COMPARISONS BETWEEN METHODS OF ESTIMATION OF THE RANDOM STANDARD DEVIATION IN FACTORIAL EXPERIMENTS WITH TWO LEVELS BY FACTOR AND WITHOUT REPEAT.
Main Article Content
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.
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).