A simple method to identify significant effects in unreplicated two-level factorial designs

Ruiz, Jesús Juan; Pefña, Daniel

doi:10.1080/03610929208830854

Cited by 24 publications

(19 citation statements)

References 11 publications

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“…In a similar vein, Juan and Peña [14] deal with the problem by identifying outliers (significant effects) in a sample and, under certain circumstances, the Lenth method is a particular case of the one they propose. They claim that their method works better than Lenth when the number of active effects is large (greater than 20%), but it is more complicated.…”

Section: Alternatives To the Lenth Methodsmentioning

confidence: 99%

Proposal of a Single Critical Value for the Lenth Method

Fontdecaba

Cintas

Tort‐Martorell

2015

Quality Technology & Quantitative Management

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Different critical values deduced by simulation have been proposed that greatly improve Lenth's original proposal. However, these simulations assume that all effects are zerosomething not realistic--producing bigger than desired critical values and thus significance levels lower that intended. This article, in accordance with George Box [2] well known idea that Experimental Design should be about learning and not about testing and based on studying how the presence of a realistic number and size of active effects affects critical values, proposes to use t = 2 for any number of runs equal or greater than 8. And it shows that this solution, in addition of being simpler, provides under reasonable realistic situations better results than those obtained by simulation.

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Section: Alternatives To the Lenth Methodsmentioning

confidence: 99%

Proposal of a Single Critical Value for the Lenth Method

Fontdecaba

Cintas

Tort‐Martorell

2015

Quality Technology & Quantitative Management

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“…With the purpose of eliminating the subjectivity of the graphical methods for detecting significant contrasts, a large number of formal procedures have been proposed: Birnbaum (1959Birnbaum ( , 1961, Holms and Berrettoni (1969), Zahn (1975b), Seheult and Tukey (1982), Box and Meyer (1986), Johnson and Tukey (1987), Voss (1988), Benski (1989), Lenth (1989), Bissell (1989Bissell ( , 1992, Le and Zamar (1992), Juan and Pena (1992), Loh (1992), Dong (1993), Schneider et al (1993), Venter and Steel (1996), Loughin and Noble (1997), Hamada and Balakrishnan (1998), Lawson et al (1998), Al-Shiha and Yang (1999), Voss and Wang (1999), Schoen and Kaul (2000), Ye et al (2001), etc.…”

Section: Introductionmentioning

confidence: 99%

A New Quantitative Method for Analysing Unreplicated Factorial Designs

Chen¹,

Kunert

2004

Biometrical J

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SummaryThe paper proposes a new method for the analysis of unreplicated factorial designs. The new method does not use an estimate of the error variance and has the potential to identify up to m À 1 active contrasts, where m is the number of contrasts in the study. It can be shown that the proposed test statistic, called MaxU r , is a function of the generalized likelihood ratio test statistic under normality, which was also used by Al-Shiha and Yang (1999). Our strategy to identify active contrasts using MaxU r , however, is different from the multistage procedure proposed by Al-Shiha and Yang (1999). Additionally, our simulation study seems to show that the new method is superior to Al-Shiha and Yang's (1999) method.In order to test the performance of the new method, we did an extensive simulation study based on 10,000 samples to compare the new method with 12 other methods from the literature. To reasonably compare these methods, some of the 12 existing methods had to be slightly modified, such that the probability of falsely rejecting the global null hypothesis of no active factors was 0.05 for all methods. Two types of evaluation standard were used, the empirical power and the loss of decision. The results show that the new method performs very well, especially for large number of active contrasts (say more than 3 out of 15).A second purpose of the simulation study was to compare the performance of two well-known estimates for the variance. One is the PSE introduced by Lenth (1989), the other the ASE introduced by Dong (1993). The simulation study confirmed the approximations of Kunert (1997) which indicate that Dong's (1993) estimate should perform better for small numbers of active factors.

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“…Other authors propose using different methods from Lenth but based on similar procedures, such as Dong [9], who instead of using the effects' median to calculate the estimator, uses the average of the squares and states that when the number of significant effects is low (less than 20%) and its value is not small (its tests are performed with a ≥ 5 value of significant effects), his method delivers better results than that of Lenth. In a similar vein, Juan and Peña [14] deal with the problem by identifying outliers (significant effects) in a sample and, under certain circumstances, the Lenth method is a particular case of the one they propose. They claim that their method works better than Lenth when the number of active effects is large (greater than 20%), but it is more complicated.…”

Section: Introductionmentioning

confidence: 99%

Selecting significant effects in factorial designs: Lenth's method versus using negligible interactions

Xampeny

Cintas

Tort‐Martorell

2017

Communications in Statistics - Simulation and Computation

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Different critical values deduced by simulation have been proposed that greatly improve Lenth's original proposal. However, these simulations assume that all effects are zerosomething not realistic-producing bigger than desired critical values and thus significance levels lower that intended. This article, in accordance with George Box [2] well known idea that Experimental Design should be about learning and not about testing and based on studying how the presence of a realistic number and size of active effects affects critical values, proposes to use t = 2 for any number of runs equal or greater than 8. And it shows that this solution, in addition of being simpler, provides under reasonable realistic situations better results than those obtained by simulation.

show abstract

A simple method to identify significant effects in unreplicated two-level factorial designs

Cited by 24 publications

References 11 publications

Proposal of a Single Critical Value for the Lenth Method

Proposal of a Single Critical Value for the Lenth Method

A New Quantitative Method for Analysing Unreplicated Factorial Designs

Selecting significant effects in factorial designs: Lenth's method versus using negligible interactions

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