulledge, Thomas R.

Research output: Contribution to journal › Article

*Journal of Statistical Computation and Simulation*, vol. 20, no. 2, pp. 115-127. https://doi.org/10.1080/00949658408810761

}

TY - JOUR

T1 - Regression Tests of Fit and Probability Plotting Positions

AU - Looney, Stephen W.

AU - Gulledge, Thomas R.

PY - 1984/1/9

Y1 - 1984/1/9

N2 - 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 pi =(i — 0.4)/(j + 0.2) is a reasonable choice for a powerful regression test of fit for normality.

AB - 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 pi =(i — 0.4)/(j + 0.2) is a reasonable choice for a powerful regression test of fit for normality.

KW - Correlation coefficient

KW - Empirical power comparison

KW - Filliben test

KW - Plotting position

KW - Shapiro-Francia test

KW - Shapiro-Wilk test

UR - http://www.scopus.com/inward/record.url?scp=84948327445&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84948327445&partnerID=8YFLogxK

U2 - 10.1080/00949658408810761

DO - 10.1080/00949658408810761

M3 - Article

AN - SCOPUS:84948327445

VL - 20

SP - 115

EP - 127

JO - Journal of Statistical Computation and Simulation

JF - Journal of Statistical Computation and Simulation

SN - 0094-9655

IS - 2

ER -