COMPARISONS BETWEEN METHODS OF ESTIMATION OF THE RANDOM STANDARD DEVIATION IN FACTORIAL EXPERIMENTS WITH TWO LEVELS BY FACTOR AND WITHOUT REPEAT.

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Juliana Vieira GOMES
José Ivo RIBEIRO JÚNIOR
Camila Rafaela Gomes DIAS

Abstract

To obtain the estimate of random variance in complete and fractional factorial experiments with two levels per factor evaluated without repetition, Hamada and Balakrishnan (1998) provide a list of several methods. Thus, based on this review, the objective of the present study was to compare the estimates of standard deviations with only influences of random causes according to four methods: de Lenth (1989), Juan and Pena (1992), Dong (1993) and without any restriction on data, here called total standard deviation. For this, a normal random variable with 10.000 values was simulated, whose simulation was repeated 16 times. Subsequently, they were replaced in each of the 16 data sets, 0%, 1%, 2%, 3% and 4% of the random values by outliers in order to break the simulated variable randomness. Based on the estimate of the mean absolute percentage error (MAPE) obtained in relation to the parametric random standard deviation, it was concluded, through regression analysis, that it increased due to the increase in the percentage of substitution of random values for outliers, with the exception of that obtained according to the method of Juan and Pena (1992). Even so, for data sets with up to 3.68% outliers, the best methods for estimating the random standard deviation (Srandom) were those of Lenth (1989) and Dong (1993), as they provided the lowest estimates MAPE. Above this percentage and up to 4% of outliers, the method of Juan and Pena (1992) proved to be better. However, as the highest MAPE estimate provided by the three estimation methods was very low (4.00%), and yet, as the differences observed between them were practically negligible, it was concluded that the three methods provided good estimates of Srandom  and that, consequently, can be recommended to estimate the mean square of the residue in complete and fractional factorial experiments with two levels per factor and with individual observations per treatment. On the other hand, the total standard deviation method was unable to avoid the effect of non-randomness on the estimate of the Srandom.

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