### Abstract

Logit and probit are two regression methods which are categorised under Generalized Linear Models. Both models can be used when the response variables in the analyses are categorical in nature. For the case of the strength of gear teeth data, it can be in terms of counted proportions, such as r teeth fail out of n teeth tested. In this paper, the two models, logit and probit are discussed and the methods of analysis are compared for simulated data sets obtained from experimental procedure called staircase design (SCD) experiment. For the analysis, the response variable is the proportion failing and the explanatory variable is the corresponding load. The analysis is also compared with the explanatory variable of logarithm of load. The population distributions of strengths considered are normal and Weibull distribution and 1000 SCD experiments are simulated. The sampling distributions of the various estimators are then compared for bias, standard deviation, and mean squared error for the two contrasting population distributions of strength. It is found that, a regression of the logit on the logarithm of load seems to be the most robust approach if normality of strengths is in doubt.

Original language | English |
---|---|

Pages (from-to) | 548-553 |

Number of pages | 6 |

Journal | European Journal of Scientific Research |

Volume | 27 |

Issue number | 4 |

Publication status | Published - 2009 |

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### Keywords

- Counted proportion
- Gear teeth
- Logit
- Probit
- Regression analysis
- Staircase design

### ASJC Scopus subject areas

- General

### Cite this

*European Journal of Scientific Research*,

*27*(4), 548-553.

**The comparison logit and probit regression analyses in estimating the strength of gear teeth.** / Shariff, A. A.; Zaharim, Azami; Sopian, Kamaruzzaman.

Research output: Contribution to journal › Article

*European Journal of Scientific Research*, vol. 27, no. 4, pp. 548-553.

}

TY - JOUR

T1 - The comparison logit and probit regression analyses in estimating the strength of gear teeth

AU - Shariff, A. A.

AU - Zaharim, Azami

AU - Sopian, Kamaruzzaman

PY - 2009

Y1 - 2009

N2 - Logit and probit are two regression methods which are categorised under Generalized Linear Models. Both models can be used when the response variables in the analyses are categorical in nature. For the case of the strength of gear teeth data, it can be in terms of counted proportions, such as r teeth fail out of n teeth tested. In this paper, the two models, logit and probit are discussed and the methods of analysis are compared for simulated data sets obtained from experimental procedure called staircase design (SCD) experiment. For the analysis, the response variable is the proportion failing and the explanatory variable is the corresponding load. The analysis is also compared with the explanatory variable of logarithm of load. The population distributions of strengths considered are normal and Weibull distribution and 1000 SCD experiments are simulated. The sampling distributions of the various estimators are then compared for bias, standard deviation, and mean squared error for the two contrasting population distributions of strength. It is found that, a regression of the logit on the logarithm of load seems to be the most robust approach if normality of strengths is in doubt.

AB - Logit and probit are two regression methods which are categorised under Generalized Linear Models. Both models can be used when the response variables in the analyses are categorical in nature. For the case of the strength of gear teeth data, it can be in terms of counted proportions, such as r teeth fail out of n teeth tested. In this paper, the two models, logit and probit are discussed and the methods of analysis are compared for simulated data sets obtained from experimental procedure called staircase design (SCD) experiment. For the analysis, the response variable is the proportion failing and the explanatory variable is the corresponding load. The analysis is also compared with the explanatory variable of logarithm of load. The population distributions of strengths considered are normal and Weibull distribution and 1000 SCD experiments are simulated. The sampling distributions of the various estimators are then compared for bias, standard deviation, and mean squared error for the two contrasting population distributions of strength. It is found that, a regression of the logit on the logarithm of load seems to be the most robust approach if normality of strengths is in doubt.

KW - Counted proportion

KW - Gear teeth

KW - Logit

KW - Probit

KW - Regression analysis

KW - Staircase design

UR - http://www.scopus.com/inward/record.url?scp=65349148680&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=65349148680&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:65349148680

VL - 27

SP - 548

EP - 553

JO - European Journal of Scientific Research

JF - European Journal of Scientific Research

SN - 1450-202X

IS - 4

ER -