### Abstract

The use of the correlation coefficient is suggested as a technique for summarizing and objectively evaluating the information contained in probability plots. Goodness-of-fit tests are constructed using this technique for several commonly used plotting positions for the normal distribution. Empirical sampling methods are used to construct the null distribution for these tests, which are then compared on the basis of power against certain nonnormal alternatives. Commonly used regression tests of fit are also included in the comparisons. The results indicate that use of the plotting position pi = (i – .375)/(n + .25) yields a competitive regression test of fit for normality.

Original language | English (US) |
---|---|

Pages (from-to) | 75-79 |

Number of pages | 5 |

Journal | American Statistician |

Volume | 39 |

Issue number | 1 |

DOIs | |

State | Published - 1985 |

Externally published | Yes |

### Fingerprint

### Keywords

- Empirical power comparison
- Filliben test
- Plotting position
- Regression tests of fit
- Shapiro-Francia test
- Shapiro-Wilk test

### ASJC Scopus subject areas

- Mathematics(all)
- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

*American Statistician*,

*39*(1), 75-79. https://doi.org/10.1080/00031305.1985.10479395

**Commentaries : Use of the correlation coefficient with normal probability plots.** / Looney, Stephen Warwick; Gulledge, Thomas R.

Research output: Contribution to journal › Article

*American Statistician*, vol. 39, no. 1, pp. 75-79. https://doi.org/10.1080/00031305.1985.10479395

}

TY - JOUR

T1 - Commentaries

T2 - Use of the correlation coefficient with normal probability plots

AU - Looney, Stephen Warwick

AU - Gulledge, Thomas R.

PY - 1985

Y1 - 1985

N2 - The use of the correlation coefficient is suggested as a technique for summarizing and objectively evaluating the information contained in probability plots. Goodness-of-fit tests are constructed using this technique for several commonly used plotting positions for the normal distribution. Empirical sampling methods are used to construct the null distribution for these tests, which are then compared on the basis of power against certain nonnormal alternatives. Commonly used regression tests of fit are also included in the comparisons. The results indicate that use of the plotting position pi = (i – .375)/(n + .25) yields a competitive regression test of fit for normality.

AB - The use of the correlation coefficient is suggested as a technique for summarizing and objectively evaluating the information contained in probability plots. Goodness-of-fit tests are constructed using this technique for several commonly used plotting positions for the normal distribution. Empirical sampling methods are used to construct the null distribution for these tests, which are then compared on the basis of power against certain nonnormal alternatives. Commonly used regression tests of fit are also included in the comparisons. The results indicate that use of the plotting position pi = (i – .375)/(n + .25) yields a competitive regression test of fit for normality.

KW - Empirical power comparison

KW - Filliben test

KW - Plotting position

KW - Regression tests of fit

KW - Shapiro-Francia test

KW - Shapiro-Wilk test

UR - http://www.scopus.com/inward/record.url?scp=84952511519&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84952511519&partnerID=8YFLogxK

U2 - 10.1080/00031305.1985.10479395

DO - 10.1080/00031305.1985.10479395

M3 - Article

VL - 39

SP - 75

EP - 79

JO - American Statistician

JF - American Statistician

SN - 0003-1305

IS - 1

ER -